Evaluate ((2/5)^2)÷(2/5-1/15)

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Simplify the numerator.

Apply the product rule to $\frac{2}{5}$ .

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

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

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

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

$\frac{\frac{4}{25}}{\frac{2}{5} - \frac{1}{15}}$

Step 3

Simplify the denominator.

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{4}{25}}{\frac{2}{5} \cdot \frac{3}{3} - \frac{1}{15}}$

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

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$\frac{\frac{4}{25}}{\frac{2 \cdot 3}{5 \cdot 3} - \frac{1}{15}}$

Multiply $5$ by $3$ .

$\frac{\frac{4}{25}}{\frac{2 \cdot 3}{15} - \frac{1}{15}}$

Combine the numerators over the common denominator.

$\frac{\frac{4}{25}}{\frac{2 \cdot 3 - 1}{15}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{\frac{4}{25}}{\frac{6 - 1}{15}}$

Subtract $1$ from $6$ .

$\frac{\frac{4}{25}}{\frac{5}{15}}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5$ .

$\frac{\frac{4}{25}}{\frac{5 (1)}{15}}$

Cancel the common factors.

Factor $5$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{\frac{4}{25}}{\frac{1}{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{25} \cdot 3$

Step 5

Multiply $\frac{4}{25} \cdot 3$ .

Combine $\frac{4}{25}$ and $3$ .

$\frac{4 \cdot 3}{25}$

Multiply $4$ by $3$ .

$\frac{12}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{25}$

Decimal Form:

$0.48$

Evaluate ((2/5)^2)÷(2/5-1/15)

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