Basic Math Examples

$({(\frac{2}{3})}^{2} \div \frac{9}{16}) \cdot \frac{1}{6} + \sqrt[3]{8} - \frac{5}{2}$

Step 1

Simplify each term.

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Step 1.1

Combine.

$\frac{{(\frac{2}{3})}^{2} \cdot 1}{\frac{9}{16} \cdot 6} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.2

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

$\frac{{(\frac{2}{3})}^{2}}{\frac{9}{16} \cdot 6} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.3

Combine $\frac{9}{16}$ and $6$ .

$\frac{{(\frac{2}{3})}^{2}}{\frac{9 \cdot 6}{16}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.4

Multiply $9$ by $6$ .

$\frac{{(\frac{2}{3})}^{2}}{\frac{54}{16}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

$\frac{\frac{2^{2}}{3^{2}}}{\frac{54}{16}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.5.2

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

$\frac{\frac{4}{3^{2}}}{\frac{54}{16}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.5.3

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

$\frac{\frac{4}{9}}{\frac{54}{16}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.6

Cancel the common factor of $54$ and $16$ .

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Step 1.6.1

Factor $2$ out of $54$ .

$\frac{\frac{4}{9}}{\frac{2 (27)}{16}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $16$ .

$\frac{\frac{4}{9}}{\frac{2 \cdot 27}{2 \cdot 8}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.6.2.2

Cancel the common factor.

$\frac{\frac{4}{9}}{\frac{2 \cdot 27}{2 \cdot 8}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.6.2.3

Rewrite the expression.

$\frac{\frac{4}{9}}{\frac{27}{8}} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.7

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{9} \cdot \frac{8}{27} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.8

Multiply $\frac{4}{9} \cdot \frac{8}{27}$ .

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Step 1.8.1

Multiply $\frac{4}{9}$ by $\frac{8}{27}$ .

$\frac{4 \cdot 8}{9 \cdot 27} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.8.2

Multiply $4$ by $8$ .

$\frac{32}{9 \cdot 27} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.8.3

Multiply $9$ by $27$ .

$\frac{32}{243} + \sqrt[3]{8} - \frac{5}{2}$

Step 1.9

Rewrite $8$ as $2^{3}$ .

$\frac{32}{243} + \sqrt[3]{2^{3}} - \frac{5}{2}$

Step 1.10

Pull terms out from under the radical, assuming real numbers.

$\frac{32}{243} + 2 - \frac{5}{2}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{32}{243}$ by $\frac{2}{2}$ .

$\frac{32}{243} \cdot \frac{2}{2} + 2 - \frac{5}{2}$

Step 2.2

Multiply $\frac{32}{243}$ by $\frac{2}{2}$ .

$\frac{32 \cdot 2}{243 \cdot 2} + 2 - \frac{5}{2}$

Step 2.3

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

$\frac{32 \cdot 2}{243 \cdot 2} + \frac{2}{1} - \frac{5}{2}$

Step 2.4

Multiply $\frac{2}{1}$ by $\frac{486}{486}$ .

$\frac{32 \cdot 2}{243 \cdot 2} + \frac{2}{1} \cdot \frac{486}{486} - \frac{5}{2}$

Step 2.5

Multiply $\frac{2}{1}$ by $\frac{486}{486}$ .

$\frac{32 \cdot 2}{243 \cdot 2} + \frac{2 \cdot 486}{486} - \frac{5}{2}$

Step 2.6

Multiply $\frac{5}{2}$ by $\frac{243}{243}$ .

$\frac{32 \cdot 2}{243 \cdot 2} + \frac{2 \cdot 486}{486} - (\frac{5}{2} \cdot \frac{243}{243})$

Step 2.7

Multiply $\frac{5}{2}$ by $\frac{243}{243}$ .

$\frac{32 \cdot 2}{243 \cdot 2} + \frac{2 \cdot 486}{486} - \frac{5 \cdot 243}{2 \cdot 243}$

Step 2.8

Reorder the factors of $243 \cdot 2$ .

$\frac{32 \cdot 2}{2 \cdot 243} + \frac{2 \cdot 486}{486} - \frac{5 \cdot 243}{2 \cdot 243}$

Step 2.9

Multiply $2$ by $243$ .

$\frac{32 \cdot 2}{486} + \frac{2 \cdot 486}{486} - \frac{5 \cdot 243}{2 \cdot 243}$

Step 2.10

Multiply $2$ by $243$ .

$\frac{32 \cdot 2}{486} + \frac{2 \cdot 486}{486} - \frac{5 \cdot 243}{486}$

Step 3

Combine the numerators over the common denominator.

$\frac{32 \cdot 2 + 2 \cdot 486 - 5 \cdot 243}{486}$

Step 4

Simplify each term.

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Step 4.1

Multiply $32$ by $2$ .

$\frac{64 + 2 \cdot 486 - 5 \cdot 243}{486}$

Step 4.2

Multiply $2$ by $486$ .

$\frac{64 + 972 - 5 \cdot 243}{486}$

Step 4.3

Multiply $- 5$ by $243$ .

$\frac{64 + 972 - 1215}{486}$

Step 5

Simplify the expression.

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Step 5.1

Add $64$ and $972$ .

$\frac{1036 - 1215}{486}$

Step 5.2

Subtract $1215$ from $1036$ .

$\frac{- 179}{486}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{179}{486}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{179}{486}$

Decimal Form:

$- 0.36831275 \dots$