Simplify -5/3+4 2/3

$- \frac{5}{3} + 4 \frac{2}{3}$

Step 1

Convert $4 \frac{2}{3}$ to an improper fraction.

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

$- \frac{5}{3} + 4 + \frac{2}{3}$

Add $4$ and $\frac{2}{3}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5}{3} + 4 \cdot \frac{3}{3} + \frac{2}{3}$

Combine $4$ and $\frac{3}{3}$ .

$- \frac{5}{3} + \frac{4 \cdot 3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$- \frac{5}{3} + \frac{4 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$- \frac{5}{3} + \frac{12 + 2}{3}$

Add $12$ and $2$ .

$- \frac{5}{3} + \frac{14}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 5 + 14}{3}$

Step 3

Simplify the expression.

Add $- 5$ and $14$ .

$\frac{9}{3}$

Divide $9$ by $3$ .

$3$