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