fraction - how many parts of a certain size exist

Formula: a/b where a is the numerator and b is the denominator

$6500 is 7/10 of a number. What is the number

The number is $9,285 from our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=6500&pct1=70&pcheck=2&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']percentage-decimal-fraction calculator[/URL].

-1 3/5 divided by -2/3

-1 3/5 divided by -2/3
We write this as:
-1&3/5 / 2/3
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%263%2F5&frac2=2%2F3&pl=Divide']fraction division calculator[/URL], we get:
[B]12/5[/B]

1/2n + 1&1/2n = -10

1/2n + 1&1/2n = -10
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%261%2F2&frac2=3%2F8&pl=Simplify']1&1/2 = 3/2[/URL] so we have:
n/2 + 3n/2 = -10
4n/2 = -10
2n = -10
Divide each side by 2:
2n/2 = -10/2
n = [B]-5[/B]

1/3 + 1/7 =

1/3 + 1/7 =
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=1%2F7&pl=Add']fraction calculator[/URL], we get:
[B]10/21[/B]

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?
If 1/3 are boys, then the number of boys is:
600 * 1/3
600/3
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=600%2F3&frac2=3%2F8&pl=Simplify']type this fraction into our search engine to simplify[/URL], and we get:
200
Now we need to find how many girls are at the school:
Girls = Total Students - Boys
Girls = 600 - 200
Girls = [B]400[/B]

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students?
12/14 is the initial ratio. However, we can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F14&frac2=3%2F8&pl=Simplify']So we type 12/14 into our search engine and choose simplify.[/URL] We get:
6/7

15 mins into fraction of an hour

15 mins into fraction of an hour
[URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=hour']An hour is 60 minutes[/URL], so we have the fraction:
15/60
But we can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F60&frac2=3%2F8&pl=Simplify']type in 15/60 into our search engine[/URL], click Simplify, and we get:
[B]1/4[/B]

15 of the 45 students have brown eyes. What fraction of the students have brown eyes

15 of the 45 students have brown eyes. What fraction of the students have brown eyes?
15/45 can be [URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F45&frac2=3%2F8&pl=Simplify']simplified using our fraction simplify calculator[/URL]:
[B]1/3[/B]

15 out of 18 students agreed. What percentage did not?

18 - 15 = 3 student disagreed.
3/18 is the fraction of student who disagreed.
[URL='http://www.mathcelebrity.com/perc.php?num=3&den=18&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Converting to a percentage using our fraction to decimal calculator, we get:[/URL]
16.67%

175 out of 200 students have a cell phone. What fraction of the students have a cell phone?

175 out of 200 students have a cell phone. What fraction of the students have a cell phone?
175 out of 200 can be written as:
175/200
This can be simplified, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=175%2F200&frac2=3%2F8&pl=Simplify']type it in our math engine[/URL] and we get:
[B]7/8[/B]

18 - 6 & 1/9 =

18 - 6 & 1/9 =
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=18&frac2=6%261%2F9&pl=Subtract']fraction calculator[/URL], we get:
[B]107/9 [URL='https://www.mathcelebrity.com/fraction.php?frac1=107%2F9&frac2=6%261%2F9&pl=Simplify']or[/URL] 11 & 8/9[/B]

2 coins are tossed. Find the probability of getting 1 head and 1 tail

2 coins are tossed. Find the probability of getting 1 head and 1 tail
We can either flip HT or TH. Let's review probabilities:
[LIST]
[*]HT = 1/2 * 1/2 = 1/4 <-- We multiply since each event is independent
[*]TH = 1/2 * 1/2 = 1/4 <-- We multiply since each event is independent
[/LIST]
P(1 H, 1 T) = P(HT) + P(TH)
P(1 H, 1 T) = 1/4 + 1/4
P(1 H, 1 T) = 2/4
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 2/4 to 1/2
P(1 H, 1 T) = [B]1/2[/B]

22 & 1/2 / 1/8 =

22 & 1/2 / 1/8 =
22 & 1/2 = 45/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=45%2F2&frac2=1%2F8&pl=Divide']45/2 / 1/8[/URL] = [B]180[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

3/10 of a circle equal how many degrees

3/10 of a circle equal how many degrees
A circle is 365 degrees. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=365&frac2=3%2F10&pl=Multiply']we multiply 365 * 3/10 in our search engine[/URL] and get:
219/2
219/2 = [B]109.5 degrees[/B]

3/4 a number b divided by 5

3/4 a number b divided by 5
3/4 a number b:
3b/4
Divided by 5:
3b/4/5
We multiply top and bottom by 5 to remove the double fraction:
3b*5/4
[B]15b/4[/B]

3/4 of the students went skiing.there are 24 students in the class. How’s many went?

3/4 of the students went skiing.there are 24 students in the class. How’s many went?
We want 3/4 of 24. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=24&frac2=3/4&pl=Multiply']type 3/4 of 24 into our search engine[/URL] and get:
[B]18 students[/B]

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fra

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fraction in simplest form
The percent that do not live in blue houses is found by:
Not in blue = 100% - 35%
Not in blue = 65%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=65&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Typing 65% in our search engine[/URL], we see that the decimal and fraction is:
[LIST]
[*]65% as a decimal: [B]0.65[/B]
[*]65% as a fraction in simplest form: [B]13/20[/B]
[/LIST]

5 girls share 4 sandwiches. What fraction of the sandwich does each girl get

5 girls share 4 sandwiches. What fraction of the sandwich does each girl get?
We want to know sandwiches per girls. So we divide:
4 sandwiches per 5 girls
[B]4/5[/B]

5/12 of a circle what measure in degrees

5/12 of a circle what measure in degrees
A circle measures 360 degrees. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F12&frac2=360&pl=Multiply']multiply as follows[/URL]:
5/12 * 360 = [B]150 degrees[/B]

5/8 Of a class are boys. what fraction of the class are girls

5/8 Of a class are boys. what fraction of the class are girls?
The total class equals 1. Since 5/8 are boys, we subtract 5/8 from 1:
1 - 5/8
But we can write 1 as 8/8. So we have
8/8 - 5/8
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F8&frac2=5%2F8&pl=Subtract']Type this fraction operation into our search engine[/URL] and we get:
[B]3/8[/B] are girls

6 & 1/8 x 1/7

6 & 1/8 x 1/7
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F8&frac2=1%2F7&pl=Multiply']fraction calculator[/URL], we get:
[B]7/8[/B]

6 red marbles 9 green marbles and 5 blue marbles two marbles are drawn without replacement what is t

6 red marbles 9 green marbles and 5 blue marbles two marbles are drawn without replacement what is the probability of choosing a green and then a blue marble
First draw:
there are 6 red + 9 green + 5 blue = 20 marbles
We draw 9 possible green out of 20 total marbles = 9/20
Second draw:
We don't replace, so we have 6 red + 8 green + 5 blue = 19 marbles
We draw 5 possible blue of out 19 total marbles = 5/19
Our total probability, since each event is independent, is:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F20&frac2=5%2F19&pl=Multiply']9/20 * 5/19[/URL] = [B]9/76[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we have a fraction:
[B]6y/x^2[/B]

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that i

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that it is not gray
[U]Find the total shirts:[/U]
Total shirts = Black Shirts + White Shirts + Gray Shirts
Total shirts = 7 + 5 + 10
Total shirts = 22
[U]Calculate the probability of choosing a gray shirt:[/U]
P(Gray) = Number of Gray shirts / Total Shirts
P(Gray) = 10/22
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F22&frac2=3%2F8&pl=Simplify']type in 10/22 into our search engine, choose simplify[/URL], and we get:
P(Gray) = [B]5/11[/B]

7 ½ decimal

7 ½ decimal
Convert the mixed fractions 7 & 1/2 to an improper fraction
[URL='https://www.mathcelebrity.com/fraction.php?frac1=7%261%2F2&frac2=3%2F8&pl=Simplify']7 1/2[/URL] = 15/2
Convert the improper fraction to a decimal:
[URL='https://www.mathcelebrity.com/perc.php?num=15&den=2&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']15/2[/URL] = [B]7.5[/B]

84% as a fraction in simplest form

84% as a fraction in simplest form
Enter [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=84&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']84% as a fraction into our search engine[/URL] and we get:
[B]21/25[/B]

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates w

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates would be needed and how many bottles will remain?
Let c equal the number of crates
9 bottles per crate * c = 993
9c = 993
Solve for [I]c[/I] in the equation 9c = 993
[SIZE=5][B]Step 1: Divide each side of the equation by 9[/B][/SIZE]
9c /9 = 993/9
c = 110.33333333333
Since we can't have fractional crates, we round up 1 to the next full crate
c = [B]111[/B]

A 3 gallon bottle of bleach cost $16.32. What is the price per cup?

A 3 gallon bottle of bleach cost $16.32. What is the price per cup?
We're given 16.32 / 3 gallons
Divide the top and bottom of the fraction by 3 to get the cost per gallon:
16.32/3 = 5.44 gallon
Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=1&pl=Calculate&type=gallon']measurement converter[/URL], we see that:
1 gallon = 16 cups
So 5.44 /16 cups=[B]$0.34 per cup[/B]

A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosi

A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a blue marble, replacing it, drawing a green marble, replacing it, and then drawing a red marble?
Calculate total marbles in the bag:
Total marbles in the bag = Red Marbles + Blue Marbles + Green Marbles
Total marbles in the bag = 2 + 3 + 4
Total marbles in the bag = 9
[U]First choice, blue marble[/U]
P(blue) = Total Blue Marbles / Total Marbles in the bag
P(blue) = 3/9
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see:
P(blue) = 1/3
[U]Second choice, green marble with all the marbles back in the bag after replacement[/U]
P(green) = Total Green Marbles / Total Marbles in the bag
P(green) = 4/9
[U]Third choice, red marble with all the marbles back in the bag after replacement[/U]
P(red) = Total Red Marbles / Total Marbles in the bag
P(red) = 2/9
Since each event is independent, we multiply each probability:
P(blue, green, red) = P(blue) * P(green) * P(red)
P(blue, green, red) = 1/3 * 4/9 * 2/9
P(blue, green, red) = [B]8/243[/B]

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random f

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random from the bag. What is P(blue)
P(blue) = Number of blue marbles / Total Marbles
P(blue) = 5 / (5 + 6 + 4)
P(blue) = 5/15
We can reduce this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']type in 5/15 into our search engine, choose simplify[/URL], and we get:
P(blue) = [B]1/3[/B]

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be rando

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be randomly selected from the bag . What is the probability that the tile selected will be green
P(green) = Number of green tiles / Total Tiles
P(green) = 6 / (3 + 6 + 3)
P(green) = 6 / 12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F12&frac2=3%2F8&pl=Simplify']type in 6/12 into our search engine, pick simplify[/URL], and we get:
P(green) = [B]1/2 or 0.5[/B]

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good?

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good?
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=2%2F3&pl=Subtract']fraction operator calculator[/URL], we see that:
1 - 2/3 = 1/3 of the oranges are good.
We want 1/3 of 45. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/3&pl=Multiply']Typing this expression into our search engine[/URL], we get:
[B]15 good oranges[/B]

A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of p

A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of picking two bells of the same color if the bell is replaced after each pick?
If there are 6 red bells, then we have 10 - 6 = 4 silver bells.
The problem asks for the probability of picking two bells of the same color. Which mean we have 2 scenarios:
[LIST=1]
[*]Silver, Silver
[*]Red, Red
[/LIST]
Find the probability of Silver, Silver:
Since each draw is independent, and we replace the bells, we have a 4/10 chance of picking silver. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F10&frac2=3%2F8&pl=Simplify']Simplified, this is 2/5[/URL].
(2/5)(2/5) = 4/25
Find the probability of Red, Red:
Since each draw is independent, and we replace the bells, we have a 6/10 chance of picking silver. [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F10&frac2=3%2F8&pl=Simplify']Simplified, this is 3/5[/URL].
(3/5)(3/5) = 9/25
Because we want Silver, Silver [B][U]or[/U][/B] Red, Red, we add the two probabilities.
4/25 + 9/25 = [B]13/25[/B]

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probabilit

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probability of drawing 2 black balls.
First draw probability of black is:
Total Balls in box = Black balls + white balls
Total Balls in Box = 5 + 2
Total Balls in Box = 7
P(Black) = Black Balls / Total balls in box
P(Black) = 5/7
Second draw probability of black (with no replacement) is:
Total Balls in box = Black balls + white balls
Total Balls in Box = 4 + 2
Total Balls in Box = 6
P(Black) = Black Balls / Total balls in box
P(Black) = 4/6
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we see that 4/6 is:
2/3
Since each event is independent, we can multiply them to find the probability of drawing 2 black balls:
P(Black, Black) = 5/7 * 2/3
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F7&frac2=2%2F3&pl=Multiply']P(Black, Black)[/URL] = 10/21

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons . One

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected
[U]Calculate the probability of a plain pencil in the first box:[/U]
P(plain pencil in the first box) = Total Pencils / Total Objects
P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens)
P(plain pencil in the first box) = 5/8
[U]Calculate the probability of a color pencil in the first box:[/U]
P(color in the second box) = Total Pencils / Total Objects
P(color in the second box) = 2 pencils / (2 pencils + 2 crayons)
P(color in the second box) = 2/4
We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Type 2/4 into our search engine[/URL] and we get 1/2
Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected.
Since each event is independent, we multiply them together to get our answer:
P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box)
P(plain pencil in the first box, color in the second box) = 5/8 * 1/2
P(plain pencil in the first box, color in the second box) = [B]5/16[/B]

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, i

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, it is not replaced, then another is chosen. What is the probability of choosing a red followed by a green?
We have 6 + 3 + 5 + 7 = 21 total pencils
P(Red on the first draw) = Total Red / Total pencils
P(Red on the first draw) = 3/21
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F21&frac2=3%2F8&pl=Simplify']P(Red on the first draw)[/URL] = 1/7
We're drawing without replacement, this means on the next draw, we have 21 - 1 = 20 pencils
P(Green on the second draw) = Total Green / Total pencils
P(Green on the second draw) = 5/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']P(Green on the second draw) [/URL]= 1/4
Since each event is independent, we have:
P(Red on first, green on second) = P(Red on First) * P(green on second)
P(Red on first, green on second) = 1/7 * 1/4
P(Red on first, green on second) = [B]1/28[/B]

