Multiplicative property of equality with fractions

Introduction

The multiplicative property of equality states that we can multiply ordivide both sides of an equation by the same nonzero fractional number oralgebraicexpression 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

Example 1

Solve for w

14=2w3

Solution

Step 1:

In this equation, w is multiplied by 23

We can undo this by multiplying both sides of equation by reciprocal 32.

Step 2:

Then, we simplify

14×32=2w3×32

21=1w

Step 3:

w=21

The solution is w=21

Example 2

Solve for w

5w=209

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

5w5=209÷5

Step 3:

1w=209×15

w=49

The solution is w=49