remainder - The portion of a division operation leftover after dividing two integers

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted 35m. This pattern continues to the end of the track. What percentage of the park did each child paint?
70 + 15 + 35 = 120
When we take[URL='https://www.mathcelebrity.com/modulus.php?num=5000mod120&pl=Calculate+Modulus'] 5000 divided by 120[/URL], we get:
41 remainder 80
So we have:
[LIST]
[*]Alex: 70 * 41 = 2870
[*]Dell: 15 * 41 = 615
[*]Tony: 35 * 41 = 1435
[/LIST]
Now Alex goes next, and paints the full 70. So he has:
2870 + 70 = 2940
Dell goes next, and paints the last 10
615 + 10 = 625
Now for percentages:
[LIST]
[*]Alex: 2940/5000 = [B]58.8%[/B]
[*]Dell: 625/5000 = [B]12.5%[/B]
[*]Tony: 1435/5000 = [B]28.7%[/B]
[/LIST]

9 friends brought 178 tickets How many more ticket would they have to buy for all of them could have

9 friends brought 178 tickets How many more ticket would they have to buy for all of them could have the same amount?
If we take [URL='https://www.mathcelebrity.com/modulus.php?num=178mod9&pl=Calculate+Modulus']178 mod 9[/URL] to find the remainder, we get 7.
If we buy the 7 more (remainder) tickets, we have:
9 friends - 7 remainder = 2 tickets
To prove our work, we add the 2 tickets + 178 tickets = 180 tickets
180 tickets / 9 friends = 20 tickets per friends
So our answer is [B]2 tickets[/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 farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all

A farmer is taking her eggs to the market in a cart, but she hits a
pothole, which knocks over all the containers of eggs. Though she is
unhurt, every egg is broken. So she goes to her insurance agent, who
asks her how many eggs she had. She says she doesn't know, but she
remembers somethings from various ways she tried packing the eggs.
When she put the eggs in groups of two, three, four, five, and six
there was one egg left over, but when she put them in groups of seven
they ended up in complete groups with no eggs left over.
What can the farmer figure from this information about the number of
eggs she had? Is there more than one answer?
We need a number (n) that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6 but no remainder when divided by 7.
217 + 84 = [B]301[/B].
Other solutions are multiples of 3 x 4 x 5 x 7, but we want the lowest one here.

A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the investm

A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the investments is $1456, how much does he have invested at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=15000&i1=12&i2=8&itot=1456&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*]Fund 1 Investment @ 12% = [B]6,400[/B]
[*]Fund 2 Investment @ 8% =[B] [B]8,600[/B][/B]
[/LIST]

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remai

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remainder. How much commission is received on the sale of a $450,000 property?
Calculate commission on first $100,000 (Commission 1):
Commission 1 = $100,000 * 0.035
Commission 1 = $3,500
Calculate commission on the remainder (Commission 2):
Commission 2 = 0.025 * ($450,000 - $100,000)
Commission 2 = 0.025 * ($350,000)
Commission 2 = $8,750
Calculate Total Commission:
Total Commission = Commission 1 + Commission 2
Total Commission = $3,500 + $8,750
Total Commission = [B]$12,250[/B]

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads a

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads as she can afford, how much money will the real estate agent have left over?
We want to know the remainder of 920/6. We can type 920 mod 6 into our search engine and get:
[URL='https://www.mathcelebrity.com/modulus.php?num=920mod6&pl=Calculate+Modulus']920 mod 6[/URL] = [B]2[/B]

A street sign is 85 inches tall. How tall is it in feet and inches?

A street sign is 85 inches tall. How tall is it in feet and inches?
Since 12 inches is a foot, we have:
12 goes into 85 7 times remainder 1
So we have [B]7 feet, 1 inch[/B]

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rat

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4000&i1=10&i2=15&itot=430&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]3,400[/B] @ 10%
[*][B]600[/B] @ 15%
[/LIST]

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearl

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearly interest amounted to $315, how much was invested at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4300&i1=6+&i2=9&itot=315&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1: 2,400[/B]
[*][B]Fund 2: 1,900[/B]
[/LIST]

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interes

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interest earned was $450. How much was invested at each rate?
Using our split fund interest calculator, we get:
[LIST]
[*][B]1500 in 6% fund[/B]
[*][B]4500 in 8% fund[/B]
[/LIST]

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate if the annual interest is $550?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=9&itot=550&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1: $4,000[/B]
[*][B]Fund 2: $3,000[/B]
[/LIST]

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate i

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate if the annual interest is 710
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=13&itot=710&pl=Calculate']split fund interest calculator[/URL], we get:
1,400
4,600

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumpin

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 18 minutes. The other bucket dumps water every 21 minutes. It is currently 1:15 P.M. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time.
We want to find the Least Common Multiple between 18 minutes and 21 minutes. This shows us when both bucket dumping cycles happen simultaneously. So we[URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=21&num3=&pl=GCF+and+LCM'] type in LCM(18,21) into our search engine and we get[/URL]:
LCM(18, 21) = 126
This means, in 126 minutes, both buckets will dump water. Since 60 minutes is in an hour, we find out how many full hours we have. To find the full hours and remainder, we [URL='https://www.mathcelebrity.com/modulus.php?num=126mod60&pl=Calculate+Modulus']type in 126 mod 60[/URL] into our search engine and we get:
6. This means 126 minutes is 2 hours and 6 minutes.
Find the next bucket dumping time:
[LIST=1]
[*]We start at 1:15 PM
[*]Add 2 hours and we get 3:15 PM
[*]Add 6 minutes and we get [B]3:21 PM[/B]
[/LIST]

An investor has $300,000 to invest, part at 12% and the remainder in a less risky investment at 7%.

