Math Core

Multiplication puts equal groups together. Division pulls a total apart into equal groups. They undo each other, so if you know a multiplication fact, you already know two division facts!

One picture, four facts

Look at this array. It has 3 rows with 5 dots in each row.

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You can describe it in four ways:

What you think	Equation
3 rows of 5 make 15	$3 \times 5 = 15$
5 columns of 3 make 15	$5 \times 3 = 15$
15 split into 3 rows gives 5 in each row	$15 \div 3 = 5$
15 split into 5 columns gives 3 in each column	$15 \div 5 = 3$

All four equations use the same three numbers: 3, 5 and 15.

Definition

Fact family

A fact family is a group of related multiplication and division facts that use the same three numbers. The fact family for 3, 5 and 15 is:

3 \times 5 = 15 \qquad 5 \times 3 = 15 \qquad 15 \div 3 = 5 \qquad 15 \div 5 = 3

The biggest number, the product, comes last in a multiplication fact and first in a division fact.

Division is a missing factor

Here is the big idea. Every division problem is really a multiplication problem with a number missing.

To find $20 \div 4$ , ask yourself: "4 times what makes 20?"

4 \times \boxed{\phantom{0}} = 20

You know $4 \times 5 = 20$ . So the missing number is 5, and $20 \div 4 = 5$ .

Think multiplication to divide

To divide, turn the problem into a multiplication with a missing number. Find the missing number, and you have the answer.

18 \div 6 = 3 \quad \text{because} \quad 6 \times 3 = 18

Worked example: Write a fact family

Write the fact family for 2, 7 and 14.

The product is 14. The two factors are 2 and 7.

2 \times 7 = 14 \qquad 7 \times 2 = 14 \qquad 14 \div 2 = 7 \qquad 14 \div 7 = 2

Worked example: Use multiplication to divide

Find $24 \div 3$ .

Think: $3 \times \boxed{\phantom{0}} = 24$ . Count by 3s: 3, 6, 9, 12, 15, 18, 21, 24. That is 8 threes.

So $3 \times 8 = 24$ , and $24 \div 3 = 8$ .

Worked example: Find the unknown number

What number goes in the box? $\boxed{\phantom{0}} \times 5 = 35$

We need a number that, times 5, makes 35. That is the same as $35 \div 5$ .

Count by 5s: 5, 10, 15, 20, 25, 30, 35. That is 7 fives.

The missing number is 7. Check: $7 \times 5 = 35$ . ✓

Common mistake

In a division fact, the total goes first. $15 \div 3 = 5$ is true, but $3 \div 15 = 5$ is not. When you turn $3 \times 5 = 15$ into division, start with the 15.

Tip

Check any division answer by multiplying. If $28 \div 4 = 7$ , then $4 \times 7$ should give back 28. It does!

Practice

Practice 1

Use the fact $2 \times 4 = 8$ to find $8 \div 2$ .

Type a number.

Practice 2

Look at this array.

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It shows $6 \times 3 = 18$ . What is $18 \div 3$ ?

Type a number.

Practice 3

What number goes in the box? $4 \times \boxed{\phantom{0}} = 12$

Type a number.

Practice 4

Which fact is not in the fact family for 4, 6 and 24?

Practice 5

Find $21 \div 3$ . Use a multiplication fact to help.

Type a number.

Practice 6

What number goes in the box? $\boxed{\phantom{0}} \times 2 = 20$

Type a number.

Practice 7

A garden has 30 plants in 6 equal rows. How many plants are in each row?

Type a number.

Practice 8

Jen says, " $36 \div 4 = 8$ ." Which multiplication shows whether she is right?