A box is filled with 5 blue cards,2 red cards, and 5 yellow cards. A card is chosen at random from t

A box is filled with 5 blue cards,2 red cards, and 5 yellow cards. A card is chosen at random from the box. What is the probability that it is a blue or a yellow card? Write your answer as a fraction in simplest form.
We want P(B) + P(Y)
P(B) = 5/12
P(Y) = 5/12
P(B) + P(Y) = 5/12 + 5/12 = 10/12
Reduce this fraction using 2 as our common factor:
[B]5/6[/B]

a card is chosen at a random from a deck of 52 cards. it is then replaced and a second card is chose

a card is chosen at a random from a deck of 52 cards. it is then replaced and a second card is chosen. what is the probability of getting a jack and then an eight?
Calculate the probability of drawing a jack from a full deck
There are 4 jacks in a deck of 52 cards
P(J) = 4/52
P(J) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4
Calculate the probability of drawing an eight from a full deck
There are 4 eights in a deck of 52 cards. We[I] replaced[/I] the first card giving us 52 cards to choose from.
P(8) = 4/52
P(8) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4
Since each event is independent, we multiply:
P(J, 8) = P(J) * P(8)
P(J, 8) = 1/13 * 1/13
P(J, 8) = [B]1/169[/B]

a card is drawn at random from a standard 52 card deck. find the probability that the card is not a

a card is drawn at random from a standard 52 card deck. find the probability that the card is not a king.
There are 4 kings in a standard 52 card deck. To not get a king, we'd have 52 - 4 = 48 possible cards.
The probability of not drawing a King is 48/52.
But we can simplify this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=48%2F52&frac2=3%2F8&pl=Simplify']type the fraction 48/52 into our search engine[/URL], and get:
[B]12/13[/B]

A card is drawn from a pack of 52 cards. The probability that the card drawn is a red card is

A card is drawn from a pack of 52 cards. The probability that the card drawn is a red card is
The deck is split evenly between red and black cards.
So we have 52/2 = 26 red cards
P(Red) = # of Red Cards / Total Deck Cards
P(Red) = 26/52
We can simplify this fraction. [URL='https://www.mathcelebrity.com/fraction.php?frac1=26%2F52&frac2=3%2F8&pl=Simplify']Using our fraction calculator[/URL], we get:
P(Red) = [B]1/2 or 0.5[/B]

A card is drawn from a standard deck of 52 cards. What is the probability of drawing an ace or a 6

A card is drawn from a standard deck of 52 cards. What is the probability of drawing an ace or a 6?
There are 4 Ace's in a standard 52 card deck. There are 4 6's as well.
So we have 4 + 4 = 8 possible cards out of 52:
8/52
To simplify, [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']we type this into our search engine[/URL] and we get:
[B]2/13[/B]

A card is picked from a deck of 52 cards. Find the probability of getting a black ace or a red queen

A card is picked from a deck of 52 cards. Find the probability of getting a black ace or a red queen.
In a standard deck of 52 cards, we have:
[LIST]
[*]2 black Aces with probability 2/52 = 1/26 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F52&frac2=3%2F8&pl=Simplify']using our fraction simplifier[/URL]
[*]2 red Queens with probability 2/52 = 1/26 [URL='http://using our fraction simplifier']using our fraction simplifier[/URL]
[/LIST]
The problems asks for P(Red Queen Or Black Ace). Or means we add, so we have:
P(Red Queen Or Black Ace) = P(Red Queen) + P(Black Ace)
P(Red Queen Or P Black Ace) = 1/26 + 1/26
P(Red Queen Or P Black Ace) = 2/26
P(Red Queen Or P Black Ace) = [B]1/13[/B] [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F26&frac2=3%2F8&pl=Simplify']using our fraction simplifier[/URL]

a card selected from a deck of 52 cards what is the probability it is a black card or face card

a card selected from a deck of 52 cards what is the probability it is a black card or face card
Facts:
[LIST]
[*]Half the cards in the deck are black (26/52)
[*]There are 12 face cards (K, Q, J) in a deck (12/52)
[*]Black and Face = 6/52 (Duplicates from above)
[/LIST]
P(Black or Face) = P(Black) + P(Face) - P(Black And Face)
P(Black or Face) = 26/52 + 12/52 - 6/52
P(Black or Face) = 32/52
We can simplify this. We use our [URL='https://www.mathcelebrity.com/fraction.php?frac1=32%2F52&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL] to get:
P(Black or Face) = [B]8/13[/B]

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequalities represents the situation if r is the number of rides?
We set up our inequality using less than or equal to, since our cash is capped at $50. We use S for our :
Cost per ride * r + Admission <= 50
Plugging in our numbers, we get:
2.50r + 6 <= 50
[B][/B]
Now, if the problem asks you to put this in terms of r, then [URL='https://www.mathcelebrity.com/1unk.php?num=2.50r%2B6%3C%3D50&pl=Solve']we plug this inequality into our search engine[/URL] and we get:
r <= 17.6
Since we cannot do fractional rides, we round down to 17:
[B]r <= 17[/B]

a class has 24 people and 1/6 of them have blue eues. what fraction of the class has blue eyes, usin

a class has 24 people and 1/6 of them have blue eues. what fraction of the class has blue eyes, using 24 as the denominator
Blue eyes = 1/6 * 24
Blue Eyes = 24/6
Blue Eyes = 4
Since 6*4 = 24, we have:
24/6 * 4/4 = [B]96/24[/B]

A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public tran

A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public transportation, 1/9 cycle, and the remainder use other methods of transportation. How many employees use each method of transportation?
Find the remainder fraction:
Remainder = 1 - (1/4 + 1/6 + 1/8 + 1/9)
The least common multiple of 4, 6, 8, 9 is 72. So we divide 72 by each fraction denominator to get our multiplier:
1/4 = 18/72
1/6 = 12/72
1/8 = 9/72
1/9 = 8/72
Add those all up:
(18 + 12 + 9 + 8)/72
47/72
Now subtract the other methods out from 1 to get the remainder of who use other methods:
Remainder = 1 - 47/72
Since 1 = 72/72, we have:
(72 - 47)/72
[B]25/72[/B]

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price.

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price. How much is the computer now?
We want 5/6 of 900. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=900&frac2=5/6&pl=Multiply']type this in our search engine[/URL] and we get:
[B]750[/B]

A cook has 2 3/4 pounds of ground beef. How many quarter-pound burgers can he make?

A cook has 2 3/4 pounds of ground beef. How many quarter-pound burgers can he make?
Using [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%263%2F4&frac2=3%2F8&pl=Simplify']our mixed number calculator[/URL], we see:
2&3/4 = 11/4
A quarter pounder is 1/4, so we have:
11 * (1/4) = 11/4
So we can make [B]11 [/B]quarter pound burgers

A cook has 2 3/4 pounds of ground beef.How many quarter-pound burgers can he make?

A cook has 2 3/4 pounds of ground beef.How many quarter-pound burgers can he make?
2 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%263%2F4&frac2=3%2F8&pl=Simplify']converts to 11/4 in our fraction converter[/URL].
A quarter-pound burger is 1/4 of a pound.
11/4 = 1/4 * 11, so the cook can make [B]11 quarter-pound burgers[/B]

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds
Set up a proportion of copies to minutes where c is the number of copies for 5 minutes and 45 seconds.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=45%2F60&frac2=3%2F8&pl=Simplify']Since 45 seconds[/URL] is:
45/60 = 3/4 of a minute, we have:
5 minutes and 45 seconds = 5.75 minutes
44/1 = c/5.75
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=44&num2=c&den1=1&den2=5.75&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]253[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?
Area of a cube is length times width:
A = 8 & 3/4 * 6 & 1/2
We need to convert these to improper fractions.
[LIST]
[*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4
[*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2
[/LIST]
Multiply the improper fractions together:
A = 35/4 * 13/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get:
[B]455/8 sq ft[/B]
If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get:
[B]56 & 7/8 sq ft[/B]

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you dra

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green?
We are drawing without replacement. Take each draw probability:
[LIST=1]
[*]First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25
[*]Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24
[/LIST]
Since both events are independent, we have:
P(Green) * P(Green) = 8/25 * 7/24
P(Green) * P(Green) = 56/600
Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=56&num2=600&num3=&pl=GCF']GCF Calculator[/URL], we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8.
[B]P(Green) * P(Green) = 7/75[/B]

A drawer is filled with 9 black shirts , 6 white shirts, and 5 gray shirts one shirt is chosen at ra

A drawer is filled with 9 black shirts , 6 white shirts, and 5 gray shirts one shirt is chosen at random from the drawer find the probability that it is not a white shirt
P(Not White) = P(Black or Gray)
P(Black or Gray) = (Total Black + Total Gray)/Total Shirts
P(Black or Gray) = (9 + 5)/(9 + 6 + 5)
P(Black or Gray) = 14/20
Simplifying this [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F20&frac2=3%2F8&pl=Simplify']using our fraction simplify calculator[/URL], we get:
P(Black or Gray) = [B]7/10, or 0.7 or 70%[/B]

A fair die is rolled. What is the probability of rolling a 3 or a 6?

A fair die is rolled. What is the probability of rolling a 3 or a 6?
P(3 or 6) can be written as:
P(3) + P(6)
A fair die means all faces have an equal probability of 1/6
P(3) = 1/6
P(6) = 1/6
P(3 or 6) = P(3) + P(6)
P(3 or 6) = 1/6 + 1/6
P(3 or 6) = 2/6
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']Using our fractions simplifier for 2/6[/URL], we get:
P(3 or 6) = [B]1/3[/B]

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his l

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his land to grow green beans. He uses the remaining 7 acres to grow wheat.How many total acres does the farmer own?
Convert all land portions to fractions or decimals. We will do fractions:
[LIST]
[*]1/3 for corn
[*][I]A quarter[/I] means 1/4 for lettuce
[*]12.5% is 12.5/100 or 1/8 for green beans
[/LIST]
Now add all these up:
1/3 + 1/4 + 1/8
We need a common factor for 3, 4, and 8. Using our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=4&num3=8&pl=LCM']LCM Calculator[/URL], we get 24.
1/3 = 8/24
1/4 = 6/24
18 = 3/24
Add them all up:
(8 + 6 + 3)/24
17/24
This means 17/24 of the land is used for everything but wheat. Wheat occupies (24-17)/24 = 7/24 of the land.
We'll use a for the number of acres on the farm.
7a/24 = 7
[B]a = 24[/B]

A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to th

A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the original fraction.
Let the fraction be x/y. We're given two equations:
[LIST=1]
[*]x/y = 3/4
[*](x + 7)/y = 4/3. [I](The reciprocal of 3/4 is found by 1/(3/4)[/I]
[/LIST]
Cross multiply equation 1 and equation 2:
[LIST=1]
[*]4x = 3y
[*]3(x + 7) = 4y
[/LIST]
Simplifying, we get:
[LIST=1]
[*]4x = 3y
[*]3x + 21 = 4y
[/LIST]
If we divide equation 1 by 4, we get:
[LIST=1]
[*]x = 3y/4
[*]3x + 21 = 4y
[/LIST]
Substitute equation (1) into equation (2) for x:
3(3y/4) + 21 = 4y
9y/4 + 21 = 4y
Multiply the equation by 4 on both sides to eliminate the denominator:
9y + 84 = 16y
To solve this equation for y, we type it in our math engine and we get:
y = [B]12
[/B]
We then substitute y = 12 into equation 1 above:
x = 3 * 12/4
x = 36/4
x = [B]9
[/B]
So our original fraction x/y = [B]9/12[/B]

A group of 30 students from your school is part of the audience for a TV game show. The total number

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?
We want the probability a student from your school is chosen out of total students times total ways to choose students from your school:
[U]a) P(5 students being selected):[/U]
5/30 * 4/(120 - 30)
5/30 * 4/90
20/2700
[URL='https://www.mathcelebrity.com/fraction.php?frac1=20%2F2700&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
1/135
[U]b) Total Ways 9 students can be picked from your school:[/U]
9/120
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F120&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
3/40
Divide a by b:
1/135 / 3/40
40/405
[URL='https://www.mathcelebrity.com/fraction.php?frac1=40%2F405&frac2=3%2F8&pl=Simplify']Simplifying[/URL], we get:
[B]8/81[/B]

A gym has 18 exercise stations, including 2 rowing machines. What is the probability that a randoml

A gym has 18 exercise stations, including 2 rowing machines. What is the probability that a randomly selected exercise station will be a rowing machine?
The probability is 2/18.
We can simplify this fraction. Divide top and bottom by 2:
[B]1/9[/B]

A helicopter blade does 3206 full turns in 7 minutes , work out the number of full turns per minute

A helicopter blade does 3206 full turns in 7 minutes , work out the number of full turns per minute
3206 full turns / 7 minutes
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3206%2F7&frac2=3%2F8&pl=Simplify']Divide the fraction by 7 to get turns per minute[/URL]
[B]458 turns per minute[/B]

A hill rises 60 ft for every horizontal 96 ft. Find the slope.

