Pre-Algebra Examples

$\frac{5}{12} - \frac{3}{4} \cdot {(\frac{9}{5})}^{- 1}$

Step 1

Simplify each term.

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Step 1.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{5}{12} - \frac{3}{4} \cdot \frac{5}{9}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{5}{12} + \frac{- 3}{4} \cdot \frac{5}{9}$

Step 1.2.2

Factor $3$ out of $- 3$ .

$\frac{5}{12} + \frac{3 (- 1)}{4} \cdot \frac{5}{9}$

Step 1.2.3

Factor $3$ out of $9$ .

$\frac{5}{12} + \frac{3 \cdot - 1}{4} \cdot \frac{5}{3 \cdot 3}$

Step 1.2.4

Cancel the common factor.

$\frac{5}{12} + \frac{3 \cdot - 1}{4} \cdot \frac{5}{3 \cdot 3}$

Step 1.2.5

Rewrite the expression.

$\frac{5}{12} + \frac{- 1}{4} \cdot \frac{5}{3}$

Step 1.3

Multiply $\frac{- 1}{4}$ by $\frac{5}{3}$ .

$\frac{5}{12} + \frac{- 1 \cdot 5}{4 \cdot 3}$

Step 1.4

Multiply $- 1$ by $5$ .

$\frac{5}{12} + \frac{- 5}{4 \cdot 3}$

Step 1.5

Multiply $4$ by $3$ .

$\frac{5}{12} + \frac{- 5}{12}$

Step 1.6

Move the negative in front of the fraction.

$\frac{5}{12} - \frac{5}{12}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 - 5}{12}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $5$ from $5$ .

$\frac{0}{12}$

Step 2.2.2

Divide $0$ by $12$ .

$0$