Evaluate -5/9+(-7/12)

$- \frac{5}{9} + (- \frac{7}{12})$

Step 1

Remove parentheses.

$- \frac{5}{9} - \frac{7}{12}$

Step 2

To write $- \frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{5}{9} \cdot \frac{4}{4} - \frac{7}{12}$

Step 3

To write $- \frac{7}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5}{9} \cdot \frac{4}{4} - \frac{7}{12} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{9}$ by $\frac{4}{4}$ .

$- \frac{5 \cdot 4}{9 \cdot 4} - \frac{7}{12} \cdot \frac{3}{3}$

Multiply $9$ by $4$ .

$- \frac{5 \cdot 4}{36} - \frac{7}{12} \cdot \frac{3}{3}$

Multiply $\frac{7}{12}$ by $\frac{3}{3}$ .

$- \frac{5 \cdot 4}{36} - \frac{7 \cdot 3}{12 \cdot 3}$

Multiply $12$ by $3$ .

$- \frac{5 \cdot 4}{36} - \frac{7 \cdot 3}{36}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 4 - 7 \cdot 3}{36}$

Step 6

Simplify the numerator.

Multiply $- 5$ by $4$ .

$\frac{- 20 - 7 \cdot 3}{36}$

Multiply $- 7$ by $3$ .

$\frac{- 20 - 21}{36}$

Subtract $21$ from $- 20$ .

$\frac{- 41}{36}$

Step 7

Move the negative in front of the fraction.

$- \frac{41}{36}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{41}{36}$

Decimal Form:

$- 1.13\overline{8}$

Mixed Number Form:

$- 1 \frac{5}{36}$