
- Equations and Applications
- Home
- 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
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