A hill rises 60 ft for every horizontal 96 ft. Find the slope.
Slope = Rise / Run
Slope = 60/96
Using [URL='https://www.mathcelebrity.com/fraction.php?frac1=60%2F96&frac2=3%2F8&pl=Simplify']our fraction simplifier, we reduce 60/96 [/URL]to [B]5/8[/B]

A jar contains 7 red marbles, 8 green marbles, and 6 blue marbles. What is the probability that you

A jar contains 7 red marbles, 8 green marbles, and 6 blue marbles. What is the probability that you draw 4 green marbles in a row if you do not replace the marbles after each draw?
The key phrase in this problem is [I]do not replace[/I].
[U]Draw #1:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 8
Total Marbles in the Jar = 7 red + 8 green + 6 blue = 21
P(Green) = 8/21
[U]Draw #2:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 8 - 1 = 7
Total Marbles in the Jar = 7 red + 7 green + 6 blue = 20
P(Green) = 7/20
[U]Draw #3:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 7 - 1 = 6
Total Marbles in the Jar = 7 red + 6 green + 6 blue = 19
P(Green) = 6/19
[U]Draw #4:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 6 - 1 = 5
Total Marbles in the Jar = 7 red + 5 green + 6 blue = 18
P(Green) = 5/18
We want P(Green, Green, Green, Green)
Because each draw is [U][B]independent[/B][/U] of all other draws, we multiply each draw to get the final probability
P(Green, Green, Green, Green) = P(Green on Draw 1) * P(Green on Draw 2) * P(Green on Draw 3) * P(Green on Draw 4) *
P(Green, Green, Green, Green) = 8/21 * 7/20 * 6/19 * 5/18
P(Green, Green, Green, Green) = 1680/143640
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1680%2F143640&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we get:
P(Green, Green, Green, Green) = [B]2/171
[MEDIA=youtube]b2C_D4_d0Ug[/MEDIA][/B]

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by rand

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by random, find the probability that their sum is $15
To get a sum of $15, we'd need to pull the $5 and the $10.
Since both events are indepdenent, we have:
P($5 or 10) or P(whatever is not pulled in the first pull)
First Pull: 2/4 (We can pull either a $10 or a $5, so 2 choices out of 4 bills)
Second Pull: 1/3 <-- since there are only 3 bills and 1 bill to pull
Each pull is independent, so we multiply:
2/4 * 1/3 = 2/12
We can simply this, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F12&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL] and we get:
[B]1/6[/B]

a landscaper buys 1 gallon of plant fertilizer. he uses 1/5 of the fertilizer, and then divides the

a landscaper buys 1 gallon of plant fertilizer. he uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. how many gallons does he put into each bottle?
First, we find the remaining fraction of fertilizer after using 1/5. [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F5&pl=Subtract']Using our fraction calculator[/URL], we see:
1 - 1/5 = 4/5
To find the amount of fertilizer per bottle, we then [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F5&frac2=3&pl=Divide']divide 4/5 by 3 and we get[/URL]:
[B]4/15 gallon per bottle[/B]

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats 9 slices. What fraction of the loaf is left?
[U]Calculate total slices eaten:[/U]
Slices eaten = Ann + Betty + Carl + Derrick
Slices eaten = 8 + 6 + 5 + 9
Slices eaten = 28
[U]Calculate remaining slices:[/U]
Remaining slices = Slices in loaf - Slices Eaten
Remaining slices = 35 - 28
Remaining slices = 7
[U]Calculate fraction of the loaf left:[/U]
Fraction left = Remaining Slices / Slices in Loaf
Fraction left = 7/35
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%2F35&frac2=3%2F8&pl=Simplify']type 7/35 into our search engine[/URL], choose simplify, and we get:
Fraction left = [B]1/5[/B]

A marathon runner took 2 hours and 15 minutes to complete the race. During that time he spent 50 min

A marathon runner took 2 hours and 15 minutes to complete the race. During that time he spent 50 minutes in the lead. Write down, in its simplest form, the fraction of time he spent in the lead.
[U]Calculate total race time in minutes[/U]
[URL='https://www.mathcelebrity.com/timecon.php?quant=2&pl=Calculate&type=hour']2 hours[/URL] = 120 minutes
120 minutes + 15 minutes = 135 minutes
[U]Calculate fraction of lead time[/U]
Fraction of lead time = Time spent in lead / total race time
Fraction of lead time = 50/135
Simplifying this fraction, we get:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=50%2F135&frac2=3%2F8&pl=Simplify']Fraction of lead time[/URL] = [B]10/27[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form
Let's review the vitals of this question:
[LIST]
[*]The probability of heads on a fair coin is 1/2.
[*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
[*]So we have a combination of outcomes below:
[/LIST]
Outcomes
[LIST=1]
[*]Heads and 4
[*]Heads and 5
[*]Heads and 6
[/LIST]
For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
[LIST=1]
[*]P(Heads and 4) = 1/2 * 1/6 = 1/12
[*]P(Heads and 5) = 1/2 * 1/6 = 1/12
[*]P(Heads and 6) = 1/2 * 1/6 = 1/12
[/LIST]
Since we want any of those events, we add all three probabilities
1/12 + 1/12 + 1/12 = 3/12
This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL].
We get a probability of [B]1/4[/B].
By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
[URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL]
Alternative Answers:
[LIST]
[*]For a decimal, we get [B]0.25[/B]
[*]For a percentage, we get [B]25%[/B]
[/LIST]

A number multiplied by 6 and divided by 5 give four more than a number?

A number multiplied by 6 and divided by 5 give four more than a number?
A number is represented by an arbitrary variable, let's call it x.
Multiply by 6:
6x
Divide by 5
6x/5
The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4.
6x/5 = x + 4
Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side:
6x(5)/5 = 5(x + 4)
The 5's cancel on the left side, giving us:
6x = 5x + 20
Subtract 5x from each side
[B]x = 20[/B]
Check our work from our original equation:
6x/5 = x + 4
6(20)/5 ? 20 + 4
120/5 ?24
24 = 24 <-- Yes, we verified our answer

A number of dogs are to equally share a bag of dog food. If there are n dogs in the group and one do

A number of dogs are to equally share a bag of dog food. If there are [I]n[/I] dogs in the group and one dog eats its share, what percent of the bag is left?
Fraction of the bag left is:
(n - 1)/n
Multiply by 100 to get a percentage:
[B]100(n - 1)/n[/B]

A pair of dice are rolled. Find the probability for P(Not 2 or Not 12).

A pair of dice are rolled. Find the probability for P(Not 2 or Not 12).
P(Not 2 or Not 12) = 1 - P(2) - P(12)
P(Not 2 or Not 12) = 1 - [URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=2&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']1/36[/URL] - [URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']1/36[/URL]
P(Not 2 or Not 12) = 34/36
[URL='https://www.mathcelebrity.com/fraction.php?frac1=34%2F36&frac2=3%2F8&pl=Simplify']P(Not 2 or Not 12)[/URL] = [B]17/18[/B]

A Pairs of fair dice is tossed. What is the probability of not getting a sum 7 or 8?

A Pairs of fair dice is tossed. What is the probability of not getting a sum 7 or 8?
Not a 7 or 8 means 2 - 6 or 9 - 12
[URL='https://www.mathcelebrity.com/2dice.php?gl=5&pl=6&opdice=1&rolist=+&dby=&ndby=&montect=+']Using our 2-dice calculator[/URL], P(2 - 6) = 5/12
[URL='https://www.mathcelebrity.com/2dice.php?gl=3&pl=9&opdice=1&rolist=+&dby=&ndby=&montect=+']Using our 2-dice calculator[/URL], P(9 - 12) = 5/18
Since the sum could be either of these, we add probabilities:
P(Not a 7 or 8) = P(2 - 6) + P(9 - 12)
P(Not a 7 or 8) = 5/12 + 5/18
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F12&frac2=5%2F18&pl=Add']P(Not a 7 or 8) [/URL]= [B]25/36[/B]

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the learners in the class have black hair. How many learners in the class if 9 of them have blonde hair?
Total learners = Blond + Brown + Black
Total Learners = 1/4 + 2/3 + Black
Total Learners will be 1, the sum of all fractions
1/4 + 2/3 + Black = 1
Using common denominators of 12, we have:
3/12 + 8/12 + Black = 12/12
11/12 + Black = 12/12
Subtract 11/12 from each side:
Black = 1/12
Let t be the total number of people in class. We are given for blondes:
1/4t = 9
Multiply each side by 4
[B]t = 36[/B]
Brown Hair
2/3(36) = 24
Black Hair
1/12(36) = 3

A recipe calls for 2 ½ cup of flour, but Paul only has 2 ?. How much more flour does he need?

A recipe calls for 2 ½ cup of flour, but Paul only has 2 ?. How much more flour does he need?
Convert to improper fractions
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F2&frac2=3%2F8&pl=Simplify']2 & 1/2 [/URL]= 5/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F6&frac2=3%2F8&pl=Simplify']2 & 1/6[/URL] = 13/6
[URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=5%2F2&pl=Equivalent+Fractions']Convert 5/2 to an equivalent fraction with a denominator[/URL] of 6:
15/6
[URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F6&frac2=13%2F6&pl=Subtract']We subtract 13/6 from 15/6[/URL]
15/6 - 13/6 = 2/6
2/6 = [B]1/3[/B]

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni.

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni. Of these, 2/3 also have peppers. How many pizzas have pepperoni and peppers?
We multiply the pizzas sold by the percentage of pepperoni times the fraction of peppers. Since 70% is 7/10, we have:
Pizzas with pepperoni and peppers = 15,000 * 7/10 * 2/3
7/10 * 2/3 = 14/30. [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F30&frac2=3%2F8&pl=Simplify']Using our fraction simplifier calculator[/URL], we can reduce this to 7/15
Pizzas with pepperoni and peppers = 15,000 * 7/15
Pizzas with pepperoni and peppers = [B]7,000[/B]

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof.

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof.
Slope = Rise or Drop / Run
Slope = 4/12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F12&frac2=3%2F8&pl=Simplify']type 4/12 into our search engine[/URL] and get:
Slope. = [B]1/3[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope is y/x,so we have 27/36.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 27/36 to 3/4. So this is our slope.
[B]3/4[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope = Rise/Run or y/x
Since tests are on the y-axis and time is on the x-axis, we have:
Slope = 27/36
We can simplify this, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']type in 27/36 into our search engine[/URL], and get:
[B]Slope = 3/4[/B]

A section of land measuring 3 & 3/6 acres is divided equally among 7 people. How many acres will eac

A section of land measuring 3 & 3/6 acres is divided equally among 7 people. How many acres will each person get?
We want 3&3/6 /7
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%263%2F6&frac2=7&pl=Divide']Using our fraction calculator[/URL], we get:
[B]1/2 acre per person[/B]

A Septonian said he had eaten .5 of his cookie while an American said he had eaten .5 of his cookie.

A Septonian said he had eaten .5 of his cookie while an American said he had eaten .5 of his cookie. Who ate more? Why?
[LIST]
[*]The Septon ate 5 groups of 1/7 or 5/7
[*]The American ate 5 groups of 1/10 or 5/10 which is 1/2
[/LIST]
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5/7&frac2=5/10&pl=Compare']5/7 is larger[/URL], so the Septoian ate more.

a shop has a sale of 1/5 off all items in stock. if the original price of a dress is £45, what would

a shop has a sale of 1/5 off all items in stock. if the original price of a dress is £45, what would be its sale price?
[URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/5&pl=Multiply']1/5 of 45[/URL] = 9
45 - 9 = [B]36[/B]

A single card is drawn from a standard 52 card deck. What is the possibility that the card drawn is

A single card is drawn from a standard 52 card deck. What is the possibility that the card drawn is either a 4 or a 6
There are 4 (4's) and 4 (6's) in a standard 52 card deck.
P(4 or 6) = P(4) + P(6)
P(4 or 6) = 4/52 + 4/52
P(4 or 6) = 8/52
We can simplify this fraction by [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']typing it in our search engine and choosing simplify[/URL]:
P(4 or 6) = [B]2/13[/B]

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.
Declare variables:
[LIST]
[*]Let f be the father's age
[*]Let s be the son's age
[/LIST]
We're given two equations:
[LIST=1]
[*]s = f/4
[*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I]
[/LIST]
Using substitution, we substitute equaiton (1) into equation (2) for s:
f - f/4 = 30
To remove the denominator/fraction, we multiply both sides of the equation by 4:
4f - 4f/4 = 30 *4
4f - f = 120
3f = 120
To solve for f, we divide each side of the equation by 3:
3f/3 = 120/3
Cancel the 3's on the left side and we get:
f = [B]40[/B]

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is t

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second lands on gray?
P(blue) = Blue sections / Total Sections
P(blue) = 8/10
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get:
P(blue) = 4/5
P(gray) = Gray sections / Total Sections
P(blue) = 2/10
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get:
P(gray) = 1/5
We want the probability of blue,gray. Since each spin is independent, we multiply the two probabilities to get our answer:
P(blue, gray) = P(blue) * P(gray)
P(blue, gray) = 4/5 * 1/5
P(blue, gray) = [B]4/25[/B]

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the prob

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the probability that it will land on a green section? Write your answer as a fraction or whole number.
P(green) = Total Green / Total spaces
P(green) = 2/6
We can simplify this fraction. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type 2/6 into our search engine[/URL], choose Simplify, and we get:
P(green) = [B]1/3[/B]

A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there?

A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there?
We want 21 / 1 & 3/4
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=21&frac2=1%263%2F4&pl=Divide']fraction operation calculator[/URL], we get:
[B]12 boards[/B]

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many doctors use brand A aspirin?
We want 3/5 of 2000. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=2000&frac2=3/5&pl=Multiply']type this expression into our search engine[/URL] and we get:
[B]1,200[/B]

A teacher who makes $54000 per year $8400 in taxes, and $1200 in union does what fraction of the tea

A teacher who makes $54000 per year $8400 in taxes, and $1200 in union does what fraction of the teacher’s income does she have left
Calculate Net Income:
Net income = Earnings - Taxes - Union Dues
Net income = 54000 - 8400 - 1200
Net income = 44,400
Net Income Percent = 100% * Net Income / Earnings
Net Income Percent = 100% * 44,400/54,000
Net Income Percent = 100% * 0.8222
Net Income Percent = [B]82.22%[/B]

A test has 90 questions and you answered 69 correctly. What fraction did you get correct?

A test has 90 questions and you answered 69 correctly. What fraction did you get correct?
69/90
Divide top and bottom by 3 to simplify:
[B]23/30[/B]

A wood screw advances 1/16 inch for each complete turn. How far will the screw advance in 8 complete

A wood screw advances 1/16 inch for each complete turn. How far will the screw advance in 8 complete turns
1/6 inch per turn x 8 complete turns = 8/16.
Enter 8/16 into the search engine. Choose simplify. Using our [URL='http://www.mathcelebrity.com/fraction.php?frac1=8%2F16&frac2=3%2F8&pl=Simplify']simplify fraction calculator,[/URL] we get 8/16 simplified is [B]1/2[/B] of a turn.

