Basic Math Examples

${(\frac{2}{3})}^{2} \div (\frac{5}{6} - \frac{2}{9})$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{2}{3})}^{2}}{\frac{5}{6} - \frac{2}{9}}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{\frac{2^{2}}{3^{2}}}{\frac{5}{6} - \frac{2}{9}}$

Step 2.2

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

$\frac{\frac{4}{3^{2}}}{\frac{5}{6} - \frac{2}{9}}$

Step 2.3

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

$\frac{\frac{4}{9}}{\frac{5}{6} - \frac{2}{9}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{\frac{4}{9}}{\frac{5}{6} \cdot \frac{3}{3} - \frac{2}{9}}$

Step 3.2

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

$\frac{\frac{4}{9}}{\frac{5}{6} \cdot \frac{3}{3} - \frac{2}{9} \cdot \frac{2}{2}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{\frac{4}{9}}{\frac{5 \cdot 3}{6 \cdot 3} - \frac{2}{9} \cdot \frac{2}{2}}$

Step 3.3.2

Multiply $6$ by $3$ .

$\frac{\frac{4}{9}}{\frac{5 \cdot 3}{18} - \frac{2}{9} \cdot \frac{2}{2}}$

Step 3.3.3

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

$\frac{\frac{4}{9}}{\frac{5 \cdot 3}{18} - \frac{2 \cdot 2}{9 \cdot 2}}$

Step 3.3.4

Multiply $9$ by $2$ .

$\frac{\frac{4}{9}}{\frac{5 \cdot 3}{18} - \frac{2 \cdot 2}{18}}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{\frac{4}{9}}{\frac{5 \cdot 3 - 2 \cdot 2}{18}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $5$ by $3$ .

$\frac{\frac{4}{9}}{\frac{15 - 2 \cdot 2}{18}}$

Step 3.5.2

Multiply $- 2$ by $2$ .

$\frac{\frac{4}{9}}{\frac{15 - 4}{18}}$

Step 3.5.3

Subtract $4$ from $15$ .

$\frac{\frac{4}{9}}{\frac{11}{18}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{9} \cdot \frac{18}{11}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Factor $9$ out of $18$ .

$\frac{4}{9} \cdot \frac{9 (2)}{11}$

Step 5.2

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 \cdot 2}{11}$

Step 5.3

Rewrite the expression.

$4 (\frac{2}{11})$

Step 6

Combine $4$ and $\frac{2}{11}$ .

$\frac{4 \cdot 2}{11}$

Step 7

Multiply $4$ by $2$ .

$\frac{8}{11}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{11}$

Decimal Form:

$0.\overline{72}$