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division

Checking division with multiplication

Use inverse operations and remainders to check division.

Quick answer

You can check if your division is correct by multiplying your answer (quotient) by the number you divided by (divisor), and adding any remainder. If this matches your original number (dividend), your division is correct.

Learning outcome

By the end of this page, you will be able to check your division answers using multiplication and remainders. Success signs:
  • You can multiply the quotient by the divisor and add the remainder
  • You can tell if a division is correct or not
  • You can use this method to fix mistakes in division
  • You can explain why checking division works

Why this matters

Checking your division with multiplication helps you be sure you did your maths correctly. This is useful in school, when you are sharing things, solving puzzles, or working out how many items you need. If you are baking a cake and need to divide 24 eggs among 6 bowls, you can check that you are putting 4 eggs in each bowl. If you get 24 eggs back when you multiply 4 by 6, you know your division is right!

How it works

Division and multiplication are connected. When you divide a number, you split it into equal groups. To check, you multiply the number of groups by the number in each group and add any leftover pieces (remainder). If this matches your original number, you did it right! Let’s break it down:
  1. Start with your division problem
  2. Multiply the answer (quotient) by the number you divided by (divisor)
  3. Add any remainder
  4. If your result matches the original number, your division is correct

Examples you can see

Let’s look at some examples to see how this works. Example 1: 15 ÷ 3 = 5
  • Check: 5 × 3 = 15
  • No remainder, so 15 = 15. Correct!
Example 2: 17 ÷ 4 = 4 remainder 1
  • Check: 4 × 4 = 16
  • Then: 16 + 1 = 17
  • So 17 = 17. Correct!
Example 3: 22 ÷ 5 = 4 remainder 2
  • Check: 4 × 5 = 20
  • Then: 20 + 2 = 22
  • So 22 = 22. Correct!
Example 4: 30 ÷ 6 = 5
  • Check: 5 × 6 = 30
  • No remainder, so 30 = 30. Correct!

Try it as a mini adventure

Adventure: The Great Cookie Sharing You and your friends are sharing 36 cookies for a party. You want to put them into 6 bags, so each bag has the same number of cookies. How many cookies go in each bag? Then, check your answer using multiplication.
  1. First, divide: 36 ÷ 6 = ?
  2. Then, multiply the answer by 6
  3. Add any remainder
  4. See if you get 36 back
If you get 6 cookies in each bag, check: 6 × 6 = 36. That’s right!

Common mistakes

  • Mistake: Forgetting to add the remainder when checking.
    • Why it happens: Kids might think the remainder is already included in the multiplication.
    • Fix: Always remember to add the remainder after multiplying.
  • Mistake: Multiplying the wrong numbers.
    • Why it happens: Mixing up the divisor and quotient.
    • Fix: Double-check which number is the quotient and which is the divisor.
  • Mistake: Thinking that if the check doesn’t match, the original division was wrong.
    • Why it happens: Not understanding that checking is a way to verify, not to find the answer.
    • Fix: If your check doesn’t match, go back to your division and try again.

Parent and carer guide

Parents and carers can help by:
  • Practising with real objects, like cookies or blocks
  • Repeating the steps together, saying them out loud
  • Encouraging children to explain their thinking
  • Letting children make mistakes and then fix them
  • Using everyday examples like sharing snacks or dividing toys
It’s okay if your child gets confused at first. The more they practice, the easier it becomes. Don’t worry if they get the check wrong the first few times – it’s part of learning!

Practice questions

  1. 35 ÷ 7 = 5. Check with multiplication.
  2. 43 ÷ 5 = 8 remainder 3. Check with multiplication.
  3. 64 ÷ 8 = 8. Check with multiplication.
  4. 71 ÷ 9 = 7 remainder 8. Check with multiplication.
  5. 28 ÷ 4 = 7. Check with multiplication.
Answers:
  1. 5 × 7 = 35. No remainder. 35 = 35. Correct!
  2. 8 × 5 = 40. 40 + 3 = 43. 43 = 43. Correct!
  3. 8 × 8 = 64. No remainder. 64 = 64. Correct!
  4. 7 × 9 = 63. 63 + 8 = 71. 71 = 71. Correct!
  5. 7 × 4 = 28. No remainder. 28 = 28. Correct!

FAQ

What is the relationship between division and multiplication?

Division and multiplication are inverse operations. When you divide a number, you split it into equal parts. When you multiply, you put equal parts together. You can use one to check the other.

Why do we add the remainder when checking division?

The remainder is what’s left over after you divide. To get back to your original number, you must include it in the multiplication check.

Can I use this method for any division problem?

Yes! This method works for all division problems, whether there is a remainder or not.

What if my check doesn’t match?

If your check doesn’t match, go back and recheck your division. The method is correct, so the error is likely in the original division.

Is checking division only for school?

No! Checking division helps in real life, like when you’re sharing food, dividing chores, or planning a party.