- 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 fractions

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