Math Core

Sometimes you know how many should go in each group, but not how many groups you can make. If you have 12 eggs and each carton holds 4, how many cartons do you fill? That is also division. This time you are making groups.

Making equal groups

Let's put 12 eggs into cartons of 4. Take 4 eggs at a time and put them in a carton until no eggs are left.

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You filled 3 cartons. So:

12 \div 4 = 3

Here is how to read $12 \div 4 = 3$ when you make groups: "12 split into groups of 4 makes 3 groups."

Two kinds of division

Division can answer two different questions. The equation looks the same, but the missing piece is different.

	You know	You find
Sharing	the total and the number of groups	how many in each group
Grouping	the total and how many in each group	the number of groups

Division as grouping

To find $\text{total} \div \text{size of each group}$ :

Take out one group of that size.
Keep taking out groups until nothing is left.
Count the groups. That is the answer.

Counting back on a number line

You can also make groups on a number line. Start at the total and jump back by the group size until you reach 0. Each jump takes away one group. Count the jumps.

Here is $12 \div 4$ . Start at 12 and jump back by 4s:

It takes 3 jumps to get to 0. So $12 \div 4 = 3$ .

This is like subtracting the same number over and over:

12 - 4 - 4 - 4 = 0

You subtracted 4 three times, so there are 3 groups of 4 in 12.

Worked example: Packing muffins

A baker has 10 muffins. Each box holds 2 muffins. How many boxes does she need?

Make groups of 2:

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There are 5 groups. She needs 5 boxes.

$10 \div 2 = 5$ .

Worked example: Jumping back by 3s

Use a number line to find $15 \div 3$ .

Start at 15 and jump back by 3 until you land on 0:

Count the jumps: 15 to 12, 12 to 9, 9 to 6, 6 to 3, 3 to 0. That is 5 jumps.

$15 \div 3 = 5$ .

Worked example: Teams at recess

There are 24 students. The coach makes teams of 6. How many teams are there?

We know the total, 24, and the size of each team, 6. We need the number of teams, so we find $24 \div 6$ .

Subtract 6 until nothing is left: $24 - 6 = 18$ , $18 - 6 = 12$ , $12 - 6 = 6$ , $6 - 6 = 0$ .

We subtracted 6 four times. There are 4 teams.

$24 \div 6 = 4$ .

Common mistake

When you count back on a number line, count the jumps, not the numbers you land on. For $12 \div 4$ you land on 8, 4 and 0, but the answer is the number of jumps: 3.

Tip

Check with repeated addition. For $24 \div 6 = 4$ , add 6 four times: $6 + 6 + 6 + 6 = 24$ . ✓

Practice

Practice 1

Put these 8 socks into pairs (groups of 2).

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How many pairs do you get?

Type a number.

Practice 2

Look at the number line. It shows $9 \div 3$ .

What is $9 \div 3$ ?

Type a number.

Practice 3

Dan has 20 cards. He puts 5 cards in each pile. Which question does $20 \div 5$ answer?

Practice 4

Mr. Lee has 25 markers. He puts 5 markers in each cup. How many cups does he fill?

Type a number.

Practice 5

Find $18 \div 3$ . Picture jumping back by 3s from 18 on a number line.

Type a number.

Practice 6

Ava wrote this subtraction:

28 - 7 - 7 - 7 - 7 = 0

Use it to find $28 \div 7$ .

Type a number.

Practice 7

A toy shop has 32 wheels. Each toy car needs 4 wheels. How many toy cars can the shop build?

Type a number.