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar cookies and 6 oatmeal raisin cookies. What it’s the probability that Aaron randomly selects a peanut butter cookie from the bag, eats it,, then randomly selects another peanut butter cookie?
First draw out of the bag is a peanut butter cookie:
P(PB) = Total Peanut Butter Cookies / Total Cookies
P(PB) = 6/27
Second draw out of the bag is a peanut butter cookie, but we have one less since Aaron ate one:
P(PB) = Total Peanut Butter Cookies - 1 / Total Cookies - 1
P(PB) = (6 - 1)/(27 - 1)
P(PB) = 5/26
Now, since each event is independent, we multiply them to see the probability of choosing a peanut butter cookie, eating it, then reaching in and choosing another peanut butter cookie:
P(PB, PB) = 6/27 * 5/26
[URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F27&frac2=5%2F26&pl=Multiply']P(PB, PB)[/URL] = [B]5/117[/B]

About 3/5th of the registered voters participated in 2016 election. California has 25 million regist

About 3/5th of the registered voters participated in 2016 election. California has 25 million registered voters. Find the number of registered voters who participated in 2016 election.
3[URL='https://www.mathcelebrity.com/fraction.php?frac1=25000000&frac2=3/5&pl=Multiply']/5 of 25000000[/URL] = [B]15,000,000[/B]

Adam ate 1/5 of a cake and Matt ate the rest. What fraction did Matt eat

Adam ate 1/5 of a cake and Matt ate the rest. What fraction did Matt eat?
The rest of the cake is 1 - 1/5.
1 as a fraction is 5/5. So we have:
5/5 - 1/5
Using our f[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F5&frac2=1%2F5&pl=Subtract']raction calculator[/URL], we get [B]4/5[/B]

Adrienne brings home $1580 per month. She spends $316 on food. What is the fraction of what she spen

Adrienne brings home $1580 per month. She spends $316 on food. What is the fraction of what she spends on food
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=316%2F1580&frac2=3%2F8&pl=Simplify']fraction calculator[/URL], we see that:
316/1580 = [B]1/5[/B]

Alex rode his bike to school at a speed of 12 mph. He then walked home at a speed of 5 mph. What was

Alex rode his bike to school at a speed of 12 mph. He then walked home at a speed of 5 mph. What was Alex's average speed for his trip to school and back?
Say the distance was 1 mile from school to home
D = rt
To school
1 = 12t
t = 1/12
From school:
1 = 5t
t = 1/5
1/2(1/12 + 1/5)
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F24&frac2=1%2F10&pl=Add']1/24 + 1/10[/URL] = 17/120
120 = Average speed * 17
Average speed = 120/17 = [B]7.06 mph[/B]

Alvin, an HR Director has 12 employees in his department. There are still 3 positions to be filled u

Alvin, an HR Director has 12 employees in his department. There are still 3 positions to be filled up. What fraction of the entire staff are still available?
If 3 spots need to be filled, then we have 12 - 3 = 9 people still available.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F12&frac2=3%2F8&pl=Simplify']9/12 =[/URL] 3[B]/4[/B]

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike. If she rode her bike for 45 minutes in a week, how much time did she devote to homework in the same week
If Amanda spent 2/5 of her time after school doing homework, she has 1 - 2/5 time left over.
We convert 1 to a fraction using a denominator of 5, we get:
5/5 - 2/5 = 3/5
And Amanda spent 1/4 of 3/5 of her time bike riding, which means she spent:
1(3)/4(5) = 3/20 of her time.
If the total time after school is t, we have:
3t/20 = 45
[URL='https://www.mathcelebrity.com/prop.php?num1=3t&num2=45&den1=20&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing in 3t/20 = 45 to our search engine[/URL], we get t = 300.
So Amanda has 300 total minutes after school, which means she spent 2/5(300) = [B]120 minutes (2 hours)[/B] doing homework.

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. I

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. If she earns a total of 87400 dollars per year, what is her monthly salary in dollars?
Calculate the annual salary without bonus:
Annual Salary = Total Pay - Christmas Bonus
Annual Salary = 87400 - 6400
Annual Salary = 81000
Now calculate the monthly salary. [I]Note: there are 12 months in a year[/I]:
Monthly Salary = Annual Salary / 12
Monthly Salary = 81000/12
[URL='https://www.mathcelebrity.com/fraction.php?frac1=81000%2F12&frac2=3%2F8&pl=Simplify']Monthly Salary[/URL] = [B]6750[/B]

An experienced accountant can balance the books twice as fast as a new accountant. Working together

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone?
Person A: x/2 job per hour
Person B: 1/x job per hour
Set up our equation:
1/x + 1/(2x) = 1/10
Multiply the first fraction by 2/2 to get common denominators;
2/(2x) + 1/(2x) = 1/10
Combine like terms
3/2x = 1/10
Cross multiply:
30 = 2x
Divide each side by 2:
[B]x = 15[/B]

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of milk last him?
Milk Days = Total Pints of Milk / pints drank per day
Milk Days = 8 / 1/4
Dividing by a fraction is the same as multiplying by it's reciprocal.
The [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=3%2F8&pl=Reciprocal']reciprocal of[/URL] 1/4 is 4/1, so we have:
8 * 4/1 = [B]32 days[/B]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community col

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register?
We set up the Tuition function T(c), where c is the number of courses:
T(c) = Cost per course * c + Registration Fee
T(c) = 35c + 375
The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below:
35c + 375 <= 1000
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]:
c <= 17.85
Since we cannot have fractional courses, we round down and get:
c[B] <= 17[/B]

Angie knew 90% of the answers on a worksheet. What fraction of the answers did she know?

Angie knew 90% of the answers on a worksheet. What fraction of the answers did she know?
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=90&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]90% as a fraction[/I] into our search engine[/URL] and we get:
[B]9/10[/B]

Anna made $60 babysitting. She spent 4/5 of the money on new shoes. How much money does she have lef

Anna made $60 babysitting. She spent 4/5 of the money on new shoes. How much money does she have left?
[U]Calculate shoe spend[/U]
[URL='https://www.mathcelebrity.com/fraction.php?frac1=60&frac2=4/5&pl=Multiply']4/5 of 60[/URL] = 48
[U]Calculate leftover money[/U]
Leftover money = Babysitting money - shoe spend
Leftover money = 60 - 48
Leftover money = [B]12[/B]

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how lon

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates per hour:
[LIST]
[*]Anna paints 1/4 of a fence per hour
[*]Brother paints 1/5 of a fence per hour
[*]Combined, they paint [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20 of a fence per hour
[/LIST]
Setup a proportion of time to hours where h is the number of hours needed to paint the fence
9/20 of a fence the first hour
18/20 of a fence the second hour
2/20 is left. Each 1/20 of the fence takes 60/9 = 6 & 2/3 minutes
6 & 2/3 minutes * 2 = 13 & 1/3 minutes
Final time is:
[B]2 hours and 13 & 1/3 minutes[/B]

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have?
Let the April sweets be a.
Let the May sweets be m.
Let the June sweets be j.
We're given the following equations:
[LIST=1]
[*]m = 3j/4
[*]a = 2m/3
[*]a + j + m = 90
[/LIST]
Cross multiply #2;
3a = 2m
Dividing each side by 2, we get;
m = 3a/2
Since m = 3j/4 from equation #1, we have:
3j/4 = 3a/2
Cross multiply:
6j = 12a
Divide each side by 12:
a = j/2
So we have:
[LIST=1]
[*]m = 3j/4
[*]a = j/2
[*]a + j + m = 90
[/LIST]
Now substitute equation 1 and 2 into equation 3:
j/2 + j + 3j/4 = 90
Multiply each side by 4 to eliminate fractions:
2j + 4j + 3j = 360
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get:
j = [B]40[/B]

Arthur had $90. He spent $40 and gave $20 to his brother. What fraction of Arthur's money is left

Arthur had $90. He spent $40 and gave $20 to his brother. What fraction of Arthur's money is left?
Arthur starts with $90.
He gives away $40, so now he has $90 - $40 = $50.
Next, he gives $20 to his brother, so now he has $50 - $20 = $30.
So Arthur has 30/90 left.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=30%2F90&frac2=3%2F8&pl=Simplify']We type 30/90 into our search engine[/URL] and simplify to get:
[B]1/3[/B]

Assume that you make random guesses for 5 true-or-false questions

Assume that you make random guesses for 5 true-or-false questions.
(a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain.
(a) Correct Answer on each one is 1/2 or 0.5. Since all are independent events, we have:
(1/2)^5 = [B]1/32[/B]
(b) We have [B]1/2[/B]
(1/2)^4 * 1/2/((1/2)^4)
c) [B]Independent since you could have gotten correct or wrong on any of the 4 and the probability does not change[/B]

Assuming a standard 52-card deck, what's the probability of dealing three eights in a row when the c

Assuming a standard 52-card deck, what's the probability of dealing three eights in a row when the cards are returned and the deck is shuffled between each draw?
There are four (8's) in a standard 52 card deck. The probability of drawing an 8 is:
4/52
[URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F52&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we get:
1/13
Now, with each draw, we replace the deck. So each draw of an 8 has a 1/13 probability. And since each of the three draws is independent, we multiply each probability:
1/13 * 1/13 * 1/13 = [B]1/2197 or 0.00045516613[/B]

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.
[LIST]
[*]How many men at the party?
[*]How many ladies at the party?
[*]How many kids at the party?
[/LIST]
Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party
[U]Calculate ratios:[/U]
[LIST]
[*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B]
[*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B]
[*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B]
[/LIST]
[U]Check our work:[/U]
Men + Ladies + Kids = 32 + 24 + 16
Men + Ladies + Kids = 72 <-- This checks out!

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting?
Let the original amount of money earned for babysitting be b. We're given:
[LIST=1]
[*]Start with b
[*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65
[*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35
[*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b
[/LIST]
b - 14.65 - 1.35 = b/3
Multiply each side of the equation by 3 to remove the fraction
3(b - 14.65 - 1.35) = 3b/3
3b - 43.95 - 4.05 = b
To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get:
b =[B] 24[/B]

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How long is each piece of rope?
Using our mixed number converter, we see that:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=7%261%2F3&frac2=3%2F8&pl=Simplify']7&1/3[/URL] = 22/3
Split into [URL='https://www.mathcelebrity.com/fraction.php?frac1=22%2F9&frac2=3&pl=Simplify']3 equal pieces[/URL], we have:
22/3 / 3 = 22/9 or 2&4/9

Benchmark Fractions

Adds or Subtracts or Compares 2 fractions using estimating sums or estimating differences with benchmark fractions.

Bob can complete 35 math problems in 5 minutes how many can he complete in 1 minute

Bob can complete 35 math problems in 5 minutes how many can he complete in 1 minute
35 math problems / 5 minutes
Divide the top and bottom of the fraction by 5:
35 math problems / 5 minutes =[B] 7 math problems per minute[/B]

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will bo

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will both of them get?
If Bob shares the fudge with Sue, we assume they split equal parts. This means:
We take 4/5 total and divide into 2 for 2 people:
4/5/2
This is the same as 4/5 * 1/2
4/10
This fraction is not simplified.
Factor of 4 = {1, [U]2[/U], 4}
Factors of 10 = {1, [U]2[/U], 5, 10}
In both of these lists, we see the greatest common factor is 2.
So we divide top and bottom of 4/10 by 2:
4/2 / 10 / 2
[B]2/5
Bob gets 2/5 of a pound of fudge and Sue gets [B]2/5 of a pound of fudge[/B][/B]

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. I

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk?
Set up unit rates:
[LIST]
[*]Brandon can shovel 1/8 of a sidewalk per minute
[*]His brother can shovel 1/12 of a sidewalk per minute
[/LIST]
Together, they can shovel:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute
1 minute = 60 seconds
5/24 / 60 seconds = 1/x seconds
5/24 * 60 = 1/x
5/1440 = 1/x
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
x = 288
288/60 = [B]4 minutes and 48 seconds[/B]

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy.

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy. Write and solve and inequality to find how many on demand movies could you buy if you want your bill to be less than $150 for the month.
Let x equal to the number room movie rentals per month. Our inequality is:
120 + 2.99x < 150
To solve for the number of movies, Add 120 to each side
2.99x < 30
Divide each side by 2.99
x < 10.03, which means 10 since you cannot buy a fraction of a movie

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange cards to purple cards.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=80&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']80% as a fraction [/URL]is 4/5.
Fractions to ratios can be written as numerator : denominator, so we have:
[B]4:5[/B]

Classify Fraction

Determines the if a fraction is proper, improper, or whole.

Closest Fraction

Determines the closest fraction in a list to a target fraction

Conjugates

Simplifies a fraction with conjugates in the denominator

Continued Fraction

Shows the continued fraction for a fraction

convert 5 minutes to hours expressing your answer as a fraction in its lowest terms

convert 5 minutes to hours expressing your answer as a fraction in its lowest terms
1 hour has 60 minutes, so we have:
5/60
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F60&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we get:
[B]1/12[/B]

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of 7900 adults, how many of these adults would you expect to drink coffee ever
We'd multiply 16/25 times 7900:
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=7900&frac2=16/25&pl=Multiply']fraction multiplication calculator by type 16/25 of 7900[/URL], we get:
[B]5056[/B]

Dan needs 309 programs for the school play on Thursday. How many boxes of programs will he need, giv

Dan needs 309 programs for the school play on Thursday. How many boxes of programs will he need, given that each box contains 41 programs?
Each box contains 41 programs, so we divide 309 programs by 41 programs per box to get our boxes:
309/41 using our [URL='https://www.mathcelebrity.com/longdiv.php?num1=309&num2=41&pl=Long%20Division%20%28Decimals%29']division calculator[/URL] is 7.5365.
Since we don't have fractional boxes, we round up to the next highest integer. [B]8 boxes[/B]

Danny's mom ate 1/6 of an ice cream cake. Danny and his sister want to split the remainder of it. Ho

Danny's mom ate 1/6 of an ice cream cake. Danny and his sister want to split the remainder of it. How much of the cake would each get?
If Danny's mom ate 1/6 of the cake, then we have:
1 - 1/6 of the cake left.
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F6&pl=Subtract']use our fraction subtraction calculator[/URL] for 1 - 1/6 to get:
5/6
If Danny and his sister split the remainder, then we divide 5/6 by 2. It's also the same as multiplying 5/6 by 1/2:
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F6&frac2=1%2F2&pl=Multiply']use our fraction multiplication calculator[/URL] to get:
[B]5/12 for Danny and his sister[/B]

David obtained 5 out of 20 votes in the election. What percentage of the votes did david receive?

