modulus - the remainder of a division, after one number is divided by another.

Formula: a mod b

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 baker makes 387 cupcakes. They are sold in packs of six. How many full packs can be made? How many

A baker makes 387 cupcakes. They are sold in packs of six. How many full packs can be made? How many cupcakes are leftover?
Full packs = Lowest Rounded Integer of (Total cupcakes / packs)
Full packs = Lowest Rounded Integer of 387/6
Full Packs = Lowest Rounded Integer of 64.5
Full Packs = [B]64[/B]
Leftover = [URL='https://www.mathcelebrity.com/modulus.php?num=387mod6&pl=Calculate+Modulus']387 mod 6[/URL]
Leftover = [B]3[/B]

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, an

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, and zinnias. if the gardener planted 47 plants, what kind of flower did he plant last?
Let c be carnations, d be daffodils, l be larkspurs, t be tiger lillies, and z be zinnias. The order goes as follows:
c, d, l, t, z.
So each cycle of plants counts as 5 plants. We know that 9 * 5 = 45. So the gardener plants 9 full cycles. Which means they have 47 - 45 = 2 plans left over.
In the order above, the second plant is the daffodil. So the gardener planted the [B]daffodil[/B] last.
Now, can we shortcut this problem? Yes, using modulus.
47 plants, with 5 plants per cycle, we do [URL='https://www.mathcelebrity.com/modulus.php?num=47mod5&pl=Calculate+Modulus']47 mod 5 through our calculator[/URL], and get 2. So we have 2 plants left over, and the daffodil is the second plant.

A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that

A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 120 popped kernels. There are 1,600 kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last partially filled box?
Using modulus calculator, we know [URL='https://www.mathcelebrity.com/modulus.php?num=1600mod120&pl=Calculate+Modulus']1600 mod 120[/URL] gives us [B]13 full boxes[/B] of unpopped popcorn.
We also know that 13*120 = 1,560. Which means we have 1,600 - 1,560 = [B]40[/B] popped kernels left in the last box.
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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 sewing class has 205 yards off a bric to make quilts. Each quilt requires 7 yards off a bric. How

A sewing class has 205 yards off a bric to make quilts. Each quilt requires 7 yards off a bric. How much will remain after all the quilts are made?
Calculate the number of full quilts:
205/7 = 29.2857 so 29 full quilts.
29 * 7 = 203
205 - 203 = [B]2 yards remaining[/B].
You can also use the [URL='http://www.mathcelebrity.com/modulus.php?num=205mod7&pl=Calculate+Modulus']modulus calculator[/URL]

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]

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

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.

Hero cards come in packs of 6. Max has 8 packs of hero cards. He decides to give as many of his frie

Hero cards come in packs of 6. Max has 8 packs of hero cards. He decides to give as many of his friends as he can 9 cards each. How many cards are left over after he does this?
Calculate the number of cards Max starts with:
8 packs * 6 cards per pack = 48 total cards
If he gives as many friends as he can 9 cards each, we want to know how many left over after giving as many friends as he can 9 cards. So we have:
[URL='https://www.mathcelebrity.com/modulus.php?num=48mod9&pl=Calculate+Modulus']48 mod 9[/URL] = [B]3 left over[/B]

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]

Modulus

Free Modulus Calculator - Given 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5

Sarah splits her 87 Pokémon cards into 9 piles. How many are left over?

Sarah splits her 87 Pokémon cards into 9 piles. How many are left over?
We want the reminder of 87/9, so we t[URL='https://www.mathcelebrity.com/modulus.php?num=87mod9&pl=Calculate+Modulus']ype 87 mod 9 into our search engine and we get[/URL]:
87 mod 9 =[B] 6[/B]

Youngs Modulus-Stress-Strain

Free Youngs Modulus-Stress-Strain Calculator - Calculates any of the 3 items in the Youngs Modulus equation with stress and strain.