Evaluate 2 1/3+(-1 2/3)

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

Step 1

Remove parentheses.

$2 \frac{1}{3} - 1 \frac{2}{3}$

Step 2

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

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

$2 + \frac{1}{3} - 1 \frac{2}{3}$

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

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

$2 \cdot \frac{3}{3} + \frac{1}{3} - 1 \frac{2}{3}$

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

$\frac{2 \cdot 3}{3} + \frac{1}{3} - 1 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 1}{3} - 1 \frac{2}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 + 1}{3} - 1 \frac{2}{3}$

Add $6$ and $1$ .

$\frac{7}{3} - 1 \frac{2}{3}$

Step 3

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

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

$\frac{7}{3} - (1 + \frac{2}{3})$

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

Write $1$ as a fraction with a common denominator.

$\frac{7}{3} - (\frac{3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{7}{3} - \frac{3 + 2}{3}$

Add $3$ and $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Subtract $5$ from $7$ .

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$