David obtained 5 out of 20 votes in the election. What percentage of the votes did david receive?
5/20 is the fraction.
You can simplify by dividing top and bottom by 5 to get 1/4
As a decimal, this is 0.25
To get a percentage, multiply the decimal by 100
100 * 0.25 = 25%
You can also use our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+20&pcheck=1&num1=6500&pct1=70&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']decimal-percentage-fraction converter[/URL]

Decompose Fraction

Decomposes a Fraction. Shows you the work behind decomposing a fraction

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left ove

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left over, how much did each person eat?
This means 4 full pizzas - 1/4 of a pizza = 3 & 3/4 pizzas eaten
Del and his 5 friends means 6 people total. Since they ate equal amounts, we divide pizzas eaten by total people:
3 & 3/4 / 6
Convert 3 & 3/4 to a mixed fraction:
(4*3 + 3)/4 = 15/4
15/4/6
Divide by a fraction is the same as multiply by a reciprocal:
15/4 * 1/6 = [B]15/24 pizzas per person[/B]

Divide 10 by the difference of z and y

[U]The difference of z and y means we subtract y from z[/U]
z - y
[U]Now, we form a fraction, where 10 is the numerator and z - y is the denominator[/U]
10/(z - y)

double v, add u, then divide t by what you have

double v, add u, then divide t by what you have
Double v means we multiply the variable v by 2:
2v
Add u:
2v + u
We build a fraction, with t as the numerator, and 2v + u as the denominator
[B]t/(2v + u)[/B]

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be P or R?
PROPER has 6 letters in it. It has 2 P's and 2 R's. So we have:
Pr(P or R) = Pr(P) + Pr(R)
Pr(P or R) = 2/6 + 2/6
Pr(P or R) = 4/6
We can simplify this. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL], choose simplify, and we get:
Pr(P or R) = [B]2/3[/B]

Equivalent Fractions

Given a fraction, this will determine equivalent fractions

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an eve

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an even number on one cube and a prime number on the other?
P(Even on first cube) = (2,4,6) / 6 total choices
P(Even on first cube) = 3/6
P(Even on first cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
P(Prime on second cube) = (2,3,5) / 6 total choices
P(Prime on second cube) = 3/6
P(Prime on second cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
Since each event is independent, we have:
P(Even on the first cube, Prime on the second cube) = P(Even on the first cube) * P(Prime on the second cube)
P(Even on the first cube, Prime on the second cube) = 1/2 * 1/2
P(Even on the first cube, Prime on the second cube) = [B]1/4[/B]

Estimate Fraction

Estimates a fraction using a benchmark fractions of 1/2.

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept
Get this in slope-intercept form by adding 5y to each side:
4x - 5y + 5y = 5y + 20
Cancel the 5y's on the left side and we get:
5y + 20 = 4x
Subtract 20 from each side
5y + 20 - 20 = 4x - 20
Cancel the 20's on the left side and we get:
5y = 4x - 20
Divide each side by 5:
5y/5 = 4x/5 - 4
y = 4x/5 - 4
So we have a slope of 4/5
to find our y-intercept, we set x = 0:
y = 4(0)/5 - 4
y = 0 - 4
y = -4
If we want a line perpendicular to the line above, our slope will be the negative reciprocal:
The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator:
m = 5/4
Next, we multiply this by -1:
-5/4
So our slope-intercept of the perpendicular line with the same y-intercept is:
[B]y = -5x/4 - 4[/B]

Factoring and Root Finding

This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

find the probability of drawing a 4 or an ace

find the probability of drawing a 4 or an ace.
In a 52 card deck, there are 4 (4's) and 4 (Aces), for a total of 8 cards:
The probability is 8 cards / 52 total cards:
8/52 using our s[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']implify fractions calculator[/URL] = [B]2/13[/B]

Four fifths of 300

Four fifths of 300.
Multiply 4/5 by 300:
4(300)/5
1200/5
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1200%2F5&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
240

Fraction Cancellation Property

Demonstrates the Fraction Cancellation Property also known as Cancellation Property of Fractions
Numerical Properties

Fraction with variable x in numerator and 6 in the denominator.

Fraction with variable x in numerator and 6 in the denominator.
The numerator is the top of the fraction.
The denominator is the bottom of the fraction.
[B]x/6[/B]

Fractions and Mixed Numbers

Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability tha

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability that the next card you turn over will be a face card?
Key phrases: 52 card standard deck so you know there's no tricks or missing cards.
[U]Calculate the number of face cards in a standard 52 card deck[/U]
First, we know that face cards = (J, K, Q)
We also know that there are 4 suits (Hearts, Diamonds, Spades, Clubs)
Total Face Cards = 3 face card types * 4 possible suits = 12 face cards
[U]Calculate total face down cards[/U]
First card, you turn over a 6
Next card, you turn over a 7
This means, we have 52 cards - 2 cards from the draws = 50 cards left in the deck which are face down.
P(Face Card) = Total Face Cards / Total Cards in the Deck Face Down
P(Face Card) = 12/50
Simplifying this fraction [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F50&frac2=3%2F8&pl=Simplify']using our math engine[/URL], we get:
P(Face Card) = [B]6/25[/B]

Gino has 7 whole pineapples. He cuts each whole into 4 equal parts. Write an improper fraction for t

Gino has 7 whole pineapples. He cuts each whole into 4 equal parts. Write an improper fraction for the cut parts of pineapples.
Take our whole pineapples divided by the number of equal parts:
[B]7/4[/B]

Glen got 48 out of 64 correct in his test. What fraction of the marks did he get wrong? Give your a

Glen got 48 out of 64 correct in his test. What fraction of the marks did he get wrong? Give your answer in its simplest form.
Glen got 64 - 48 = 16 questions wrong
16/64 [URL='http://www.mathcelebrity.com/fraction.php?frac1=16%2F64&frac2=3%2F8&pl=Simplify']as a fraction[/URL] is 1/4

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both o

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both of them are red?
Half means 4 cards are red and 4 cards are black.
The first draw probability of red is:
4 total red cards out of 8 total cards = 4/8.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F8&frac2=3%2F8&pl=Simplify']Simplified, this is[/URL] 1/2
The second draw is 3 total red cards out of 7 remaining cards. Since 1 red was drawn (4 - 1) = 3 reds left and 1 card was drawn (8 -1) = left
3/7
Since each draw is independent, we multiply the probabilities:
1/2 * 3/7 = [B]3/14[/B]

gy=-g/v+w for g

gy=-g/v+w for g
Multiply each side of the equation by v to eliminate fractions:
gvy = -g + vw
Add g to each side:
gvy + g = -g + g + vw
Cancel the g's on the right side and we geT:
gvy + g = vw
Factor out g on the left side:
g(vy + 1) = vw
Divide each side of the equation by (vy + 1):
g(vy + 1)/(vy + 1) = vw/(vy + 1)
Cancel the (vy + 1) on the left side and we geT:
g = [B]vw/(vy + 1)[/B]

Harry got 42 out of 49 correct in his test. What fraction of the marks did he get correct?

Harry got 42 out of 49 correct in his test. What fraction of the marks did he get correct?
The fraction correct is:
42/49
Both the numerator and denominator [URL='http://www.mathcelebrity.com/gcflcm.php?num1=42&num2=49&num3=&pl=GCF']have a common factor[/URL] of 7
Reducing top and bottom by 7, we get:
[B]6/7[/B]

Hayden bought 48 new trading cards. Three-fourths of the new cards are baseball cards. How many base

Hayden bought 48 new trading cards. Three-fourths of the new cards are baseball cards. How many baseball cards did Hayden buy?
We want 3/4 of 48. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=48&frac2=3/4&pl=Multiply']type this statement into our calculator[/URL] and we get:
[B]36[/B]

Hose A can fill a pool in 4 hours. Hose B can fill the pool in 2 hours. If both hoses are turned on

Hose A can fill a pool in 4 hours. Hose B can fill the pool in 2 hours. If both hoses are turned on at the same time how long will it take to fill the pool?
[LIST]
[*]Hose A can fill the pool in 1/4 of the pool an hour
[*]Hose B can fill the pool in 1/2 of the pool an hour
[/LIST]
In one hour using combined effort, we have:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F4&pl=Add']1/2 + 1/4[/URL] = 3/4 of the pool will be filled.
3/4 of the pool gets filled in 60 minutes. We set up a proportion of proportion filled to time where t is the time to fill the full pool:
3/4/60 = 1/t
3/240 = 1/t
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=t&propsign=%3D&pl=Calculate+missing+proportion+value']proportion solver[/URL], we get:
t = [B]80 minutes or 1 hour and 20 minutes[/B]

How many 1/4 sheets are there in 5 sheets

How many 1/4 sheets are there in 5 sheets
We divide 5 sheets by 1/4 sheets:
5/1/4
However, when we divide by a fraction, it's the same as multiplying by the reciprocal of the fraction:
The reciprocal of 1/4 is 4/1, so we have:
5 * 4/1 = 20/1 = [B]20[/B]

How many 2/4 pound pieces can be cut from a giant 1200 pound thumbnail?

How many 2/4 pound pieces can be cut from a giant 1200 pound thumbnail?
Using a fraction:
1200 pounds of meatball / 3/4 pound pieces = [B]1,600 pieces
[/B]
Using a decimal 0.75 for 3/4:
1200 pounds of meatball / 0.75 pound pieces = [B][B]1600 pieces[/B][/B]

How many one-fifths are there in 200?

How many one-fifths are there in 200?
Using the rule of dividing by a fraction is the same as multiplying by the reciprocal, we have:
200 / 1/5 = 200 * 5 = [B]1000[/B]

I have 6 cakes and I want to divide them between 8 people how much does each person get?

6 cakes for 8 people. Divide by 8 people to get the cakes for each person.
6/8 cake per person. However, this fraction can be simplified.
Divide the top and bottom by 2.
We get 3/4, or 0.75 cake for each person.

If 1/8 = y%, find y

If 1/8 = y%, find y
Using our [URL='https://www.mathcelebrity.com/perc.php?num=1&den=8&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']fraction to percentage calculation[/URL], we see that:
1/8 = [B]12.5[/B]%

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numer

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.
Convert 2 to a fraction with a denominator of 10:
20/2 = 10, so we multiply 2 by 10/10:
2*10/10 = 20/10
Add 2 to the numerator and denominator:
(n + 2)/(d + 2) = 9/10
Cross multiply and simplify:
10(n + 2) = 9(d + 2)
10n + 20 = 9d + 18
Move constants to right side by subtracting 20 from each side and subtracting 9d:
10n - 9d = -2
Subtract 3 from the numerator and denominator:
(n - 3)/(d - 3) = 4/5
Cross multiply and simplify:
5(n - 3) = 4(d - 3)
5n - 15 = 4d - 12
Move constants to right side by adding 15 to each side and subtracting 4d:
5n - 4d = 3
Build our system of equations:
[LIST=1]
[*]10n - 9d = -2
[*]5n - 4d = 3
[/LIST]
Multiply equation (2) by -2:
[LIST=1]
[*]10n - 9d = -2
[*]-10n + 8d = -6
[/LIST]
Now add equation (1) to equation (2)
(10 -10)n (-9 + 8)d = -2 - 6
The n's cancel, so we have:
-d = -8
Multiply through by -1:
d = 8
Now bring back our first equation from before, and plug in d = 8 into it to solve for n:
10n - 9d = -2
10n - 9(8) = -2
10n - 72 = -2
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=10n-72%3D-2&pl=Solve']plug this equation into our search engine[/URL] and we get:
n = 7
So our fraction, n/d = [B]7/8[/B]

If 3/5 of a bun is shared equally between 4 people, what fraction of the bun would each receive?

If 3/5 of a bun is shared equally between 4 people, what fraction of the bun would each receive?
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F5&frac2=1%2F4&pl=Multiply']We divide 3/5 by 4[/URL] to get [B]3/20[/B]

If 3x - y = 12, what is the value of 8^x/2^y

If 3x - y = 12, what is the value of 8^x/2^y
We know 8 = 2^3
So using a rule of exponents, we have:
(2^3)^x/2^y
2^(3x)/2^y
Using another rule of exponents, we rewrite this fraction as:
2^(3x -y)
We're given 3x - y = 12, so we have:
[B]2^12[/B]

If 9/20 of a salad is eaten, how much is leftover?

If 9/20 of a salad is eaten, how much is leftover?
The full salad is 1. Using a common denominator, we have 1 = 20/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=9%2F20&pl=Subtract']So the leftover is 20/20 - 9/20[/URL] = [B]11/20[/B]

If a person from Septon at .1 of their cookie, what fraction of the cookie did they eat using base 1

If a person from Septon at .1 of their cookie, what fraction of the cookie did they eat using base 10
(1/7)^1 = 1/7

If a pound of coffee costs $4, how many ounces can be bought for $1.80

If a pound of coffee costs $4, how many ounces can be bought for $1.80
Using our conversion calculator, we find
[URL='https://www.mathcelebrity.com/weightcon.php?quant=1&pl=Calculate&type=pound']1 pound [/URL]= 16 ounces
$4 per 16 ounces = 4/16
[URL='https://www.mathcelebrity.com/perc.php?num=4&den=16&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']We can simplify this fraction[/URL] to 0.25 per ounce
We take our 1.80 divided by 0.25 per ounce
1.80/0.25 = [B]7.2 ounces of coffee[/B]

if I have 1/4 of a tank of gas. what fractions represents the amount required to fill my gas tank th

if I have 1/4 of a tank of gas. what fractions represents the amount required to fill my gas tank the rest of the way?
A full tank of gas is 1. You can also write 1 as 4/4.
So we take 4/4 - 1/4 = [B]3/4 tank remaining[/B]

If Susie sleeps for 8 hours, what fraction of the day is she asleep?

If Susie sleeps for 8 hours, what fraction of the day is she asleep?
A day has 24 hours, so Susie slept 8/24 of a day.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F24&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we get 8/24 = [B]1/3[/B] of a day.

If x/2y = 3/4, what is the value of y/x?

