Pre-Algebra Examples

$\frac{4}{\frac{5}{\frac{7}{8}}} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 1

Simplify the denominator.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{5 (\frac{8}{7})} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 1.2

Multiply $5 (\frac{8}{7})$ .

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Step 1.2.1

Combine $5$ and $\frac{8}{7}$ .

$\frac{4}{\frac{5 \cdot 8}{7}} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 1.2.2

Multiply $5$ by $8$ .

$\frac{4}{\frac{40}{7}} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$4 (\frac{7}{40}) \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Factor $4$ out of $40$ .

$4 \frac{7}{4 (10)} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 3.2

Cancel the common factor.

$4 \frac{7}{4 \cdot 10} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 3.3

Rewrite the expression.

$\frac{7}{10} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $10$ .

$\frac{7}{2 (5)} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 4.2

Cancel the common factor.

$\frac{7}{2 \cdot 5} \cdot \frac{2}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 4.3

Rewrite the expression.

$\frac{7}{5} \cdot \frac{1}{3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 5

Multiply $\frac{7}{5}$ by $\frac{1}{3}$ .

$\frac{7}{5 \cdot 3} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 6

Multiply $5$ by $3$ .

$\frac{7}{15} + \frac{17}{30} x^{3} \cdot \frac{17}{20}$

Step 7

Combine $\frac{17}{30}$ and $x^{3}$ .

$\frac{7}{15} + \frac{17 x^{3}}{30} \cdot \frac{17}{20}$

Step 8

Combine.

$\frac{7}{15} + \frac{17 x^{3} \cdot 17}{30 \cdot 20}$

Step 9

Multiply $17$ by $17$ .

$\frac{7}{15} + \frac{289 x^{3}}{30 \cdot 20}$

Step 10

Multiply $30$ by $20$ .

$\frac{7}{15} + \frac{289 x^{3}}{600}$