An investor has $300,000 to invest, part at 12% and the remainder in a less risky investment at 7%. If the investment goal is to have an annual income of $27,000, how much should be put in each investment?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=300000&i1=12&i2=7&itot=27000&pl=Calculate']split-fund interest calculator[/URL], we get:
[LIST]
[*][B]$120,000 in the 12% Fund[/B]
[*][B]$180,000 in the 7% Fund[/B]
[/LIST]

Basic Math Operations

Free Basic Math Operations Calculator - Given 2 numbers, this performs the following arithmetic operations:

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

Chinese Remainder Theorem

Free Chinese Remainder Theorem Calculator - Given a set of modulo equations in the form:

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n_{i} portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n

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]

Eric is taking a trip of 245 miles. If he has traveled x miles, represent the remainder of the trip

Eric is taking a trip of 245 miles. If he has traveled x miles, represent the remainder of the trip in terms of x.
Remaining distance = [B]245 - x[/B]

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of 7.
From our [URL='http://www.mathcelebrity.com/divisibility.php?num=120&pl=Divisibility']divisibility calculator[/URL], we see a number is divisible by 9 if the sum of its digits is divisible by 9.
Starting from 1 to 99, we find all numbers with a digit sum of 9.
This would be digits with 0 and 9, 1 and 8, 2 and 7, 3 and 6, and 4 and 5.
9
18
27
36
45
54
63
72
81
90
Now remove even numbers since the problem asks for odd numbers
9
27
45
63
81
Now, divide each number by 10, and find the remainder
9/10 = 0
[URL='http://www.mathcelebrity.com/modulus.php?num=27mod10&pl=Calculate+Modulus']27/10[/URL] = 2 R 7
We stop here. [B]27[/B] is an odd number, less than 100, with a remainder of 7 when divided by 10.

If x is divided by 9, the remainder is 5. What is the remainder if 3x is divided by 9?

If x is divided by 9, the remainder is 5. What is the remainder if 3x is divided by 9?
pick an integer x where when dividing by 9, we get a remainder of 5.
14/9 gives us a remainder of 5.
Now multiply 14 by 3:
14 * 3 = 42
[URL='https://www.mathcelebrity.com/modulus.php?num=42mod9&pl=Calculate+Modulus']42/9 gives a remainder of[/URL] [B]6[/B]

Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies

Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies home. The most he wants to spend on the truck is $56.00. If Home Depot charges $17.00 for the first 75 minutes and $5.00 for each additional 15 min, for how long can Oscar keep the truck and remain within his budget?
Set up the cost equation C(m) where m is the number of minutes for rental:
C(m) = 17 * min(m, 75) + max(0, 5(m - 75))
If Oscar uses the first 75 minutes, he spends $17. So he's left with:
$56 - $17 = $38
$38 / $5 = 7 Remainder 3
We remove the remainder 3, since it's not a full 15 minute block. So Oscar can rent the truck for:
7 * 15 minute blocks = [B]105 minutes[/B]

Quotient-Remainder Theorem

Free Quotient-Remainder Theorem Calculator - Given 2 positive integers n and d, this displays the quotient remainder theorem.

Set C is the set of two-digit even numbers less than 56 that are divisible by 5

[U]Two digit Numbers less than 56:[/U]
{10, 11, 12, ..., 55}
[U]Two Digit Even Numbers of that Set:[/U]
{10, 12, 14, ..., 54}
[U]Two Digit Even numbers Divisible by 5[/U]
[B]C = {10, 20, 30, 40, 50}[/B]
[I]Note: Even means you can divide it by 2 with no remainder. Divisible by 5 means the number ends in 5 or 0. Since it is even numbers only, end in 0.[/I]

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x.
[U]Use the quotient remainder theorem[/U]
A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B
Plugging in our numbers for Equation 1 we have:
[LIST]
[*]A = x
[*]B = 7
[*]Q = q
[*]R = 6
[*]x = 7 * q + 6
[/LIST]
Plugging in our numbers for Equation 2 we have:
[LIST]
[*]A = x
[*]B = 11
[*]Q = q
[*]R = 2
[*]x = 11 * q + 2
[/LIST]
Set both x values equal to each other:
7q + 6 = 11q + 2
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=7q%2B6%3D11q%2B2&pl=Solve']equation calculator[/URL], we get:
q = 1
Plug q = 1 into the first quotient remainder theorem equation, and we get:
x = 7(1) + 6
x = 7 + 6
[B]x = 13[/B]
Plug q = 1 into the second quotient remainder theorem equation, and we get:
x = 11(1) + 2
x = 11 + 2
[B]x = 13[/B]

Synthetic Division

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem

the set of natural numbers less than 7 that are divisible by 3

the set of natural numbers less than 7 that are divisible by 3
Natural Numbers less than 7
{1, 2, 3, 4, 5, 6}
Only 2 of them are divisible by 3. Divisible means the number is divided evenly, with no remainder:
[B]{3, 6}[/B]

You and two friends share 7 cookies equally. How many cookies do you each get?

You and two friends share 7 cookies equally. How many cookies do you each get?
7/3 = 2 with a remainder of 1/3
So everybody gets 2 whole cookies, and they split the last cookie into 1/3.
[B]2 & 1/3[/B]