If x/2y = 3/4, what is the value of y/x?
Cross multiply this proportion:
4x = 3(2y)
4x = 6y
Divide each side by x:
4x/x = 6y/x
The x's cancel, and we have:
6y/x = 4
Divide each side by 6:
6y/6x = 4/6
The 6's on the left cancel, we have:
y/x = 4/6
We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']Type in Simplify 4/6 into the search engine[/URL], and we get 2/3.
y/x = [B]2/3[/B]

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Wr

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box.
Set up a proportion of dollars to boxes where b is the number of boxes for $4:
6/1/3 = 4/b
Cross multiply:
6b = 4/3
Multiply each side by 1/6 to isolate b:
b = 4/18
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=18&num3=&pl=GCF+and+LCM']Type in GCF(4,18) into the search engine[/URL]. We get a greatest common factor of 2.
Divide 4 and 18 in the fraction by 2. We get the reduced fraction of:
[B]b = 2/9[/B]

In a certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of ke

In a certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of keys to one of the cars. What is the probability of choosing a set of keys to a blue car?
[U]Our total cars are:[/U]
Total Cars = White Cars + Red Cars + Blue Cars = Black Cars
Total Cars = 16 + 7 + 8 + 9
Total Cars = 40
P(Blue) = Blue Cars / Total Cars
P(Blue) = 8/40
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F40&frac2=3%2F8&pl=Simplify']fraction simplify calculator[/URL], we get:
P(Blue) = [B]1/5[/B]

In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If

In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble from each bag, what is the probability that they are both yellow?
Bag 1 probability of drawing yellow is 7/15
Bag 2 probability of drawing yellow is 2/15
Since each event is independent, we multiply each draw to get our final probability:
P(yellow Bag 1)(yellow Bag 2) = P(Yellow Bag 1) * P(Yellow Bag 2)
P(yellow Bag 1)(yellow Bag 2) = 7/15 * 2/15
P(yellow Bag 1)(yellow Bag 2) = [B]14/225[/B]
[URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F225&frac2=3%2F8&pl=Simplify']Since we cannot simplify this fraction anymore[/URL], our answer is [B]14/225[/B]

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray,

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray, there are 13 paper clips and 16 rubber bands. Who has a higher ratio of paper clips to rubber bands?
Trina: 15/18
Kirk: 13/16
We want common denominators to compare, so we get a greatest common factor (GCF) for 16 and 18.
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=16&num2=18&num3=&pl=GCF+and+LCM']Running this through our search engine[/URL], we get GCF(16, 18) = 144
For Trina, 144/18 = 8
For Kirk, 144/16 = 9
We multiply Trina's fraction, top and bottom by 8:
15 * 8 / 18 * 8
120/144
We multiply Trina's fraction, top and bottom by 8:
13 * 8 / 16 * 8
104/144
[B]Trina[/B] has more in her numerator, so her ratio of paper clips to rubber bands is greater.

Is 20% equivalent to 2/5?

Is 20% equivalent to 2/5?
Let's compare fractions to fractions:
20% equals 1/5 from our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=20&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage-decimal-fraction calculator[/URL].
1/5 < 2/5 so these fractions are [B][I]not equivalent[/I][/B].

Is 5 over 3 equivalent to 9 over 6?

Is 5 over 3 equivalent to 9 over 6?
Using our fraction [URL='http://www.mathcelebrity.com/fraction.php?frac1=5/3&frac2=9/6&pl=Compare']comparison calculator[/URL]:
[B]5/3 > 9/6[/B]

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?
We setup a proportion of time to puzzles where p is the number of puzzles Cindy can complete in 3 hours:
3/4/1 = 3/p
Dividing by 1 means the same as the original fraction, so we have:
3/4 = 3/p
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=3&den1=4&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get:
p = [B]4[/B]

It takes Deanna 7 hours to paint a fence. Who fraction of the fence does she paint in one hour?

It takes Deanna 7 hours to paint a fence. Who fraction of the fence does she paint in one hour?
7 hours for 1 fence = [B]1/7 of the fence per hour[/B]

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour
90 pages / 6 hour = 90/6
Type [URL='https://www.mathcelebrity.com/fraction.php?frac1=90%2F6&frac2=3%2F8&pl=Simplify']90/6 in our search engine, click simplify[/URL], and we get:
[B]15 pages per hour[/B]

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered fro

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered from 1 to 25. What is the probability of drawing a number that is square?
The squares from 1 - 25 less than or equal to 25 are as follows:
[LIST=1]
[*]1^2 = 1
[*]2^2 = 4
[*]3^2 = 9
[*]4^2 = 16
[*]5^2 = 25
[/LIST]
So the following 5 cards are squares:
{1, 4, 9, 16, 25}
Therefore, our probability of drawing a square is:
P(square) = Number of Squares / Number of Cards
P(square) = 5/25
This fraction can be simplified. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F25&frac2=3%2F8&pl=Simplify']we type in 5/25 into our search engine, choose simplify[/URL], and we get:
P(square) = [B]1/5[/B]

Jeremy ran 27 laps on a track that was 1/8 mile long. Jimmy ran 15 laps on a track that as 1/4 mile

Jeremy ran 27 laps on a track that was 1/8 mile long. Jimmy ran 15 laps on a track that as 1/4 mile long. who ran farther
[U]Calculate Jeremy's distance:[/U]
Distance = Laps * Track length
Jeremy distance = 27 * 1/8
Jeremy distance = 27/8
[U]Calculate Jimmy's distance:[/U]
Distance = Laps * Track length
Jeremy distance = 15* 1/4
Jeremy distance = 15/4
[COLOR=#000000]Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=27/8&frac2=15/4&pl=Compare']fraction comparison calculator[/URL], we see that [B]Jimmy [/B]ran farther[/COLOR]

Joe had saved $264. He spent 3/8 of that to buy a camera. How much did the camera cost?

Joe had saved $264. He spent 3/8 of that to buy a camera. How much did the camera cost?
[URL='https://www.mathcelebrity.com/fraction.php?frac1=264&frac2=3%2F8&pl=Multiply']264 *3/8[/URL] = [B]99[/B]

John and Maria bought a medium pizza that has 8 slices. If John ate 2/4 slices and Maria ate 3/8, w

John and Maria bought a medium pizza that has 8 slices. If John ate 2/4 slices and Maria ate 3/8, who ate more pizza?
Using our [URL='http://www.mathcelebrity.com/fraction.php?frac1=2/4&frac2=3/8&pl=Compare']compare fractions,[/URL] we see 2/4 is greater than 3/8. So [B]John [/B]ate more pizza.

John mows 3 lawns in 4 hours, Paul mows 5 lawns in 6 hours. Who mows faster?

John mows 3 lawns in 4 hours, Paul mows 5 lawns in 6 hours. Who mows faster?
To see who mows faster, we set up fractions with a common denominator.
You can see this by running this statement in the calculator:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3/4&frac2=5/6&pl=Compare']3/4 or 5/6[/URL]
You'll see that 5/6 is larger, so Paul mores more lawns per hour.

Johnny waited 0.25 hour before his school bus arrived. How many minutes did johnny actually wait?

Johnny waited 0.25 hour before his school bus arrived. How many minutes did johnny actually wait?
An hour is 60 minutes.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+50&den1=+90&pct=+82&decimal=0.25&pcheck=5&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']0.25 = 1/4[/URL]
[URL='https://www.mathcelebrity.com/fraction.php?frac1=60%2F4&frac2=3%2F8&pl=Simplify']So we have 60 * 1/4 = 60/4[/URL] = [B]15 minutes[/B]

Jon earned money baby-sitting. He spent 1/4 of the money on a guitar and then he gave 1/4 of what wa

Jon earned money baby-sitting. He spent 1/4 of the money on a guitar and then he gave 1/4 of what was left to charity. If he has $108 left, how much money did he start with?
Calculate initial spend:
Charity = 1/4 * 3/4 left = 3/16
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=3%2F16&pl=Add']1/4 + 3/16[/URL] = 7/16
This means he has 1 = 7/16 left
16/16 - 7/16 = 9/16
Let the starting amount be s:
If he has 108 left, then we have [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=9s&num2=108&den1=16&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']9s/16 = 108[/URL]
s =$[B]192[/B]

joseph buys 3 1/2 pounds of hamburger. how many quarter -pound can he make?

joseph buys 3 1/2 pounds of hamburger. how many quarter -pound can he make?
A quarter pound is 1/4
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%261%2F2&frac2=3%2F8&pl=Simplify']3 & 1/2[/URL] = 7/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=7%2F2&frac2=1%2F4&pl=Divide']7/2 / 1/4[/URL] = [B]14 quarter pounders[/B]

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items co

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items correctly on a 40-item quiz. Do they have the same portion of correct answers?
Let's compare based on correct answers to questions:
Juliana = 42/80 = 0.525
Angela = 21/40 = 0.525
So yes, they do have the same portion of correct answers.
But there's another way to solve this:
[LIST=1]
[*]Divide Juliana's the top and bottom of Juliana's fraction by 2.
[*]We picked 2 as a GCF shown in our calculator.
[*]Type [URL='https://www.mathcelebrity.com/gcflcm.php?num1=42&num2=80&num3=&pl=GCF']GCF of 42 and 80[/URL].
[/LIST]
Divide top and bottom of Juliana's fraction by the GCF of 2
42/2 = 80/2 = 21/40
This ratio equals Angela's.

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying fo

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying for her marketing class, 12 hours studying for her statistics class, and 8 hours studying for her business law class. What percent of her study time does she spend for her statistics class?
The percentage equals hours spent on statistics divided by total hours spent studying for everything.
[U]Calculate total study hours:[/U]
Total Study Hours = Marketing Class Study Hours + Statistics Class Study Hours + Business Law Study Hours
Total Study Hours = 10 + 8 + 12
Total Study Hours = [B]30[/B]
[U]Calculate Statistics Study Hours Percentage:[/U]
Statistics Study Hours Percentage = Statistics Class Study Hours / Total Study Hours
Statistics Class Study Hours = 8/30
Using our [URL='https://www.mathcelebrity.com/perc.php?num=8&den=30&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']fraction to decimal calculator[/URL], we get
Statistics Class Study Hours = [B]26.67%[/B]

Kyle can walk ½ mile in ¼ of an hour. What is Kyle’s speed in miles per hour?

Kyle can walk ½ mile in ¼ of an hour. What is Kyle’s speed in miles per hour?
We write this in terms of miles per hour as:
1/2 / 1/4
We want 1 for the denominator to represent an hour, so we multiply top and bottom of the fraction by 4:
4/2 / 4/4
2 / 1
[B]2 miles per hour[/B]

Layla buys 2 1/2pounds of chocolate for 3.50 how much is she paying for a pound of chocolate

Layla buys 2 1/2pounds of chocolate for 3.50 how much is she paying for a pound of chocolate?
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F2&frac2=3%2F8&pl=Simplify']Using our mixed fraction converter[/URL], 2&1/2 = 5/2
Cost per pound = 3.50 / 5/2 pounds
Dividing by 5/2 is the same as multiplying by the reciprocal 2/5:
3.50 * 2/5
7/5
[B]$1.40 per pound[/B]

Marcus drives a machine that paints lines along the highway. He needs to paint a line that is 9/10 o

Marcus drives a machine that paints lines along the highway. He needs to paint a line that is 9/10 of a mile long. He is 2/3 of the way done when he runs out of paint. What fraction of a mile has he painted?
Marcus has painted 2/3 of 9/10.
If we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F3&frac2=9%2F10&pl=Multiply']type 2/3 of 91/20 in our search engine[/URL], we get:
[B]3/5[/B]

mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probabilit

mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probability of the next cap he chooses at random will be yellow?
P(yellow) = yellow caps / Total caps
P(yellow) = 12/(12 + 18)
P(yellow) = 12/30
[URL='https://www.mathcelebrity.com/fraction.php?frac1=12.%2F30&frac2=3%2F8&pl=Simplify']Simplifying this fraction,[/URL] we get:
P(yellow) = [B]2/5[/B]

Michael invited 30 of his friends to his part and a third of guest arrived late how many arrived on

Michael invited 30 of his friends to his part and a third of guest arrived late how many arrived on time
If 1/3 arrived late, then
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F3&pl=Subtract']1 - 1/3[/URL] = 2/3 arrived on time
Guests who arrived on time = 2/3 of 30
[URL='https://www.mathcelebrity.com/fraction.php?frac1=30&frac2=2/3&pl=Multiply']Guests who arrived on time[/URL] = [B]20[/B]

Mr. Vukovic is making pasta. He makes 3 ½ cups of pasta. How many ¾ cup servings can Mr. Vukovic s

Mr. Vukovic is making pasta. He makes 3 ½ cups of pasta. How many ¾ cup servings can Mr. Vukovic serve
3 & 1/2 = 7/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%261%2F2&frac2=3%2F4&pl=Divide']7/2 /3/4[/URL] = 14/3 = 4 & 2/3

Multiple Fractions (Addition or Ordering)

This adds 3 or more fractions or arranges a list of fractions from lowest to highest and highest to lowest (ordering fractions or sorting fractions)

n + n/2 + n/4 + n/8 + n/16 = 19,375

n + n/2 + n/4 + n/8 + n/16 = 19,375
Convert to like fractions with a denominator of 16:
16n/16 + 8n/16 + 4n/16 + +2n/16 + n/16 = 19,375
31n/16 = 19,375
Cross multiply:
31n = 19,375 * 16
31n = 310000
Divide each side by 1:
31n/31 = 310000/31
n = [B]10,000[/B]

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10?
Let n be the number of notebooks you can purchase. We have the following inequality:
1.39n <= 10
Divide each side by 1.39
n <= 7.194
We want whole notebooks, we cannot buy fractions of notebooks, so we have:
n <= 7
The question asks for the possible numbers of notebooks we can buy. This implies we buy at least 1, but our inequality says not more than 7. So our number set is:
[B]N = {1, 2, 3, 4, 5, 6, 7}[/B]

numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the de

numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction.
Let n be the numerator.
Let d be the denominator.
We're given 2 equations:
[LIST=1]
[*]n = d - 5
[*](n + 1)/(d + 1) = 2/3
[/LIST]
Substitute equation (1) into equation (2) for n:
(d - 5 + 1) / (d + 1) = 2/3
(d - 4) / (d + 1) = 2/3
Cross multiply:
3(d - 4) = 2(d + 1)
To solve this equation for d, we type it in our search engine and we get:
d = 14
Substitute d = 14 into equation (1) to solve for n:
n = 14 - 5
n = 9
Therefore, our fraction n/d is:
[B]9/14[/B]

n^2 = 6&1/4

n^2 = 6&1/4
[URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F4&frac2=3%2F8&pl=Simplify']6&1/4[/URL] = 25/4
n^2 = 25/4
Take the square root of each side:
n = [B]5/2 or -5/2[/B]

