# Multiplicative property of equality with fractions

#### 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 fractional number (or algebraic expression) without changing the solution.

If a, b and c are any three fractional numbers

If a = b, and c ≠ 0, then

1. a × c = b × c

2. a ÷ c = b ÷ c

Solve for w

$14 = \frac{2w}{3}$

### Solution

Step 1:

In this equation, w is multiplied by $\frac{2}{3}$

We can undo this by multiplying both sides of equation by reciprocal $\frac{3}{2}$.

Step 2:

Then, we simplify

$14 \times \frac{3}{2} = \frac{2w}{3} \times \frac{3}{2}$

$21 = 1w$

Step 3:

$w = 21$

The solution is $w = 21$

Solve for w

$5w = \frac{20}{9}$

### Solution

Step 1:

In this equation, w is multiplied by 5

We can undo this by dividing both sides of equation by 5.

Step 2:

Then, we simplify

$\frac{5w}{5} = \frac{20}{9} \div 5$

Step 3:

$1w = \frac{20}{9} \times \frac{1}{5}$

$w = \frac{4}{9}$

The solution is $w = \frac{4}{9}$