Pre-Algebra Examples

${(\frac{6}{5})}^{2} \div (\frac{6}{5} - \frac{1}{15})$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{6}{5})}^{2}}{\frac{6}{5} - \frac{1}{15}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{6}{5}$ .

$\frac{\frac{6^{2}}{5^{2}}}{\frac{6}{5} - \frac{1}{15}}$

Step 2.2

Raise $6$ to the power of $2$ .

$\frac{\frac{36}{5^{2}}}{\frac{6}{5} - \frac{1}{15}}$

Step 2.3

Raise $5$ to the power of $2$ .

$\frac{\frac{36}{25}}{\frac{6}{5} - \frac{1}{15}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{36}{25}}{\frac{6}{5} \cdot \frac{3}{3} - \frac{1}{15}}$

Step 3.2

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{6}{5}$ by $\frac{3}{3}$ .

$\frac{\frac{36}{25}}{\frac{6 \cdot 3}{5 \cdot 3} - \frac{1}{15}}$

Step 3.2.2

Multiply $5$ by $3$ .

$\frac{\frac{36}{25}}{\frac{6 \cdot 3}{15} - \frac{1}{15}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{36}{25}}{\frac{6 \cdot 3 - 1}{15}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $6$ by $3$ .

$\frac{\frac{36}{25}}{\frac{18 - 1}{15}}$

Step 3.4.2

Subtract $1$ from $18$ .

$\frac{\frac{36}{25}}{\frac{17}{15}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{36}{25} \cdot \frac{15}{17}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Factor $5$ out of $25$ .

$\frac{36}{5 (5)} \cdot \frac{15}{17}$

Step 5.2

Factor $5$ out of $15$ .

$\frac{36}{5 \cdot 5} \cdot \frac{5 \cdot 3}{17}$

Step 5.3

Cancel the common factor.

$\frac{36}{5 \cdot 5} \cdot \frac{5 \cdot 3}{17}$

Step 5.4

Rewrite the expression.

$\frac{36}{5} \cdot \frac{3}{17}$

Step 6

Multiply $\frac{36}{5}$ by $\frac{3}{17}$ .

$\frac{36 \cdot 3}{5 \cdot 17}$

Step 7

Multiply.

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Step 7.1

Multiply $36$ by $3$ .

$\frac{108}{5 \cdot 17}$

Step 7.2

Multiply $5$ by $17$ .

$\frac{108}{85}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{108}{85}$

Decimal Form:

$1.27058823 \dots$

Mixed Number Form:

$1 \frac{23}{85}$