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly selected boat will be from Massachusetts?
P(Boat from Massachusetts) = Number of Massachusetts boats / Total Boats at the Mariana
P(Boat from Massachusetts) = 10/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F20&frac2=3%2F8&pl=Simplify']Simplifying this fraction, we get[/URL]:
P(Boat from Massachusetts) = [B]1/2[/B]

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the perc

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the percent of the worlds population who lives on less than 4 per day?
We want the percentage 1.2/7.5.
[URL='https://www.mathcelebrity.com/perc.php?num=1.2&den=7.5&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Type this fraction into our search engine[/URL], choose percentage, and we get:
[B]16%[/B]

olivia earns $2 for every cup of lemonade she sells. How many cups of lemonade does olivia need to s

olivia earns $2 for every cup of lemonade she sells. How many cups of lemonade does olivia need to sell in all to earn $16?
Cups needed = Total Revenue / Cost per cup
Cups needed = 16/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F2&frac2=3%2F8&pl=Simplify']Cups needed [/URL]= [B]$8[/B]

Olivia spends 5 hours a day at school and sleeps for 9 hours a day. What fraction of the day does sh

Olivia spends 5 hours a day at school and sleeps for 9 hours a day. What fraction of the day does she have left for other activities? Write your answer as a fraction in its simplest form.
Add up existing hours for school and sleep
School + sleep = 5 + 9 = 14 hours
Since there are 24 hours in a day, she has 24 - 14 = 10 hours remaining.
The fraction we want is 10/24. But we can simplify this. Using our [URL='http://www.mathcelebrity.com/fraction.php?frac1=10%2F24&frac2=3%2F8&pl=Simplify']simplify fractions calculator[/URL], we get:
[B]5/12[/B]

On her 10 mile trip to school, Jessica's car gets 50 mpg of gas. On her way home, her car gets 40 mi

On her 10 mile trip to school, Jessica's car gets 50 mpg of gas. On her way home, her car gets 40 miles per gallon. How many miles per gallon does Jessica's car get during the entire 20 mile trip?
50 miles each gallon for a 10 mile drive = 1/5 gallon
40 miles each gallon for a 10 mile drive = 1/4 gallon
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20
20 miles driven /9/20 gallon = 400/9 = [B]44.44 miles per gallon[/B]

One fifth of the square of a number

One fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The square of a number means we raise it to the power of 2. So we have x^2
[*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below:
[/LIST]
[B]x^2/5[/B]

One positive number is one-fifth of another number. The difference between the two numbers is 192, f

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers.
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x = y/5
[*]x + y = 192
[/LIST]
Substitute equation 1 into equation 2:
y/5 + y = 192
Since 1 equals 5/5, we rewrite our equation like this:
y/5 = 5y/5 = 192
We have fractions with like denominators, so we add the numerators:
(1 + 5)y/5 = 192
6y/5 = 192
[URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get:
[B]y = 160[/B]
Substitute this value into equation 1:
x = 160/5
x = [B]32[/B]

one-fifth of forty-five

one-fifth of forty-five
one-fifth is 1/4
forty-five is 45
When you see a fraction then the word of and then a number, it means you multiply:
1/5 * 45
45/5
[B]9[/B]

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate chips
We want 2/5 of 485. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=485&frac2=2/5&pl=Multiply']type this in our search engine[/URL] and we get;
[B]194[/B]

Percentage of the Pie Word Problem

This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.

Percentage-Decimal-Fraction Relations

Calculates the relational items between a fraction, a decimal (including repeating decimal and terminating decimal), a percentage, and the numerator and denominator piece of that fraction. Also calculates the percentage change going from one number to another or the amount increase or decrease of a percentage above/below a number. Round decimals. decimals into fractions

Phyllis's mother has 6 pounds of candy to divide evenly among her 8 children. This is an average of

Phyllis's mother has 6 pounds of candy to divide evenly among her 8 children. This is an average of how many pounds per child?
6 pounds divide among 8 children can be represented as a fraction. We want to simplify this. So we use our [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F8&frac2=3%2F8&pl=Simplify']fraction simplify calculator[/URL], and we get:
3 pounds per 4 children, or 0.75 pounds per child.

Probability of getting 4 or 6 when rolling a dice

Probability of getting 4 or 6 when rolling a dice
P(4 or 6) = P(4) + P(6)
P(4 or 6) = 1/6 + 1/6
P(4 or 6) = 2/6
We can simplify this. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type this fraction into our search engine, choose simplify[/URL], and we get:
P(4 or 6) = [B]1/3[/B]

Probability of getting either a sum of 8 or at least one 4 in the roll of a pair dice

Sum of 8 equal to 5/36 shown [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=8&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']here[/URL].
At least one 4 means one of three scenarios:
[LIST=1]
[*](4, not 4) = 1/6 * 5/6 = 5/36
[*](not 4, 4) = 5/6 * 1/6 = 5/36
[*](4, 4) = 1/6 * 1/6 = 1/36
[/LIST]
The phrase "or", means we add both probabilities (sum of 8) and (at least one 4):
5/36 + (5/36 + 5/36 + 1/36)
16/36
Simplify by dividing each part of the fraction by 4
[B]4/9[/B]

raise t to the 10th power, then find the quotient of the result and s

raise t to the 10th power, then find the quotient of the result and s
Raise t to the 10th power means we use t as our variable and 10 as our exponent:
t^10
The quotient means a fraction, where the numerator is t^10 and the denominator is s:
[B]t^10/s[/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random.
a. What is the probability that you choose a red or even numbered ball?
b. What is the probability you choose a green ball or a ball numbered less than 5?
a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Red and Even balls are {2, 4, 6, 8, 10, 12}
Our probability is:
P(Red or Even) = P(Red) + P(Even) - P(Red and Even)
P(Red or Even) = 13/18 + 9/18 - 6/18
P(Red or Even) = 16/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]16/18[/B]
[B][/B]
b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Green and less than 5 does not exist, so we have no intersection
Our probability is:
P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5)
P(Green or Less Than 5) = 5/18 + 4/18 - 0
P(Green or Less Than 5) = 9/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]1/2[/B]

S equals the quotient of r and the sum of r and 8.

S equals the quotient of r and the sum of r and 8.
A quotient means a fraction, so we have:
[B]S = r/(r + 8)[/B]

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies.

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies. She takes one candy and records its color. She then puts it back in the box and draws another candy. What is the probability of taking out a pink candy followed by a blue candy?
[B][U]Calculate the total number of candies:[/U][/B]
Total candies = Pink + Purple + Blue
Total candies = 8 + 7 + 5
Total candies = 20
[B][U]Calculate the probability of drawing one pink candy:[/U][/B]
P(Pink) = 8/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink) = 2/5
[B][U]Calculate the probability of drawing one blue candy:[/U][/B]
P(Blue) = 5/20 <-- [I]20 options since Sara replaced her first draw[/I]
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Blue) = 1/4
The problem asks for the probability of a Pink followed by a Blue. Since each event is independent, we multiply:
P(Pink, Blue) = P(Pink) * P(Blue)
P(Pink, Blue) = 2/5 * 1/4
P(Pink, Blue) = 2/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink, Blue) = [B]1/10 or 10%[/B]

Sarah rolls 2 fair dice and adds the results from each. Work out the probability of getting a total

Sarah rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 6.
Factors of 6 are {6, 12}
[URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+&dby=&ndby=&montect=+']P(Roll a 6)[/URL] = 5/36
[URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+&dby=&ndby=&montect=+']P(Roll a 12)[/URL] = 1/36
P(Roll a 6 or Roll a 12) = P(Roll a 6) + P(Roll a 12)
P(Roll a 6 or Roll a 12) = 5/36 + 1/36
P(Roll a 6 or Roll a 12) = 6/36
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F36&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we see that:
P(Roll a 6 or Roll a 12) = [B]1/6[/B]

Scott and Dylan both leave the park at the same time, but in opposite directions. If Scott travels 1

Scott and Dylan both leave the park at the same time, but in opposite directions. If Scott travels 12 mph and Dylan travels 19 mph, how long until they are 186 miles apart?
Hour 1, they are 19 + 12 = 31 miles apart. So each hour, they get 31 miles more apart.
When they are [URL='https://www.mathcelebrity.com/fraction.php?frac1=186%2F31&frac2=3%2F8&pl=Simplify']186 miles apart[/URL], we divide this by 31 miles apart per hour:
186/31 = [B]6 hours[/B]

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LC

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive?
Our ratio denominator is:
3 + 5 + 7 = 15
Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see that 5/15 = 1/3
So we take 360 rounds of ammunition times 1/3:
360/3 = [B]120[/B]

Solve 100 / 1/2

Solve 100 / 1/2
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&pl=Reciprocal']Reciprocal of 1/2[/URL] = 2
100 * 2 = [B]200[/B]

Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v

Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v
1/2(2/5) = 1/5 since the 2's cancel
r^2/r^2 = 1
So we simplify, and get:
mgh=1/2mv^2+1/5(mv^2) for v
Divide each side by m, so m's cancel in each term on the left and right side:
gh = 1/2v^2 + 1/5(v^2)
Combine like terms for v^2 on the right side:
1/2 + 1/5 = 7/10 from our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F5&pl=Add']fraction calculator[/URL]
So we have:
gh = 7v^2/10
Multiply each side by 10:
10gh = 7v^2
Now divide each side by 7
10gh/7 = v^2
Take the square root of each side:
[B]v = sqrt(10gh/7)[/B]

Square Roots and Exponents

Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.

Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.
Let the amount Steven started with be s. We're given:
s - 9 = 3s/5
Multiply each side through by 5 to eliminate the fraction:
5(s - 9) = 5(3s/5)
Cancel the 5's on the right side and we get:
5s - 45 = 3s
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=5s-45%3D3s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]22.5[/B]

Sum of a number and it's reciprocal is 6. What is the number?

Sum of a number and it's reciprocal is 6. What is the number?
Let the number be n.
The reciprocal is 1/n.
The word [I]is[/I] means an equation, so we set n + 1/n equal to 6
n + 1/n = 6
Multiply each side by n to remove the fraction:
n^2 + 1 = 6n
Subtract 6n from each side:
[B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression
If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].

The anti-inflammation drug Advil has a half-life of 2 hours. That is, the amount of the drug present

The anti-inflammation drug Advil has a half-life of 2 hours. That is, the amount of the drug present in the body is halved every two hours. What fraction of the initial amount of the drug will be left in the body after 4 hours?
[LIST]
[*]At time 0, we have 100%
[*]At time 2, we have 100% * 1/2 = 50% or 1/2
[*]At time 4, we have 1/2 * 1/2 = [B]1/4[/B]
[/LIST]

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction.
Let the original fraction be n/d.
We're given:
[LIST=1]
[*]d = n + 4
[*](n + 4) / (d + 7) = 1/2
[/LIST]
Cross multiply Equation 2:
2(n + 4) = d + 7
2n + 8 = d + 7
Now substitute equation (1) into tihs:
2n + 8 = (n + 4) + 7
2n + 8 = n + 11
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B8%3Dn%2B11&pl=Solve']Type this equation into our search engine[/URL], and we get:
n = 3
This means from equation (1), that:
d = 3 + 4
d = 7
So our original fraction n/d = [B]3/7[/B]

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number
Let the smaller number be s. Let the larger number be l. We're given two equations:
[LIST=1]
[*]l - s = 25
[*]s = l/6
[/LIST]
Plug in equation (2) into equation (1):
l - l/6 = 25
Multiply each side of the equation by 6 to remove the fraction:
6l - l = 150
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l-l%3D150&pl=Solve']type this equation into our search engine[/URL] and we get:
l = 30
To solve for s, we plug in l = 30 into equation (2) above:
s = 30/6
[B]s = 5[/B]

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the f

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction?
We're given two equations with a fraction with numerator (n) and denominator (d):
[LIST=1]
[*]n + d = 40
[*]n/d = 3/5
[/LIST]
Cross multiply equation 2, we get:
5n = 3d
Divide each side by 5:
5n/5 = 3d/5
n = 3d/5
Substitute this into equation 1:
3d/5 + d = 40
Multiply through both sides of the equation by 5:
5(3d/5) = 5d = 40 * 5
3d + 5d =200
To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%2B5d%3D200&pl=Solve']type it in our search engine and we get[/URL]:
d = [B]25
[/B]
Now substitute that back into equation 1:
n + 25 = 40
Using [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B25%3D40&pl=Solve']our equation solver again[/URL], we get:
n = [B]15[/B]

The girl’s hockey team won 6 games, lost 3 games, and tied 2 games. What fraction of games did they

The girl’s hockey team won 6 games, lost 3 games, and tied 2 games. What fraction of games did they win?
Win Fraction = Won Games / Total Games Played
Win Fraction = 6 / (6 + 3 + 2)
Win Fraction = [B]6/11[/B]

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to rent?
Rent Payment Fraction = Rent Payment / Total Income
Rent Payment Fraction = 1600 / 3840
Our greatest common factor of 1600 and 3840 is 320.
So if we divide 1600 and 3840 by 320, we get:
Rent Payment Fraction = [B]5/12
[MEDIA=youtube]DsXk6AKT18M[/MEDIA][/B]

The quotient of 2 and the sum of a number and 1

The quotient of 2 and the sum of a number and 1.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of a number and 1 is written as:
x + 1
The word [I]quotient[/I] means a fraction. So we divide 2 by x + 1
2
--------
( x + 1)

The quotient of 49 and n squared

n squared is written as n to the power of 2, n^2
We have a fraction, where 49 is the numerator, and n^2 is the denominator
49
-----
n^2

the quotient of 77 and x

the quotient of 77 and x
Quotient means we have a fraction where 77 is the numerator and x is the denominator:
[B]77/x[/B]

the quotient of 8 and the difference of x and m

The difference of x and m means we subtract:
x - m
Quotient means a fraction. 8 is the numerator, and x - m is the denominator:
[B] 8
------
x - m[/B]

