Basic Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Find the common denominator.

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Step 2.1

Write ${(\frac{2}{3})}^{3}$ as a fraction with denominator $1$ .

$\frac{{(\frac{2}{3})}^{3}}{1} + \frac{2}{3} - (\frac{5}{9})$

Step 2.2

Multiply $\frac{{(\frac{2}{3})}^{3}}{1}$ by $\frac{9}{9}$ .

$\frac{{(\frac{2}{3})}^{3}}{1} \cdot \frac{9}{9} + \frac{2}{3} - (\frac{5}{9})$

Step 2.3

Multiply $\frac{{(\frac{2}{3})}^{3}}{1}$ by $\frac{9}{9}$ .

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

Multiply $3$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

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

$\frac{\frac{2^{3}}{3^{3}} \cdot 9 + 2 \cdot 3 - 5}{9}$

Step 4.2

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

$\frac{\frac{8}{3^{3}} \cdot 9 + 2 \cdot 3 - 5}{9}$

Step 4.3

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

$\frac{\frac{8}{27} \cdot 9 + 2 \cdot 3 - 5}{9}$

Step 4.4

Cancel the common factor of $9$ .

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Step 4.4.1

Factor $9$ out of $27$ .

$\frac{\frac{8}{9 (3)} \cdot 9 + 2 \cdot 3 - 5}{9}$

Step 4.4.2

Cancel the common factor.

$\frac{\frac{8}{9 \cdot 3} \cdot 9 + 2 \cdot 3 - 5}{9}$

Step 4.4.3

Rewrite the expression.

$\frac{\frac{8}{3} + 2 \cdot 3 - 5}{9}$

Step 4.5

Multiply $2$ by $3$ .

$\frac{\frac{8}{3} + 6 - 5}{9}$

Step 5

Find the common denominator.

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Step 5.1

Write $6$ as a fraction with denominator $1$ .

$\frac{\frac{8}{3} + \frac{6}{1} - 5}{9}$

Step 5.2

Multiply $\frac{6}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8}{3} + \frac{6}{1} \cdot \frac{3}{3} - 5}{9}$

Step 5.3

Multiply $\frac{6}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8}{3} + \frac{6 \cdot 3}{3} - 5}{9}$

Step 5.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{\frac{8}{3} + \frac{6 \cdot 3}{3} + \frac{- 5}{1}}{9}$

Step 5.5

Multiply $\frac{- 5}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8}{3} + \frac{6 \cdot 3}{3} + \frac{- 5}{1} \cdot \frac{3}{3}}{9}$

Step 5.6

Multiply $\frac{- 5}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{8}{3} + \frac{6 \cdot 3}{3} + \frac{- 5 \cdot 3}{3}}{9}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{8 + 6 \cdot 3 - 5 \cdot 3}{3}}{9}$

Step 7

Simplify each term.

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Step 7.1

Multiply $6$ by $3$ .

$\frac{\frac{8 + 18 - 5 \cdot 3}{3}}{9}$

Step 7.2

Multiply $- 5$ by $3$ .

$\frac{\frac{8 + 18 - 15}{3}}{9}$

Step 8

Simplify by adding and subtracting.

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Step 8.1

Add $8$ and $18$ .

$\frac{\frac{26 - 15}{3}}{9}$

Step 8.2

Subtract $15$ from $26$ .

$\frac{\frac{11}{3}}{9}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{3} \cdot \frac{1}{9}$

Step 10

Multiply $\frac{11}{3} \cdot \frac{1}{9}$ .

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Step 10.1

Multiply $\frac{11}{3}$ by $\frac{1}{9}$ .

$\frac{11}{3 \cdot 9}$

Step 10.2

Multiply $3$ by $9$ .

$\frac{11}{27}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{27}$

Decimal Form:

$0.\overline{407}$