Standard 3 / Standard 3 Maths

Division and Remainders – Standard 3 Maths

Aven Brisail2 Comments

What you will learn

  • Divide by sharing equally and by making equal groups.
  • Use times tables to find division facts.
  • Divide numbers up to 9 999 by a 1-digit number and explain the remainder.

Division means sharing equally or putting things into equal groups. Sometimes things share out exactly. Sometimes a few are left over, and that left over part is called the remainder. In this lesson you will divide big numbers one digit at a time and check your answers with multiplication.

A white maxi taxi with a coloured band waiting for passengers in Trinidad
A Chaguanas to Couva maxi taxi waiting for passengers. How many maxi taxis does a class trip need? Photo: Zagaboy, CC0, via Wikimedia Commons.

Sharing and grouping

The sign ÷ means divided by. 12 ÷ 3 can mean share 12 sweets between 3 children (each gets 4), or make groups of 3 from 12 sweets (you make 4 groups). Both give 4.

Division undoes multiplication. If you know 6 × 7 = 42, you also know 42 ÷ 6 = 7 and 42 ÷ 7 = 6. These are a fact family.

Remainders

Share 14 mangoes between 4 bags. Each bag gets 3 mangoes, which uses 12. There are 2 left over, not enough to go round again. We write 14 ÷ 4 = 3 remainder 2, or 3 r 2.

Worked example 1

18 ÷ 4

Show me how

Count in 4s: 4, 8, 12, 16. The next one, 20, is too many.

4 × 4 = 16, so the answer is 4.

18 − 16 = 2 are left. 18 ÷ 4 = 4 remainder 2.

Watch out! A common mistake

The remainder must always be less than the number you divide by. If you get 23 ÷ 5 = 3 r 8, the 8 is too big: another 5 can still be shared. The answer is 4 r 3.

Short division, one digit at a time

For bigger numbers, start on the left. Divide each digit, write the answer on top, and carry what is left over to the next digit. This is the same as long division: divide, multiply, take away, bring down.

Worked example 2

745 ÷ 3

Show me how

Hundreds: 7 ÷ 3 = 2, because 3 × 2 = 6. 7 − 6 = 1 left. Carry 1 to make 14.

Tens: 14 ÷ 3 = 4, because 3 × 4 = 12. 14 − 12 = 2 left. Carry 2 to make 25.

Ones: 25 ÷ 3 = 8, because 3 × 8 = 24. 25 − 24 = 1 left.

So 745 ÷ 3 = 248 remainder 1.

Worked example 3

2 436 ÷ 6

Show me how

2 is less than 6, so look at 24. 24 ÷ 6 = 4, nothing left.

3 ÷ 6 = 0. Write 0 on top, carry 3 to make 36.

36 ÷ 6 = 6.

So 2 436 ÷ 6 = 406.

Check with multiplication

To check a division, multiply the answer by the number you divided by, then add the remainder. You should get back the number you started with. For 745 ÷ 3 = 248 r 1: 248 × 3 = 744, and 744 + 1 = 745. It checks.

Try it

TRY ITShort division stepper

Divide one digit at a time, from the left. Small red numbers are the remainders you carry.

TRY ITShare, divide and check

Share sweets fairly, use times tables for division facts, and check answers with multiplication.

Let’s practise

Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.

1. What is 56 ÷ 8?

Hint

Which number times 8 makes 56?

Show answer

7

2. Share 23 marbles between 5 friends. How many each, and how many left?

Hint

Count in 5s up to 23.

Show answer

4 each, 3 left. 23 ÷ 5 = 4 r 3.

3. Work out 96 ÷ 4.

Hint

9 ÷ 4 = 2 r 1. Carry 1 to make 16.

Show answer

24

4. Work out 587 ÷ 5.

Hint

5 ÷ 5 = 1. Then 8 ÷ 5 = 1 r 3, carry 3.

Show answer

117 remainder 2

5. Work out 3 248 ÷ 8.

Hint

3 is less than 8, so look at 32 first.

Show answer

406

6. Check: is 157 ÷ 6 = 26 r 1 right?

Hint

Work out 26 × 6, then add 1.

Show answer

26 × 6 = 156 and 156 + 1 = 157. Yes, it is right.

7. Asha says 38 ÷ 7 = 4 r 10. What is wrong?

Hint

Is the remainder smaller than 7?

Show answer

The remainder 10 is bigger than 7. The answer is 5 r 3.

8. Write the fact family for 9, 6 and 54.

Hint

Two multiplications and two divisions.

Show answer

9 × 6 = 54, 6 × 9 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9.

Quiz

Lesson quiz: 10 questions

Answer every question, then press Check my answers. Score 8 or more to earn the Fair Sharer badge.

Recap

  • ÷ means share equally or make equal groups.
  • Division undoes multiplication: 6 × 7 = 42, so 42 ÷ 7 = 6.
  • The remainder is what is left over. It is always less than the number you divide by.
  • Short division: start on the left, divide each digit, carry what is left.
  • Check: answer × divisor + remainder = the number you started with.

Words to know

divide
To share equally or make equal groups.
Example: We divided 20 pens between 4 tables.
remainder
The amount left over after dividing.
Example: 17 ÷ 5 = 3 remainder 2.
divisor
The number you divide by.
Example: In 45 ÷ 9, the divisor is 9.
quotient
The answer to a division.
Example: The quotient of 24 ÷ 6 is 4.
fact family
Related multiplication and division facts.
Example: 3, 8 and 24 make a fact family.

Try it at home

  • Share a pack of biscuits or a bag of grapes equally between the people at home. How many each? How many are left?
  • Mini project: a family of 4 has $250 to spend in 4 weeks. Work out how much they can spend each week, and what is left.

Test tips

Tips for class tests

  • Always check that the remainder is less than the divisor.
  • Use your times tables. Division facts are times tables backwards.
  • Check by multiplying back. Then add the remainder.

For parents and teachers

After this lesson, your child should be able to:

  • explain division as sharing and grouping;
  • divide numbers up to 9 999 by a 1-digit number, with remainders;
  • check a division by multiplying back and adding the remainder.

The guide asks for division up to 4 digits by 1 digit and for children to explain why a remainder appears. We teach short division and say each step in long-division words (divide, multiply, take away, bring down). Counters, beans or bottle caps are great for sharing.

Quiz scores and badges are saved only in this browser on this device. Nothing is sent anywhere. If the browser data is cleared, or another device is used, the badges will be lost.

Previous: Multiplying Bigger Numbers – Standard 3 Maths
Next: Multiplication and Division Word Problems – Standard 3 Maths
Course: Standard 3 Maths

Updates

2026/11/04
– First version of this lesson.

Attributions to media used in this post:

Maxitaxi new.jpg – Zagaboy – CC0 1.0 (via Wikimedia Commons)

© 2026 Vedesh Kungebeharry. All rights reserved.

2 thoughts on “Division and Remainders – Standard 3 Maths”

Leave a Reply