The quotient of 9-x and twice x

The quotient of 9-x and twice x
Twice x means we multiply x by 2:
2x
The quotient of 9 - x and twice x is formed by the fraction:
[B](9 - x)/2x[/B]

the quotient of a variable and 7

the quotient of a variable and 7.
A variable means an arbitrary number, let's call it x.
A quotient means a fraction, where x is the numerator and 7 is the denominator:
[B] x
---
7[/B]

the quotient of m and the sum of n and p.

the quotient of m and the sum of n and p.
The sum of n and p means we add p to n:
n + p
The quotient means a fraction, so we divide m by (n + p)
[B]m/(n + p)[/B]

the quotient of the cube of a number x and 5

the quotient of the cube of a number x and 5
[LIST]
[*]A number means an arbitrary variable, let's call it x
[*]The cube of a number means raise it to the 3rd power, so we have x^3
[*]Quotient means we have a fraction, so our numerator is x^3, and our denominator is 5
[/LIST]
[B]x^3
----
5[/B]

the ratio of 50 and a number added to the quotient of a number and 10

the ratio of 50 and a number added to the quotient of a number and 10
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of 50 and x means we divide by 50 by x
50/x
The quotient of a number and 10 means we have a fraction:
x/10
The phrase [I]added to[/I] means we add 50/x to x/10
[B]50/x + x/10[/B]

the ratio of a number x and 4 added to 2

the ratio of a number x and 4 added to 2
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of this number and 4 means we have a fraction:
x/4
The phrase [I]added to[/I] means we add 2 to x/4
[B]x/4 + 2[/B]

The ratio of the number of carabaos, goats, and cows in a farm is 5:1:2. If there are 48 animals of

The ratio of the number of carabaos, goats, and cows in a farm is 5:1:2. If there are 48 animals of these kinds in his backyard how many of them are goats
Calculate total ratio:
5 + 1 + 2 = 8
Multiply fractional portion of goats by total animals in the backyard.
1/8 * 48 = [B]6 goats[/B]

There are 1 carrot, 3 onions, and 2 potatoes in a sink. What fraction of the vegetables are onions

There are 1 carrot, 3 onions, and 2 potatoes in a sink. What fraction of the vegetables are onions?
We have 1 + 3 + 2 = 6 total vegetables.
Which means we have 3/6 onions. But, we can reduce this fraction.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Simplifying 3/6 using our fraction simplifier[/URL], we get 1/2.

There are 11 kids at a birthday party. If there are 6 girls and 5 boys at the party, what fraction o

There are 11 kids at a birthday party. If there are 6 girls and 5 boys at the party, what fraction of the kids are boys?
Boys fraction = [B]5/11[/B]

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping?
3/8 of the day means we take 3/8 of 24 also written as:
3/8 * 24
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F8&frac2=24&pl=Multiply']type this expression into our search engine [/URL]and get:
[B]9 hours[/B]

There are 5 2/3 cups of milk. How many thirds are there?

Convert the mixed fraction [URL='http://www.mathcelebrity.com/fraction.php?frac1=5%262%2F3&frac2=3%2F8&pl=Simplify']using the calculator[/URL] to get 17/3.

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the p

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the probability of randomly selecting a black book and then a tan book without replacement. Write your answer as a percent.
P(black book first draw)
P(black book first draw) = 12 black / (5 orange + 12 black + 8 tan)
P(black book first draw) = 12 / 25
P(tan book second draw)
P(tan book second draw) = 8 tan / (5 orange + 11 black + 8 tan) <-- 11 black because we already drew one black
P(tan book second draw) = 8 / 24
Using our fraction reduction calculator, this simplifies to 1/3
Since each draw is independent, we multiply both probabilities:
P(black book first draw, tan book second draw) = 12/25 * 1/3
P(black book first draw, tan book second draw) = 12/75
P(black book first draw, tan book second draw) = [B]16%[/B]

There are 50 pairs of pants. One-half of the pants are black. One-fifth of the pants are tan. How ma

There are 50 pairs of pants. One-half of the pants are black. One-fifth of the pants are tan. How many pairs of pants are not black or tan.
First, determine what fraction of pants are black and tan:
1/2 + 1/5
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F5&pl=Add']fraction addition calculator[/URL], we get 7/10.
So the rest of the pants are 1 - 7/10.
1 can be written as 10/10.
So we have 10/10 - 7/10 = 3/10
3/10 * 50 = 150/10 = [B]15[/B]

There is a bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the

There is a bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting exactly 1 green?
Calculate Total marbles
Total marbles = Blue + Red + Green
Total marbles = 3 + 4 + 5
Total marbles = 12
Probability of a green = 5/12
Probability of not green = 1 - 5/12 = 7/12
To get exactly one green in two draws, we either get a green, not green, or a not green, green
[U]First Draw Green, Second Draw Not Green[/U]
[LIST]
[*]1st draw: Probability of a green = 5/12
[*]2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble
[*]To get the probability of the event, since each draw is independent, we multiply both probabilities
[*]Probability of the event is (5/12) * (7/11) = 35/132
[/LIST]
[U]First Draw Not Green, Second Draw Not Green[/U]
[LIST]
[*]1st draw: Probability of not a green = 7/12
[*]2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble
[*]To get the probability of the event, since each draw is independent, we multiply both probabilities
[*]Probability of the event is (7/12) * (5/11) = 35/132
[/LIST]
To get the probability of exactly one green, we add both of the events:
First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green
35/132 + 35/132 = 70/132
[URL='https://www.mathcelebrity.com/fraction.php?frac1=70%2F132&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL], we get:
[B]35/66[/B]

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the b

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?
Find the total number of marbles in the bag:
Total marbles = 5 blue + 6 red + 2 green
Total marbles = 13
The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows:
Blue, Not Blue
Not Blue, Blue
The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time.
The probability of not drawing a blue is (6 + 2)/13 = 8/13
And since each of the 2 draws are independent of each other, we multiply the probability of each draw:
Blue, Not Blue = 5/13 * 8/13 =40/169
Not Blue, Blue = 8/13 * 5/13 = 40/169
We add both probabilities since they both count under our scenario:
40/169 + 40/169 = 80/169
Checking our [URL='https://www.mathcelebrity.com/fraction.php?frac1=80%2F169&frac2=3%2F8&pl=Simplify']fraction simplification calculator[/URL], we see you cannot simplify this fraction anymore.
So our probability stated in terms of a fraction is 80/169
[URL='https://www.mathcelebrity.com/perc.php?num=80&den=169&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Stated in terms of a decimal[/URL], it's 0.4734

There were 500 balloons in 2 buckets. Rahul bursted 350 balloons of 1st bucket and Raghav bursted 4

There were 500 balloons in 2 buckets. Rahul bursted 350 balloons of 1st bucket and Raghav bursted 4 by 5 of the balloons of 2nd bucket. Who bursted more balloons and how many did Raghav burst?
If Rahul bursted 350 balloons, then we have:
Remaining Balloons = 500 - 350
Remaining Balloons = 150
Raghav bursted [URL='https://www.mathcelebrity.com/fraction.php?frac1=150&frac2=4/5&pl=Multiply']4/5 * 150[/URL] = [B]120[/B]
Since 350 for Rahul > 120 for Raghav, [B]Rahul bursted more balloons[/B]

Three out of every 7 houses in a neighborhood are painted white. There are 224 houses in the neighbo

Three out of every 7 houses in a neighborhood are painted white. There are 224 houses in the neighborhood. How many houses are white?
[URL='https://www.mathcelebrity.com/fraction.php?frac1=224&frac2=3/7&pl=Multiply']3/7 of 224[/URL] = [B]96 houses are white[/B]

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one yea

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be?
Let my current age be a. We're given:
4/5a > 3/4(a + 1)
Multiply through on the right side:
4a/5 > 3a/4 + 3/4
Let's remove fractions by multiply through by 5:
5(4a/5) > 5(3a/4) + 5(3/4)
4a > 15a/4 + 15/4
Now let's remove the other fractions by multiply through by 4:
4(4a) > 4(15a/4) + 4(15/4)
16a > 15a + 15
[URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get:
a > 15
This means the smallest [I]integer age[/I] which the problem asks for is:
15 + 1 = [B]16[/B]

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

Unit Fraction

Determines the unit fraction for a fraction.

What fraction lies exactly halfway between 2/3 and 3/4?

What fraction lies exactly halfway between 2/3 and 3/4?
A) 3/5
B) 5/6
C) 7/12
D) 9/16
E) 17/24
Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions:
1/2(2/3 + 3/4)
1/2(2/3) + 1/2(3/4)
1/3 + 3/8
We need common denominators, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=3%2F8&pl=Add']we type this fraction sum into our search engine[/URL] and get:
[B]17/24 - Answer E[/B]

What is a Fraction

This lesson walks you through what a fraction is and the different parts of a fraction.

What is the probability of drawing an ace from a deck of 52 cards?

What is the probability of drawing an ace from a deck of 52 cards?
With 4 Aces in the deck, the probability we draw an Ace is:
4/52
Simplifying this fraction, we get [B]1/13[/B]

What is the probability of picking a P from the word hippopotamus?

What is the probability of picking a P from the word hippopotamus?
There are 3 P's in a word with 12 characters.
So our probability is 3/12.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL], this simplifies to 1/4.
Written as a decimal, it's 0.25.
So our answer is [B]1/4 or 0.25[/B]

What is the slope of the line through (1,9) and (5,3)

What is the slope of the line through (1,9) and (5,3)
[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=9&slope=+2%2F5&xtwo=5&ytwo=3&pl=You+entered+2+points']We run this through our slope calculator[/URL], and get an initial slope of 6/4.
But this is not in simplest form. So we type 6/4 into our calculator, and s[URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F4&frac2=3%2F8&pl=Simplify']elect the simplify option[/URL].
We get [B]3/2[/B]

When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push mower, it t

When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push mower, it takes him 6 hours to mow the lawn. (His sister also can mow the lawn with the push mower in 6 hours.). Mike wanted to get the lawn mowed as quickly as possible, so he paid his sister $10 to mow with the push mower while he used the riding mower. How long will it take Mike an his sister to mow the lawn if they worked together?
Mike can mow 1/3 of the lawn in an hour.
Mike's sister can mow 1/6 the lawn in an hour.
together, they can mow [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=1%2F6&pl=Add']1/3 + 1/6 [/URL]= 1/2 of the lawn in one hour.
Which means it would take [B]2 hours [/B](2 * 1/2) = 1 to mow the full lawn.

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it tak

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidentally left open. How long until the pool is completely filled?
Set up unit fill rates per hour:
[LIST]
[*]1/4 of the pool is filled each hour
[*]1/5 of the pool is drained away each hour
[/LIST]
The amount left over after an hour of filling minus draining is:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Subtract']1/4 - 1/5[/URL] = 1/20
Therefore, it take [B]20 hours to fill the pool[/B]

Which is greater, 3/4 or 2/7

Use our [URL='http://www.mathcelebrity.com/fraction.php?frac1=3/4&frac2=2/7&pl=Compare']fraction comparison calculator[/URL]:
[B]3/4 is greater[/B]

write 8 as a whole fraction

write 8 as a whole fraction
Whole numbers can be written as whole number / 1
[B]8/1[/B]

Write a fraction with a denominator of 9. The fraction should be less than 1/2

Write a fraction with a denominator of 9. The fraction should be less than 1/2
Let n be the numerator. We have:
n/9 < 1/2
multiply each side by 9:
9n/9 < 9/2
n < 9/2
Examples are 8/2, 7/2, 6/2, 5/2, 4/2, 3/2,

x/y + 9 = n for x

x/y + 9 = n for x
Subtract 9 from each side to isolate the x term:
x/y + 9 - 9 = n - 9
Cancel the 9's on the left side and we get:
x/y = n - 9
Because we have a fraction on the left side, we can cross multiply the denominator y by n - 9
[B]x =[/B] [B]y(n - 9)[/B]

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate

You have 30 DONUTS. 1/6 of them are Boston Cream. 2/5 of them are Maple. 3/10 of them are Chocolate Dip and 1/3 are Sprinkled. IS THIS EVEN POSSIBLE?? How many donuts OVER or UNDER am I? (Show your work and use EQUIVALENTS.)
We use 30 as our common denominator. Let's get [I]equivalent fraction[/I]s for each donut type with a denominator of 30:
[LIST]
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F6&pl=Equivalent+Fractions']1/6[/URL] = 5/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=2%2F5&pl=Equivalent+Fractions']2/5 [/URL]= 12/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=3%2F10&pl=Equivalent+Fractions']3/10[/URL] = 9/30
[*][URL='https://www.mathcelebrity.com/equivalent-fractions.php?num=1%2F3&pl=Equivalent+Fractions']1/3[/URL] = 10/30
[/LIST]
Add up our numerators of the common denominator of 30:
5 + 12 + 9 + 10 = 36
So our fraction is 36/30. This makes our scenario [B]impossible[/B]. Fractions of the donut should add up to 1. Which would mean our numerators need to sum to 1 or less. Since 36 > 30, this scenario is [B]impossible.[/B]

You have 36 marbles that are red, white and blue. If 12 of the marbles are red, and 13 of the marble

You have 36 marbles that are red, white and blue. If 12 of the marbles are red, and 13 of the marbles are blue, what fraction of marbles are white?
[U]Calculate the number of white marbles:[/U]
Number of white marbles = Total marbles - Red marbles - Blue marbles
Number of white marbles = 36 - 12 - 13
Number of white marbles = 11
[U]Calculate the fraction of white marbles:[/U]
Fraction of white marbles =Number of white marbles / Total marbles
Fraction of white marbles = [B]11/36[/B]

You like to shovel snow in winter. You made them pay 7 dollars for every driveway you shoveled and e

You like to shovel snow in winter. You made them pay 7 dollars for every driveway you shoveled and earned 42 dollars. How many driveways did you shovel?
Driveways shoveled = Total Money / Dollars per Driveway
Driveways shoveled = 42/7
[URL='https://www.mathcelebrity.com/fraction.php?frac1=42%2F7&frac2=3%2F8&pl=Simplify']Driveways shoveled[/URL] = [B]6[/B]