- Equations and Applications
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- Additive property of equality with decimals
- Multiplicative property of equality with decimals
- Multiplicative property of equality with whole numbers: Fractional answers
- Multiplicative property of equality with fractions
- Using two steps to solve an equation with whole numbers
- Solving an equation with parentheses
- Solving a fraction word problem using a linear equation of the form Ax = B
- Translating a sentence into a multi-step equation

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# 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