Find the Exact Value -2 1/3-(-5)

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

Step 1

Convert $2 \frac{1}{3}$ to an improper fraction.

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

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

Add $2$ and $\frac{1}{3}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $2$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$- \frac{6 + 1}{3} - (- 5)$

Add $6$ and $1$ .

$- \frac{7}{3} - (- 5)$

Step 2

Multiply $- 1$ by $- 5$ .

$- \frac{7}{3} + 5$

Step 3

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

$- \frac{7}{3} + 5 \cdot \frac{3}{3}$

Step 4

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

$- \frac{7}{3} + \frac{5 \cdot 3}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 7 + 5 \cdot 3}{3}$

Step 6

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{- 7 + 15}{3}$

Add $- 7$ and $15$ .

$\frac{8}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$