Basic Math Examples

$\frac{13 + {(7 - 5)}^{3}}{5 - 9 \cdot \frac{3}{20}}$

Step 1

Simplify the numerator.

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Step 1.1

Subtract $5$ from $7$ .

$\frac{13 + 2^{3}}{5 - 9 \cdot \frac{3}{20}}$

Step 1.2

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

$\frac{13 + 8}{5 - 9 \cdot \frac{3}{20}}$

Step 1.3

Add $13$ and $8$ .

$\frac{21}{5 - 9 \cdot \frac{3}{20}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $- 9 (\frac{3}{20})$ .

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Step 2.1.1

Combine $- 9$ and $\frac{3}{20}$ .

$\frac{21}{5 + \frac{- 9 \cdot 3}{20}}$

Step 2.1.2

Multiply $- 9$ by $3$ .

$\frac{21}{5 + \frac{- 27}{20}}$

Step 2.2

Move the negative in front of the fraction.

$\frac{21}{5 - \frac{27}{20}}$

Step 2.3

To write $5$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{21}{5 \cdot \frac{20}{20} - \frac{27}{20}}$

Step 2.4

Combine $5$ and $\frac{20}{20}$ .

$\frac{21}{\frac{5 \cdot 20}{20} - \frac{27}{20}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{21}{\frac{5 \cdot 20 - 27}{20}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $5$ by $20$ .

$\frac{21}{\frac{100 - 27}{20}}$

Step 2.6.2

Subtract $27$ from $100$ .

$\frac{21}{\frac{73}{20}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$21 (\frac{20}{73})$

Step 4

Multiply $21 (\frac{20}{73})$ .

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Step 4.1

Combine $21$ and $\frac{20}{73}$ .

$\frac{21 \cdot 20}{73}$

Step 4.2

Multiply $21$ by $20$ .

$\frac{420}{73}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{420}{73}$

Decimal Form:

$5.75342465 \dots$

Mixed Number Form:

$5 \frac{55}{73}$