Sometimes when dividing there is something left over. It is called the remainder. Example: There are 7 bones to share with 2 pups.But 7 cannot be divided exactly into 2 groups, so each pup gets 3 bones, and there is 1 left over: We say: "7 divided by 2 equals 3 with a remainder of 1" And we write: 7 ÷ 2 = 3 R 1 As a FractionIt is also possible to cut the remaining bone in half, so each pup gets 3 ½ bones: 7 ÷ 2 = 3 R 1 = 3 ½ "7 divided by 2 equals 3 remainder 1 equals 3 and a half" Play with the IdeaTry changing the values here ... sometimes there will be a remainder: images/divide-marbles.js If we look at it "the other way around" we can check our answer: 2 × 3 + 1 = 7 "2 groups of 3, plus 1 extra, equals 7" Another Example
19 cannot be divided exactly by 5. The closest we can get (without going over) is: 3 x 5 = 15 which is 4 less than 19. So the answer of 19 ÷ 5 is: 19 ÷ 5 = 3 R 4 Check it by multiplying: 5 × 3 + 4 = 19 We can also make a fraction with:
so we also have: 19 ÷ 5 = 3 R 4 = 3 4/5 1635, 1636, 1637, 1638, 3431, 3432, 3433, 3434, 3435, 3436 Copyright © 2021 MathsIsFun.com
Here is a nifty way to find remainder on diving numbers:
To find the remainder of a number divided by 3, add the digits of the number and divide it by 3. So if the digits added together equal 8 then the number has a remainder of 2 since 8 divided by 3 has a remainder of 2. For example, find the remainder on dividing 1,342,568 by 3. The digit sum of 1342568 is 1+3+4+2+5+6+8 = 29. Again, the digit sum of 29 = 2+9 = 11 = 2 So, the remainder will be 2. Another example: Take 34,259,677,858. The digit sum of the number is 3+4+2+5+9+6+7+7+8+5+8 = 64. Now, the digit sum of 64 is 6+4 = 10 = 1. So, the remainder is 1. Similarly, the digit sum of 54,670,329,845 is 53 i.e. (5+3=) 8. When we divide 8 by 3, we get remainder 2. So the answer will be 2. Remainder on dividing by 4 To find the remainder of a number divided by 4, take the remainder of the last 2 digits. So if the last 2-digits are 13 then the number has a remainder of 1 since 13 divided by 4 has a remainder of 1. Remainder on dividing by 5 To find the remainder of a number divided by 5, simply use the last digit. If it is greater than 5, subtract 5 for the remainder. Remainder on dividing by 7 Split the digits of the number in group of 3 starting from unit’s place. Add the alternate group and then find their difference. Divide the difference by 7 and get the remainder. Consider the number 43456827.
Make triplets as written below starting from unit’s place43.........456..........827 Now alternate sum = 43+827=870 and 456 and difference of these sums =870-456=414. Divide it by 7 we get remainder as 1.
Triplets pairs are 4…523…895…099…854 Alternate sums are 4+895+854=1753 and 523+099=622 Difference =1131 Revise the same tripling process 1…131 So difference = 131-1=130 Divide it by 7 we get remainder as 4. Remainder on dividing by 8 To find the remainder of a number divided by 8, take the remainder of the last 3-digits. So if the last 3-digits are 013 then the number has a remainder of 5 since 13 divided by 8 has a remainder of 5. Remainder on dividing by 9 To find the remainder of a number divided by 9, add the digits and then divide it by 9. So if the digits added together equal 13 then the number has a remainder of 4 since 13 divided by 9 has a remainder of 4. Remainder on dividing by 10 To find the remainder of a number divided by 10 simply use the last digit. Remainder on dividing by 11 The difference of the sums of the alternate digits is the remainder after dividing by 11 if it is positive. If the number is negative add 11 to it to get the remainder. Take the number 34568286 for example. Sum of alternate digits are 6+2+6+4 = 18 and 8+8+5+3=24 And difference of these sums =18 - 24 = -6.
Remainder on dividing by 13 Split the digits of the number in group of 3 starting from unit’s place. Add the alternate group and then find their difference. Divide the difference by 13 and get the remainder. Consider the number 34568276.
Split the number as 34.........568..........276 Now alternate sum = 34+276=310 and 568 and difference of these sums =568-310=258 Divide it by 13 we get remainder as 11 Another example, consider the number 4523895099854 Triplets pairs are 4…523…895…099…854 Alternate sums are 4+895+854=1753 and 523+099=622 Difference =1131 Revise the same tripling process 1…131 So difference = 131-1=130 Divide it by 13 we get remainder as 0 Remainder on dividing by 27 and 37 Consider the number 34568276; we have to calculate the reminder on dividing the number by 27 and 37.
Make triplets as written below starting from unit’s place34.........568..........276 Now sum of all triplets = 34+568+276 = 878 Dividing it by 27 we get reminder as 14 Dividing it by 37 we get reminder as 27 Another example for the clarification of the rule; take the number 2387850765. Triplets are 2…387…850…765 sum of the triplets = 2+387+850+765=2004. On revising the steps we get 2…004 Sum =6 Dividing it by 27 we get remainder as 6. Dividing it by 37 we get remainder as 6. This quotient and remainder calculator helps you divide any number by an integer and calculate the result in the form of integers. In this article, we will explain to you how to use this tool and what are its limitations. We will also provide you with an example that will better illustrate its purpose.
When you perform division, you can typically write down this operation in the following way: a/n = q + r/nwhere:
When performing division with our calculator with remainders, it is important to remember that all of these values must be integers. Otherwise, the result will be correct in the terms of formulas, but will not make mathematical sense. Make sure to check our modulo calculator for a practical application of the calculator with remainders. 🔎 If the remainder is zero, then we say that a is divisible by n. To learn more about this concept, check out Omni's divisibility test calculator.
It's useful to remember some remainder shortcuts to save you time in the future. First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder. Lastly, you can multiply the decimal of the quotient by the divisor to get the remainder.
Learning how to calculate the remainder has many real-world uses and is something that school teaches you that you will definitely use in your everyday life. Let’s say you bought 18 doughnuts for your friend, but only 15 of them showed up, you’d have 3 left. Or how much money did you have left after buying the doughnuts? If the maximum number of monkeys in a barrel is 150, and there are 183 monkeys in an area, how many monkeys will be in the smaller group?
The quotient is the number of times a division is completed fully, while the remainder is the amount left that doesn’t entirely go into the divisor. For example, 127 divided by 3 is 42 R 1, so 42 is the quotient, and 1 is the remainder.
Once you have found the remainder of a division, instead of writing R followed by the remainder after the quotient, simply write a fraction where the remainder is divided by the divisor of the original equation. It's that easy!
There are 3 ways of writing a remainder: with an R, as a fraction, and as a decimal. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second, and 205.25 in the third.
The remainder is 2. To work this out, find the largest multiple of 6 that is less than 26. In this case, it’s 24. Then subtract the 24 from 26 to get the remainder, which is 2.
The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.
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