Multiplicative property of equality

Definition

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

Example 1

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

127=7w7

127=1w

w=127

The solution is w=127, which is a fractional answer

Example 2

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

5w5=95

1w=95

w=95

The solution is w=95, which is a fractional answer