Basic Math Examples

$\frac{4}{5^{2}} \div (\frac{4}{5} - \frac{1}{15})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{4}{5^{2}}}{\frac{4}{5} - \frac{1}{15}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{5^{2}} \cdot \frac{1}{\frac{4}{5} - \frac{1}{15}}$

Step 3

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

$\frac{4}{25} \cdot \frac{1}{\frac{4}{5} - \frac{1}{15}}$

Step 4

Simplify the denominator.

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Step 4.1

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{25} \cdot \frac{1}{\frac{4}{5} \cdot \frac{3}{3} - \frac{1}{15}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{4}{25} \cdot \frac{1}{\frac{4 \cdot 3}{5 \cdot 3} - \frac{1}{15}}$

Step 4.2.2

Multiply $5$ by $3$ .

$\frac{4}{25} \cdot \frac{1}{\frac{4 \cdot 3}{15} - \frac{1}{15}}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{4}{25} \cdot \frac{1}{\frac{4 \cdot 3 - 1}{15}}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $4$ by $3$ .

$\frac{4}{25} \cdot \frac{1}{\frac{12 - 1}{15}}$

Step 4.4.2

Subtract $1$ from $12$ .

$\frac{4}{25} \cdot \frac{1}{\frac{11}{15}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{25} (1 (\frac{15}{11}))$

Step 6

Multiply $\frac{15}{11}$ by $1$ .

$\frac{4}{25} \cdot \frac{15}{11}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Factor $5$ out of $25$ .

$\frac{4}{5 (5)} \cdot \frac{15}{11}$

Step 7.2

Factor $5$ out of $15$ .

$\frac{4}{5 \cdot 5} \cdot \frac{5 \cdot 3}{11}$

Step 7.3

Cancel the common factor.

$\frac{4}{5 \cdot 5} \cdot \frac{5 \cdot 3}{11}$

Step 7.4

Rewrite the expression.

$\frac{4}{5} \cdot \frac{3}{11}$

Step 8

Multiply $\frac{4}{5}$ by $\frac{3}{11}$ .

$\frac{4 \cdot 3}{5 \cdot 11}$

Step 9

Multiply.

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Step 9.1

Multiply $4$ by $3$ .

$\frac{12}{5 \cdot 11}$

Step 9.2

Multiply $5$ by $11$ .

$\frac{12}{55}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{55}$

Decimal Form:

$0.2\overline{18}$