Algebra Examples

$12 + (2^{3} \div \frac{2}{3}) - 2$

Step 1

Remove parentheses.

$12 + 2^{3} \div \frac{2}{3} - 2$

Step 2

Find the common denominator.

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Step 2.1

Write $12$ as a fraction with denominator $1$ .

$\frac{12}{1} + 2^{3} \div \frac{2}{3} - 2$

Step 2.2

Multiply $\frac{12}{1}$ by $\frac{\frac{2}{3}}{\frac{2}{3}}$ .

$\frac{12}{1} \cdot \frac{\frac{2}{3}}{\frac{2}{3}} + 2^{3} \div \frac{2}{3} - 2$

Step 2.3

Multiply $\frac{12}{1}$ by $\frac{\frac{2}{3}}{\frac{2}{3}}$ .

$\frac{12 (\frac{2}{3})}{\frac{2}{3}} + 2^{3} \div \frac{2}{3} - 2$

Step 2.4

Write $- 2$ as a fraction with denominator $1$ .

$\frac{12 (\frac{2}{3})}{\frac{2}{3}} + 2^{3} \div \frac{2}{3} + \frac{- 2}{1}$

Step 2.5

Multiply $\frac{- 2}{1}$ by $\frac{\frac{2}{3}}{\frac{2}{3}}$ .

$\frac{12 (\frac{2}{3})}{\frac{2}{3}} + 2^{3} \div \frac{2}{3} + \frac{- 2}{1} \cdot \frac{\frac{2}{3}}{\frac{2}{3}}$

Step 2.6

Multiply $\frac{- 2}{1}$ by $\frac{\frac{2}{3}}{\frac{2}{3}}$ .

$\frac{12 (\frac{2}{3})}{\frac{2}{3}} + 2^{3} \div \frac{2}{3} + \frac{- 2 (\frac{2}{3})}{\frac{2}{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{12 (\frac{2}{3}) + 2^{3} - 2 (\frac{2}{3})}{\frac{2}{3}}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $3$ .

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Step 4.1.1

Factor $3$ out of $12$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Multiply $4$ by $2$ .

$\frac{8 + 2^{3} - 2 (\frac{2}{3})}{\frac{2}{3}}$

Step 4.3

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

$\frac{8 + 8 - 2 (\frac{2}{3})}{\frac{2}{3}}$

Step 4.4

Multiply $- 2 (\frac{2}{3})$ .

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Step 4.4.1

Combine $- 2$ and $\frac{2}{3}$ .

$\frac{8 + 8 + \frac{- 2 \cdot 2}{3}}{\frac{2}{3}}$

Step 4.4.2

Multiply $- 2$ by $2$ .

$\frac{8 + 8 + \frac{- 4}{3}}{\frac{2}{3}}$

Step 4.5

Move the negative in front of the fraction.

$\frac{8 + 8 - \frac{4}{3}}{\frac{2}{3}}$

Step 5

Find the common denominator.

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Step 5.1

Write $8$ as a fraction with denominator $1$ .

$\frac{\frac{8}{1} + 8 - \frac{4}{3}}{\frac{2}{3}}$

Step 5.2

Multiply $\frac{8}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8}{1} \cdot \frac{3}{3} + 8 - \frac{4}{3}}{\frac{2}{3}}$

Step 5.3

Multiply $\frac{8}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8 \cdot 3}{3} + 8 - \frac{4}{3}}{\frac{2}{3}}$

Step 5.4

Write $8$ as a fraction with denominator $1$ .

$\frac{\frac{8 \cdot 3}{3} + \frac{8}{1} - \frac{4}{3}}{\frac{2}{3}}$

Step 5.5

Multiply $\frac{8}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8 \cdot 3}{3} + \frac{8}{1} \cdot \frac{3}{3} - \frac{4}{3}}{\frac{2}{3}}$

Step 5.6

Multiply $\frac{8}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8 \cdot 3}{3} + \frac{8 \cdot 3}{3} - \frac{4}{3}}{\frac{2}{3}}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{8 \cdot 3 + 8 \cdot 3 - 4}{3}}{\frac{2}{3}}$

Step 7

Simplify each term.

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Step 7.1

Multiply $8$ by $3$ .

$\frac{\frac{24 + 8 \cdot 3 - 4}{3}}{\frac{2}{3}}$

Step 7.2

Multiply $8$ by $3$ .

$\frac{\frac{24 + 24 - 4}{3}}{\frac{2}{3}}$

Step 8

Simplify by adding and subtracting.

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Step 8.1

Add $24$ and $24$ .

$\frac{\frac{48 - 4}{3}}{\frac{2}{3}}$

Step 8.2

Subtract $4$ from $48$ .

$\frac{\frac{44}{3}}{\frac{2}{3}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{44}{3} \cdot \frac{3}{2}$

Step 10

Cancel the common factor of $2$ .

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Step 10.1

Factor $2$ out of $44$ .

$\frac{2 (22)}{3} \cdot \frac{3}{2}$

Step 10.2

Cancel the common factor.

$\frac{2 \cdot 22}{3} \cdot \frac{3}{2}$

Step 10.3

Rewrite the expression.

$\frac{22}{3} \cdot 3$

Step 11

Cancel the common factor of $3$ .

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Step 11.1

Cancel the common factor.

$\frac{22}{3} \cdot 3$

Step 11.2

Rewrite the expression.

$22$