- 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 decimals

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 x

2x = 3.58

### Solution

**Step 1:**

To solve for x, we must isolate x. On left side of equation, we have 2x; to isolate x, we must divide by 2.

**Step 2:**

From the multiplicative property of equality with decimals we must divide both sides of an equation by the same number. So, we divide the both sides by 2 to get

$\frac{2x}{x} = \frac{3.58}{2}$

**Step 3:**

Simplifying

$\frac{3.58}{2} = 1.79$

So, the solution is x = 1.79

Solve for x

$\frac{x}{3} = 4.27$

### Solution

**Step 1:**

To solve for x, we must isolate x. On left side of equation, we have $\frac{x}{3}$; to isolate x, we must multiply by 3.

**Step 2:**

From the multiplicative property of equality with decimals we must multiply both sides of an equation by the same number. So, we multiply both sides by 3 to get

$\frac{x}{3} \times 3 = 4.27 \times 3$

**Step 3:**

Simplifying

4.27 × 3 = 1281

So, the solution is x = 12.81