Basic Math Examples

$\frac{8}{- 9} + \frac{- 9}{5}$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{8}{9} + \frac{- 9}{5}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{8}{9} - \frac{9}{5}$

Step 2

To write $- \frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{8}{9} \cdot \frac{5}{5} - \frac{9}{5}$

Step 3

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

$- \frac{8}{9} \cdot \frac{5}{5} - \frac{9}{5} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{8}{9}$ by $\frac{5}{5}$ .

$- \frac{8 \cdot 5}{9 \cdot 5} - \frac{9}{5} \cdot \frac{9}{9}$

Step 4.2

Multiply $9$ by $5$ .

$- \frac{8 \cdot 5}{45} - \frac{9}{5} \cdot \frac{9}{9}$

Step 4.3

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

$- \frac{8 \cdot 5}{45} - \frac{9 \cdot 9}{5 \cdot 9}$

Step 4.4

Multiply $5$ by $9$ .

$- \frac{8 \cdot 5}{45} - \frac{9 \cdot 9}{45}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 5 - 9 \cdot 9}{45}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 8$ by $5$ .

$\frac{- 40 - 9 \cdot 9}{45}$

Step 6.2

Multiply $- 9$ by $9$ .

$\frac{- 40 - 81}{45}$

Step 6.3

Subtract $81$ from $- 40$ .

$\frac{- 121}{45}$

Step 7

Move the negative in front of the fraction.

$- \frac{121}{45}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{121}{45}$

Decimal Form:

$- 2.6\overline{8}$

Mixed Number Form:

$- 2 \frac{31}{45}$