Pre-Algebra Examples

${(\frac{3}{4})}^{2} - \frac{1}{9} \cdot \frac{15}{4}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{3}{4}$ .

$\frac{3^{2}}{4^{2}} - \frac{1}{9} \cdot \frac{15}{4}$

Step 1.2

Raise $3$ to the power of $2$ .

$\frac{9}{4^{2}} - \frac{1}{9} \cdot \frac{15}{4}$

Step 1.3

Raise $4$ to the power of $2$ .

$\frac{9}{16} - \frac{1}{9} \cdot \frac{15}{4}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{9}$ into the numerator.

$\frac{9}{16} + \frac{- 1}{9} \cdot \frac{15}{4}$

Step 1.4.2

Factor $3$ out of $9$ .

$\frac{9}{16} + \frac{- 1}{3 (3)} \cdot \frac{15}{4}$

Step 1.4.3

Factor $3$ out of $15$ .

$\frac{9}{16} + \frac{- 1}{3 \cdot 3} \cdot \frac{3 \cdot 5}{4}$

Step 1.4.4

Cancel the common factor.

$\frac{9}{16} + \frac{- 1}{3 \cdot 3} \cdot \frac{3 \cdot 5}{4}$

Step 1.4.5

Rewrite the expression.

$\frac{9}{16} + \frac{- 1}{3} \cdot \frac{5}{4}$

Step 1.5

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

$\frac{9}{16} + \frac{- 1 \cdot 5}{3 \cdot 4}$

Step 1.6

Multiply $- 1$ by $5$ .

$\frac{9}{16} + \frac{- 5}{3 \cdot 4}$

Step 1.7

Multiply $3$ by $4$ .

$\frac{9}{16} + \frac{- 5}{12}$

Step 1.8

Move the negative in front of the fraction.

$\frac{9}{16} - \frac{5}{12}$

Step 2

To write $\frac{9}{16}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{16} \cdot \frac{3}{3} - \frac{5}{12}$

Step 3

To write $- \frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{16} \cdot \frac{3}{3} - \frac{5}{12} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $48$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{9}{16}$ by $\frac{3}{3}$ .

$\frac{9 \cdot 3}{16 \cdot 3} - \frac{5}{12} \cdot \frac{4}{4}$

Step 4.2

Multiply $16$ by $3$ .

$\frac{9 \cdot 3}{48} - \frac{5}{12} \cdot \frac{4}{4}$

Step 4.3

Multiply $\frac{5}{12}$ by $\frac{4}{4}$ .

$\frac{9 \cdot 3}{48} - \frac{5 \cdot 4}{12 \cdot 4}$

Step 4.4

Multiply $12$ by $4$ .

$\frac{9 \cdot 3}{48} - \frac{5 \cdot 4}{48}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 - 5 \cdot 4}{48}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $9$ by $3$ .

$\frac{27 - 5 \cdot 4}{48}$

Step 6.2

Multiply $- 5$ by $4$ .

$\frac{27 - 20}{48}$

Step 6.3

Subtract $20$ from $27$ .

$\frac{7}{48}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{48}$

Decimal Form:

$0.1458\overline{3}$