Evaluate -5/9+(-4/3)-2/3

$- \frac{5}{9} + (- \frac{4}{3}) - \frac{2}{3}$

Step 1

Combine fractions.

Remove parentheses.

$- \frac{5}{9} - \frac{4}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{- 5}{9} + \frac{- 4 - 2}{3}$

Subtract $2$ from $- 4$ .

$\frac{- 5}{9} + \frac{- 6}{3}$

Step 2

Simplify each term.

Move the negative in front of the fraction.

$- \frac{5}{9} + \frac{- 6}{3}$

Divide $- 6$ by $3$ .

$- \frac{5}{9} - 2$

Step 3

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{5}{9} - 2 \cdot \frac{9}{9}$

Step 4

Combine $- 2$ and $\frac{9}{9}$ .

$- \frac{5}{9} + \frac{- 2 \cdot 9}{9}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 5 - 2 \cdot 9}{9}$

Step 6

Simplify the numerator.

Multiply $- 2$ by $9$ .

$\frac{- 5 - 18}{9}$

Subtract $18$ from $- 5$ .

$\frac{- 23}{9}$

Step 7

Move the negative in front of the fraction.

$- \frac{23}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{23}{9}$

Decimal Form:

$- 2.\overline{5}$

Mixed Number Form:

$- 2 \frac{5}{9}$