Skill: Relate multiplication and division

Multiplication and division are inverse operations. They describe the same equal-groups situation in different ways.

If

$$a \times b = c,$$

then the related division facts are

$$c \div a = b \qquad\text{and}\qquad c \div b = a.$$

• $c$ is the total.
• One factor tells the number of groups.
• The other factor tells the number in each group.

Example: There are $24$ apples placed equally into $4$ baskets. How many apples are in each basket?

1. Use multiplication to describe the equal groups:

$$4 \times 6 = 24$$

This means $4$ groups of $6$ make $24$.

2. Use division to find the number in each basket:

$$24 \div 4 = 6$$

So, each basket has $6$ apples.

3. The other related division fact is:

$$24 \div 6 = 4$$

This tells us that $24$ apples make $4$ groups when there are $6$ apples in each group.

The related facts are:

$$4 \times 6 = 24,\qquad 6 \times 4 = 24$$ $$24 \div 4 = 6,\qquad 24 \div 6 = 4$$

Use the multiplication fact to check a division answer: since $4 \times 6 = 24$, the answer to $24 \div 4$ is $6$.