# Multiplicative property of equality with whole numbers: Fractional answers

The **multiplicative property of equality** states that we can multiply (or divide) both sides of an equation by the same nonzero number (or algebraic expression) without changing the solution.

If a, b and c are any three numbers

If a = b, and c ≠ 0, then

1. a × c = b × c

2. a ÷ c = b ÷ c

Solve for w

12 = 7w

### Solution

In this equation, w is multiplied by 7

We can undo this by dividing both sides of equation by 7. Then, we simplify

$\frac{12}{7} = \frac{7w}{7}$

$\frac{12}{7} = 1w$

$w = \frac{12}{7}$

The solution is $w = \frac{12}{7}$, which is a fractional answer

Solve for w

5w = 9

### Solution

In this equation, w is multiplied by 5

We can undo this by dividing both sides of equation by 5. Then, we simplify

$\frac{5w}{5} = \frac{9}{5}$

$1w = \frac{9}{5}$

$w = \frac{9}{5}$

The solution is $w = \frac{9}{5}$, which is a fractional answer