Division as sharing and grouping

Step 5 · Multiplication and first fractions topics

Divide by sharing things out equally or by making groups of a set size, and use a multiplication fact to find the answer.

Sharing equally

Division splits a total into equal parts. 12 ÷ 3 can mean: share 12 between 3, and see how many each one gets.

12 shared equally between 3 plates: 4 on each. 12 ÷ 3 = 4.

Deal the 12 out one at a time, like cards, until none are left. Each plate ends up with 4, so 12 ÷ 3 = 4. The answer to a division is called the quotient.

Making groups

12 ÷ 3 can also mean: how many groups of 3 can you make from 12? Take away 3 again and again and count the groups. 3, 6, 9, 12 is 4 groups.

12 put into groups of 3: 4 groups. 12 ÷ 3 = 4.

Both ways give the same answer. Use whichever fits the story: sharing when you know how many groups there are, grouping when you know how big each group is.

Example: Making groups

20 children get into teams of 5. How many teams are there?

You know the size of each team, so make groups of 5.
5, 10, 15, 20: that is 4 groups.

Answer4 teams

Division undoes multiplication

Every division hides a multiplication. To find 24 ÷ 6, ask: 6 times what makes 24? 6 × 4 = 24, so 24 ÷ 6 = 4.

Multiplication	Division
4 × 6 = 24	24 ÷ 6 = 4
6 × 4 = 24	24 ÷ 4 = 6

These four facts are a fact family: three numbers that belong together. Know one and you know all four.

Try it yourself

Work each one on paper first, then open the answer to check.

Share 18 stickers equally among 3 friends. How many does each friend get?
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6 stickers. 18 ÷ 3 = 6.
How many groups of 4 can you make from 28?
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7 groups. 28 ÷ 4 = 7.
Use 5 × 8 = 40 to find 40 ÷ 8.
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5.
Write the fact family for 3, 7 and 21.
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3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7, 21 ÷ 7 = 3.
What is 9 ÷ 1?
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9. Shared into 1 group, all 9 go in it.