Simplify 12/11-(-2/3)

$\frac{12}{11} - (- \frac{2}{3})$

Step 1

Multiply $- (- \frac{2}{3})$ .

Multiply $- 1$ by $- 1$ .

$\frac{12}{11} + 1 (\frac{2}{3})$

Multiply $\frac{2}{3}$ by $1$ .

$\frac{12}{11} + \frac{2}{3}$

Step 2

To write $\frac{12}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{12}{11} \cdot \frac{3}{3} + \frac{2}{3}$

Step 3

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{12}{11} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{11}{11}$

Step 4

Write each expression with a common denominator of $33$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{12}{11}$ by $\frac{3}{3}$ .

$\frac{12 \cdot 3}{11 \cdot 3} + \frac{2}{3} \cdot \frac{11}{11}$

Multiply $11$ by $3$ .

$\frac{12 \cdot 3}{33} + \frac{2}{3} \cdot \frac{11}{11}$

Multiply $\frac{2}{3}$ by $\frac{11}{11}$ .

$\frac{12 \cdot 3}{33} + \frac{2 \cdot 11}{3 \cdot 11}$

Multiply $3$ by $11$ .

$\frac{12 \cdot 3}{33} + \frac{2 \cdot 11}{33}$

Step 5

Combine the numerators over the common denominator.

$\frac{12 \cdot 3 + 2 \cdot 11}{33}$

Step 6

Simplify the numerator.

Multiply $12$ by $3$ .

$\frac{36 + 2 \cdot 11}{33}$

Multiply $2$ by $11$ .

$\frac{36 + 22}{33}$

Add $36$ and $22$ .

$\frac{58}{33}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{58}{33}$

Decimal Form:

$1.\overline{75}$

Mixed Number Form:

$1 \frac{25}{33}$