Evaluate ((4/2)^2)÷(4/1-1/3)

${(\frac{4}{2})}^{2} \div (\frac{4}{1} - \frac{1}{3})$

Rewrite the division as a fraction.

$\frac{{(\frac{4}{2})}^{2}}{\frac{4}{1} - \frac{1}{3}}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor of $4$ and $2$ .

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Factor $2$ out of $4$ .

$\frac{{(\frac{2 \cdot 2}{2})}^{2}}{\frac{4}{1} - \frac{1}{3}}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$\frac{{(\frac{2 \cdot 2}{2 (1)})}^{2}}{\frac{4}{1} - \frac{1}{3}}$

Cancel the common factor.

$\frac{{(\frac{2 \cdot 2}{2 \cdot 1})}^{2}}{\frac{4}{1} - \frac{1}{3}}$

Rewrite the expression.

$\frac{{(\frac{2}{1})}^{2}}{\frac{4}{1} - \frac{1}{3}}$

Divide $2$ by $1$ .

$\frac{2^{2}}{\frac{4}{1} - \frac{1}{3}}$

Simplify the expression.

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Divide $4$ by $1$ .

$\frac{2^{2}}{4 - \frac{1}{3}}$

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

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

Simplify the denominator.

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $4$ by $3$ .

$\frac{4}{\frac{12 - 1}{3}}$

Subtract $1$ from $12$ .

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

Multiply the numerator by the reciprocal of the denominator.

$4 (\frac{3}{11})$

Multiply $4 (\frac{3}{11})$ .

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Combine $4$ and $\frac{3}{11}$ .

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

Multiply $4$ by $3$ .

$\frac{12}{11}$

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{11}$

Decimal Form:

$1.\overline{09}$

Mixed Number Form:

$1 \frac{1}{11}$

Evaluate ((4/2)^2)÷(4/1-1/3)

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