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Age 9 guide to division with remainders

Age-appropriate activities, explanations and practice ideas for division with remainders.

Quick answer

Division with remainders means sharing items equally, but there are some left over. For example, if you have 13 cookies and want to share them equally among 4 friends, each friend gets 3 cookies, and there is 1 cookie left over. This leftover cookie is the remainder.

Learning outcome

By the end of this page, you will be able to:
  • Share items equally using division
  • Identify and write remainders correctly
  • Understand what a remainder means in real life
  • Solve division problems with remainders using objects or drawings

Why this matters

Division with remainders helps you solve problems where items can’t be shared perfectly. You’ll use this in everyday life, like sharing snacks with friends, dividing up toys, or planning how many tables you need for a party. Understanding remainders helps you make smart decisions and solve real problems.

How it works

Division with remainders uses the same idea as normal division, but there’s a leftover part. Here’s how to think about it:
  1. Start with a number of items (the dividend)
  2. Decide how many groups you want (the divisor)
  3. Share the items equally between the groups
  4. Count how many items each group gets (the quotient)
  5. Count how many items are left over (the remainder)
Let’s look at an example: If you have 17 pencils and want to share them among 5 friends:
  • 17 ÷ 5 = 3 remainder 2
  • Each friend gets 3 pencils
  • There are 2 pencils left over

Examples you can see

Let’s try some examples you can imagine or draw. Example 1: Sharing Pizza You have 12 slices of pizza and 5 friends. How many slices does each friend get, and how many are left over?
  • 12 ÷ 5 = 2 remainder 2
  • Each friend gets 2 slices
  • There are 2 slices left over
Example 2: Grouping Books You have 23 books and want to put them into boxes of 6. How many boxes will you need, and how many books will be left over?
  • 23 ÷ 6 = 3 remainder 5
  • You can fill 3 boxes
  • 5 books are left over
Example 3: Building Blocks You have 30 blocks and want to make towers with 7 blocks each. How many towers can you make, and how many blocks are left?
  • 30 ÷ 7 = 4 remainder 2
  • You can make 4 towers
  • 2 blocks are left over

Try it as a mini adventure

The Treasure Hunt Challenge You are going on a treasure hunt with your friends. You have 25 gold coins and 6 treasure chests. You must put the same number of coins in each chest, but you can’t split coins. How many coins go in each chest, and how many are left over? Step-by-step:
  • Start with 25 coins
  • Put coins into 6 chests
  • Each chest gets 4 coins
  • 4 × 6 = 24 coins
  • There is 1 coin left over
So, 25 ÷ 6 = 4 remainder 1 Mini Challenge: Try this with 32 coins and 7 chests. How many coins go in each chest, and how many are left over?

Common mistakes

  • Mistake: Forgetting to write the remainder
    Why it happens: Children might think that division always gives a whole number.
    Fix: Always check if there are items left over. Write the remainder after the quotient using the word "remainder" or the symbol "r".
  • Mistake: Confusing the divisor and quotient
    Why it happens: Children might mix up which number is shared and which is the result.
    Fix: Remember: the number you start with is the dividend, the number you divide by is the divisor, and the answer is the quotient.
  • Mistake: Thinking remainders are always small
    Why it happens: Children might expect the remainder to be less than 2.
    Fix: The remainder is always less than the divisor, but it can be any number from 0 up to one less than the divisor.

Parent and carer guide

You can help your child understand division with remainders by:
  • Using real objects like counters, blocks, or snacks to show sharing
  • Practising with everyday situations like sharing cookies or dividing toys
  • Encouraging your child to draw pictures of the sharing problem
  • Reinforcing that remainders are normal and useful
  • Using games and puzzles to make learning fun
What to say:
  • "Let’s count how many items are left over"
  • "What happens when we can’t share everything equally?"
  • "Can you show me how you worked that out?"
What not to worry about:
  • Your child may make mistakes at first – that’s normal
  • They don’t need to know formal long division yet
  • Focus on understanding the idea, not speed

Practice questions

  1. 15 ÷ 4 = ? remainder ?
  2. 22 ÷ 3 = ? remainder ?
  3. 31 ÷ 5 = ? remainder ?
  4. 18 ÷ 7 = ? remainder ?
  5. 27 ÷ 6 = ? remainder ?
  6. 14 ÷ 3 = ? remainder ?
  7. 29 ÷ 4 = ? remainder ?
  8. 20 ÷ 6 = ? remainder ?
  9. 33 ÷ 8 = ? remainder ?
  10. 16 ÷ 5 = ? remainder ?
Answers:
  1. 15 ÷ 4 = 3 remainder 3
  2. 22 ÷ 3 = 7 remainder 1
  3. 31 ÷ 5 = 6 remainder 1
  4. 18 ÷ 7 = 2 remainder 4
  5. 27 ÷ 6 = 4 remainder 3
  6. 14 ÷ 3 = 4 remainder 2
  7. 29 ÷ 4 = 7 remainder 1
  8. 20 ÷ 6 = 3 remainder 2
  9. 33 ÷ 8 = 4 remainder 1
  10. 16 ÷ 5 = 3 remainder 1

FAQ

What is a remainder in division?

A remainder is the number left over when you share items equally and there aren’t enough to give everyone the same amount.

Can a remainder be bigger than the number you are dividing by?

No, the remainder is always smaller than the divisor. If it’s not, you can share more items.

How do I know if I have a remainder?

If you divide and there are items left over after sharing equally, that leftover amount is the remainder.

Why do we use remainders in real life?

Remainders help us understand how to fairly share things or know how many items are left over after grouping.

How can I practice division with remainders at home?

You can use counters, snacks, or toys to practice sharing and counting what’s left over.