# Multiplicative property of equality with whole numbers: Fractional answers

#### Differential Equations

46 Lectures 2.5 hours

#### Linear Equations in Two Variables

9 Lectures 2.5 hours

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