Pre-Algebra Examples

${(\frac{2}{3})}^{2} + \frac{\frac{2}{5}}{\frac{1}{15}}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{2^{2}}{3^{2}} + \frac{\frac{2}{5}}{\frac{1}{15}}$

Step 1.2

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

$\frac{4}{3^{2}} + \frac{\frac{2}{5}}{\frac{1}{15}}$

Step 1.3

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

$\frac{4}{9} + \frac{\frac{2}{5}}{\frac{1}{15}}$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{9} + \frac{2}{5} \cdot 15$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $15$ .

$\frac{4}{9} + \frac{2}{5} \cdot (5 (3))$

Step 1.5.2

Cancel the common factor.

$\frac{4}{9} + \frac{2}{5} \cdot (5 \cdot 3)$

Step 1.5.3

Rewrite the expression.

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

Step 1.6

Multiply $2$ by $3$ .

$\frac{4}{9} + 6$

Step 2

To write $6$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{4}{9} + 6 \cdot \frac{9}{9}$

Step 3

Combine $6$ and $\frac{9}{9}$ .

$\frac{4}{9} + \frac{6 \cdot 9}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 + 6 \cdot 9}{9}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $6$ by $9$ .

$\frac{4 + 54}{9}$

Step 5.2

Add $4$ and $54$ .

$\frac{58}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{58}{9}$

Decimal Form:

$6.\overline{4}$

Mixed Number Form:

$6 \frac{4}{9}$