Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{2}{3}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.5

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

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

Step 1.5.2

Multiply $2$ by $2$ .

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 1.7

Subtract $2$ from $3$ .

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

Step 1.8

Cancel the common factor of $4$ .

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Step 1.8.1

Cancel the common factor.

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

Step 1.8.2

Rewrite the expression.

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

Step 1.9

Cancel the common factor of $2$ .

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Step 1.9.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 1.9.2

Factor $2$ out of $- 2$ .

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

Step 1.9.3

Factor $2$ out of $4$ .

$\frac{1}{9} + \frac{2 \cdot - 1}{3} \cdot \frac{1}{2 \cdot 2}$

Step 1.9.4

Cancel the common factor.

$\frac{1}{9} + \frac{2 \cdot - 1}{3} \cdot \frac{1}{2 \cdot 2}$

Step 1.9.5

Rewrite the expression.

$\frac{1}{9} + \frac{- 1}{3} \cdot \frac{1}{2}$

Step 1.10

Multiply $\frac{- 1}{3}$ by $\frac{1}{2}$ .

$\frac{1}{9} + \frac{- 1}{3 \cdot 2}$

Step 1.11

Multiply $3$ by $2$ .

$\frac{1}{9} + \frac{- 1}{6}$

Step 1.12

Move the negative in front of the fraction.

$\frac{1}{9} - \frac{1}{6}$

Step 2

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{9} \cdot \frac{2}{2} - \frac{1}{6}$

Step 3

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{9} \cdot \frac{2}{2} - \frac{1}{6} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

$\frac{2}{9 \cdot 2} - \frac{1}{6} \cdot \frac{3}{3}$

Step 4.2

Multiply $9$ by $2$ .

$\frac{2}{18} - \frac{1}{6} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$\frac{2}{18} - \frac{3}{6 \cdot 3}$

Step 4.4

Multiply $6$ by $3$ .

$\frac{2}{18} - \frac{3}{18}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 - 3}{18}$

Step 6

Subtract $3$ from $2$ .

$\frac{- 1}{18}$

Step 7

Move the negative in front of the fraction.

$- \frac{1}{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{18}$

Decimal Form:

$- 0.0\overline{5}$