Pre-Algebra Examples

${(\frac{6}{1})}^{2} \div (\frac{6}{1} - \frac{1}{3})$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{6}{1})}^{2}}{\frac{6}{1} - \frac{1}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Divide $6$ by $1$ .

$\frac{6^{2}}{\frac{6}{1} - \frac{1}{3}}$

Step 2.2

Divide $6$ by $1$ .

$\frac{6^{2}}{6 - \frac{1}{3}}$

Step 2.3

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

$\frac{36}{6 - \frac{1}{3}}$

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

Combine $6$ and $\frac{3}{3}$ .

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $6$ by $3$ .

$\frac{36}{\frac{18 - 1}{3}}$

Step 3.4.2

Subtract $1$ from $18$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

$36 (\frac{3}{17})$

Step 5

Multiply $36 (\frac{3}{17})$ .

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Step 5.1

Combine $36$ and $\frac{3}{17}$ .

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

Step 5.2

Multiply $36$ by $3$ .

$\frac{108}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{108}{17}$

Decimal Form:

$6.35294117 \dots$

Mixed Number Form:

$6 \frac{6}{17}$