Basic Math Examples

$- 5 \frac{4}{3} - 20 {(- 5)}^{\frac{1}{3}}$

Step 1

Convert $5 \frac{4}{3}$ to an improper fraction.

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A mixed number is an addition of its whole and fractional parts.

$- (5 + \frac{4}{3}) - 20 {(- 5)}^{\frac{1}{3}}$

Add $5$ and $\frac{4}{3}$ .

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To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- (5 \cdot \frac{3}{3} + \frac{4}{3}) - 20 {(- 5)}^{\frac{1}{3}}$

Combine $5$ and $\frac{3}{3}$ .

$- (\frac{5 \cdot 3}{3} + \frac{4}{3}) - 20 {(- 5)}^{\frac{1}{3}}$

Combine the numerators over the common denominator.

$- \frac{5 \cdot 3 + 4}{3} - 20 {(- 5)}^{\frac{1}{3}}$

Simplify the numerator.

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Multiply $5$ by $3$ .

$- \frac{15 + 4}{3} - 20 {(- 5)}^{\frac{1}{3}}$

Add $15$ and $4$ .

$- \frac{19}{3} - 20 {(- 5)}^{\frac{1}{3}}$

Step 2

To write $- 20 {(- 5)}^{\frac{1}{3}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{19}{3} - 20 {(- 5)}^{\frac{1}{3}} \cdot \frac{3}{3}$

Step 3

Combine $- 20 {(- 5)}^{\frac{1}{3}}$ and $\frac{3}{3}$ .

$- \frac{19}{3} + \frac{- 20 {(- 5)}^{\frac{1}{3}} \cdot 3}{3}$

Step 4

Simplify the expression.

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Combine the numerators over the common denominator.

$\frac{- 19 - 20 {(- 5)}^{\frac{1}{3}} \cdot 3}{3}$

Multiply $3$ by $- 20$ .

$\frac{- 19 - 60 {(- 5)}^{\frac{1}{3}}}{3}$

Step 5

Rewrite $- 19$ as $- 1 (19)$ .

$\frac{- 1 (19) - 60 {(- 5)}^{\frac{1}{3}}}{3}$

Step 6

Factor $- 1$ out of $- 60 {(- 5)}^{\frac{1}{3}}$ .

$\frac{- 1 (19) - (60 {(- 5)}^{\frac{1}{3}})}{3}$

Step 7

Factor $- 1$ out of $- 1 (19) - (60 {(- 5)}^{\frac{1}{3}})$ .

$\frac{- 1 (19 + 60 {(- 5)}^{\frac{1}{3}})}{3}$

Step 8

Move the negative in front of the fraction.

$- \frac{19 + 60 {(- 5)}^{\frac{1}{3}}}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{19 + 60 {(- 5)}^{\frac{1}{3}}}{3}$

Decimal Form:

$27.86618560 \dots$