Times tables and division with remainders
Use known facts to find the closest product and understand leftovers.
Quick answer
You can use your times tables to help you work out division with remainders by finding the closest multiple of the divisor and seeing what’s left over.Learning outcome
By the end of this page, you will understand how to use your times tables to work out division problems that have remainders, and you will be able to find the leftover amount when dividing. Success signs:- You can find the biggest multiple of a number that fits into a bigger number
- You can explain what a remainder is in a division problem
- You can use your times tables to solve a division problem with a remainder
- You can check your answer by multiplying and adding the remainder
Why this matters
Division with remainders is useful in many real-life situations. For example, if you have 23 cookies and want to share them equally among 5 friends, you need to know how many cookies each friend gets and how many are left over. This is division with a remainder. It helps you understand how to split things fairly and how much is left over. Knowing your times tables helps you do this quickly and correctly.How it works
To solve a division problem with remainders, follow these steps:- Think of the division problem as "How many groups of the divisor can fit into the dividend?"
- Use your times tables to find the largest multiple of the divisor that is less than or equal to the dividend
- Count how many times the divisor fits into the dividend
- Subtract the multiple from the dividend to find the remainder
- Write your answer as "quotient remainder"
Examples you can see
Let’s try a few examples to see how this works. Example 1: 23 ÷ 5- What is the largest multiple of 5 that is less than or equal to 23?
- 5 × 4 = 20
- 5 × 5 = 25 (too big)
- So 4 groups of 5 fit into 23
- 23 – 20 = 3
- Answer: 4 remainder 3
- What is the largest multiple of 6 that is less than or equal to 37?
- 6 × 6 = 36
- 6 × 7 = 42 (too big)
- So 6 groups of 6 fit into 37
- 37 – 36 = 1
- Answer: 6 remainder 1
- What is the largest multiple of 3 that is less than or equal to 19?
- 3 × 6 = 18
- 3 × 7 = 21 (too big)
- So 6 groups of 3 fit into 19
- 19 – 18 = 1
- Answer: 6 remainder 1
Try it as a mini adventure
Adventure: The Great Cookie Sharing You are the cookie chef for a school party. You have 47 cookies and 8 children to share them with. How many cookies does each child get, and how many are left over?- Start with your division problem: 47 ÷ 8
- Find the largest multiple of 8 that is less than or equal to 47
- 8 × 5 = 40
- 8 × 6 = 48 (too big)
- So 5 groups of 8 fit into 47
- 47 – 40 = 7
- Each child gets 5 cookies, and 7 cookies are left over
- 5 groups of 8 = 40 cookies
- 40 + 7 = 47 cookies
- You did it right!
Common mistakes
- Mistake: Thinking 37 ÷ 6 = 5 remainder 7
- Why it happens: The remainder is too big – it should be less than the divisor
- Fix: 6 × 6 = 36, so 37 – 36 = 1. The answer is 6 remainder 1
- Mistake: Forgetting to check the answer
- Why it happens: Not double-checking the work
- Fix: Multiply the quotient by the divisor and add the remainder. If you get the original number, your answer is correct
- Mistake: Not using the times tables to find the largest multiple
- Why it happens: Trying to guess instead of using known facts
- Fix: Use your times tables to find the closest multiple that fits
Parent and carer guide
Parents and carers can help by:- Practising times tables together using flashcards or games
- Using everyday situations to create division problems (e.g., sharing snacks, arranging chairs)
- Encouraging children to check their answers by multiplying and adding the remainder
- Using visual aids like counters or drawings to show how groups work
- Noticing when children are guessing instead of using their times tables
- “If you have 32 marbles and want to put them into 7 bags, how many marbles go in each bag?”
- “What’s the biggest multiple of 7 that fits into 32?”
- “How many marbles are left over?”
Practice questions
- 17 ÷ 3 = ? remainder ?
- 25 ÷ 4 = ? remainder ?
- 31 ÷ 5 = ? remainder ?
- 43 ÷ 6 = ? remainder ?
- 52 ÷ 7 = ? remainder ?
- 63 ÷ 8 = ? remainder ?
- 71 ÷ 9 = ? remainder ?
- 82 ÷ 10 = ? remainder ?
- 93 ÷ 11 = ? remainder ?
- 105 ÷ 12 = ? remainder ?
- 5 remainder 2
- 6 remainder 1
- 6 remainder 1
- 7 remainder 1
- 7 remainder 3
- 7 remainder 7
- 7 remainder 8
- 8 remainder 2
- 8 remainder 5
- 8 remainder 9
FAQ
What does "remainder" mean in division?
A remainder is the amount left over after dividing one number by another. For example, in 17 ÷ 3, the remainder is 2 because 3 goes into 17 five times, but 5 × 3 = 15, and 17 – 15 = 2.
How can I check if my division with remainder is correct?
You can check your answer by multiplying the quotient by the divisor and then adding the remainder. If you get the original number, your answer is correct. For example, if 23 ÷ 5 = 4 remainder 3, check: 4 × 5 = 20, and 20 + 3 = 23.
Why is it helpful to use times tables for division with remainders?
Times tables help you quickly find the largest multiple of the divisor that fits into the dividend. This makes it easier and faster to work out how many full groups there are and how much is left over.
What if the remainder is bigger than the divisor?
If your remainder is bigger than the divisor, it means you haven’t found the correct number of full groups. You need to go back and find the largest multiple that fits, then subtract to get the correct remainder.
Can I use division with remainders in real life?
Yes! Division with remainders is used in many real-life situations like sharing food, dividing up time, splitting up groups, and even in games and sports where you need to know how many full rounds or teams you can make and how many are left over.