Evaluate 9/10-(-5/3)

$\frac{9}{10} - (- \frac{5}{3})$

Step 1

Multiply $- (- \frac{5}{3})$ .

Multiply $- 1$ by $- 1$ .

$\frac{9}{10} + 1 (\frac{5}{3})$

Multiply $\frac{5}{3}$ by $1$ .

$\frac{9}{10} + \frac{5}{3}$

Step 2

To write $\frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{10} \cdot \frac{3}{3} + \frac{5}{3}$

Step 3

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{9}{10} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{10}{10}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{10}$ by $\frac{3}{3}$ .

$\frac{9 \cdot 3}{10 \cdot 3} + \frac{5}{3} \cdot \frac{10}{10}$

Multiply $10$ by $3$ .

$\frac{9 \cdot 3}{30} + \frac{5}{3} \cdot \frac{10}{10}$

Multiply $\frac{5}{3}$ by $\frac{10}{10}$ .

$\frac{9 \cdot 3}{30} + \frac{5 \cdot 10}{3 \cdot 10}$

Multiply $3$ by $10$ .

$\frac{9 \cdot 3}{30} + \frac{5 \cdot 10}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 + 5 \cdot 10}{30}$

Step 6

Simplify the numerator.

Multiply $9$ by $3$ .

$\frac{27 + 5 \cdot 10}{30}$

Multiply $5$ by $10$ .

$\frac{27 + 50}{30}$

Add $27$ and $50$ .

$\frac{77}{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{30}$

Decimal Form:

$2.5\overline{6}$

Mixed Number Form:

$2 \frac{17}{30}$