104 LearnersLast updated on July 5th, 2025
Remainder
The leftover value after division is referred to as the remainder. When the given number doesn’t get divided evenly, the leftover value will be taken as the remainder. The remainder is what’s left over when objects are divided into equal groups. A remainder will always be less than the divisor. For example, 17 cookies are being shared equally among 5 children. Here, we divide 17 by 5 to find out how much each gets and how many are remaining. So, each child gets 3 cookies, and 2 cookies remain.
What is Remainder?
The leftover value after division is referred to as the remainder. When the given number doesn’t get divided evenly, the leftover value will be taken as the remainder. The remainder is what’s left over when objects are divided into equal groups. A remainder will always be less than the divisor.
For example, 17 cookies are being shared equally among 5 children. Here, we divide 17 by 5 to find out how much each gets and how many are remaining. So, each child gets 3 cookies, and 2 cookies remain.
What are the Properties of Remainder?
- The remainder is always less than its divisor.
- If a dividend is a multiple of its divisor, the remainder is zero
- The remainder should be compared to the divisor, not the quotient.
- The remainder is ‘0’ if the dividend is divisible by the dividend.
How to Represent the Remainder
In math, we can represent the remainder of a division in two ways:
- To represent the quotient and remainder we use the letters ‘Q’ and ‘R’ respectively. For example, dividing 11 by 4, it can be written as: 11 ÷ 4. Here, Q = 2 and R = 3.
- By writing it as a mixed fraction:
11 ÷ 4 = 11/4 = 2 3/4.
Here the quotient is 2, remainder is 3 and the divisor is 4.
How to Find Remainders Using Long Division
Long division is the best method to find the remainder, especially when dealing with large numbers. It breaks the problem into smaller, easy-to-follow steps.
Example: Divide 47 by 5 using long division
- 5 goes into 47 9 times since 5 × 9 = 45
- Subtract 45 from 47 → 47 - 45 = 2
- So, here the quotient is 9,and the remainder is 2.
- Therefore, 47 ÷ 5 = 9 R2 or 9 remainder 2.
Common mistakes and How to Avoid Them in Remainder
Understanding the concept of remainders helps students solve division problems that do not result in whole numbers. However, errors can happen while they are dealing with remainders. Here are some common mistakes and useful ways to avoid them:
Mistake 1
Students might stop at the quotient but fail to account for the remainder.
Remind that division is not always accurate. For example, distributing 7 cookies between two people: each receives three cookies, and one is left over. Practice writing responses in the format quotient remainder - r.
Mistake 2
Students sometimes convert the answer into a decimal, even when the question specifically asks for the remainder to be shown.
Make sure students read the directions carefully. Teach the two forms (remainder and decimal) and when they are suitable
Mistake 3
Students may subtract incorrectly or divide unevenly, leading to wrong remainders.
Students first estimate the quotient and then multiply it by the divisor to find what remains. They use visual aids like number lines or repeated subtraction to better understand the remainder
Mistake 4
Sometimes, students mix up which number is the quotient and which is the remainder.
Quotient is the final result obtained when a number is divided by another. For example, if 20 is divided by 5, we get the final result quotient as 4 and the remainder is ‘0’. Students should check their answers by multiplying the quotient by the divisor and then adding the remainder to see if it equals the dividend.
Mistake 5
Students might get confused with remainders in word problems. They won’t know whether to round the decimal number or keep it as a fraction.
Practice different types of word problems. Discuss how the context affects the interpretation: For example, If dividing people into teams, you might round up, and If dividing candy equally, you might express the remainder as a fraction.
Real life applications of Remainders
Remainders help us understand and deal with situations where division doesn’t result in a whole number. They frequently emerge in real-world situations where items cannot be distributed evenly. Here are some practical applications of remainders:
Sharing things: When dividing a set number of objects (such as cookies, pencils, or books) among a group, the remainder indicates how many items remain after everyone has received an equal part.
Budgeting and Resource Allocation: When a budget or resources are divided equally among departments or people, the remainder shows what’s left over. This leftover amount may be allocated or handled separately.
Time Calculations: When time is divided into intervals, such as hours into minutes or days into weeks, the remainder can be used to calculate how much time remains after counting full units.
Solved examples of Remainder
Problem 1
What is the remainder when 5 × 6 × 7 is divided by 4?
2
Explanation
First, calculate the product: 5 × 6 × 7 = 210. Now divide by 4: 210 ÷ 4 = 52 remainder 2.
Problem 2
What is the remainder when 4327 is divided by 23? Check if the answer you got is correct.
3
Explanation
Divide 4327 by 23: 23 goes into 43 1 time → 1 × 23 = 23
43 – 23 = 20
Bring down the next digit → 2 → Now we have 202. 23 goes into 202 8 times → 8 × 23 = 184
202–184 = 18
Bring down the next digit → 7 → Now we have 187. 23 goes into 187 8 times → 8 × 23 = 184
187–184 = 3.
Therefore, the quotient is 188, and the remainder is 3.
Problem 3
The number of days in the year 2000 was 366, as it was a leap year. If 1st Jan 2000 was a Saturday, what day was it on 1st Jan 2001?
1st January 2001 was a Monday.
Explanation
We want to find the remainder: 366 ÷ 7 = 52 weeks + remainder 2.
Then, add the remainder to the given day. 1st Jan 2000 was a Saturday.
Now, add 2 days to Saturday:
Saturday + 1 day = Sunday
Sunday + 1 day = Monday
It is given that 1st Jan 2000 was a Saturday.
We know that every day of the week repeats exactly after 7 days.
Since 2000 is a leap year, it has 366 days.
Problem 4
Find the remainder when the sum 25 + 37 + 46 is divided by 8.
4
Explanation
25 + 37 + 46 = 108
Divide the answer by 8: 108 ÷ 8 = 13 remainder 4.
Problem 5
What is the remainder when 3^4 is divided by 5?
1
Explanation
Here, 34 = 81.
Therefore, 81 ÷ 5 = 16 remainder 1
FAQs on Remainder
1.What is a remainder?
2.Give an example of a remainder.
3.Can the remainder be zero?
4.What does it indicate when the remainder equals zero?
5.How do you calculate the remainder using a formula?
6.How can children in Indonesia use numbers in everyday life to understand Remainder?
7.What are some fun ways kids in Indonesia can practice Remainder with numbers?
8.What role do numbers and Remainder play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Remainder skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
