Basic Math Examples

$\frac{- 9}{10} + \frac{- 1}{6}$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{9}{10} + \frac{- 1}{6}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{9}{10} - \frac{1}{6}$

Step 2

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

$- \frac{9}{10} \cdot \frac{3}{3} - \frac{1}{6}$

Step 3

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{9}{10} \cdot \frac{3}{3} - \frac{1}{6} \cdot \frac{5}{5}$

Step 4

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

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Step 4.1

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

$- \frac{9 \cdot 3}{10 \cdot 3} - \frac{1}{6} \cdot \frac{5}{5}$

Step 4.2

Multiply $10$ by $3$ .

$- \frac{9 \cdot 3}{30} - \frac{1}{6} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$- \frac{9 \cdot 3}{30} - \frac{5}{6 \cdot 5}$

Step 4.4

Multiply $6$ by $5$ .

$- \frac{9 \cdot 3}{30} - \frac{5}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 9 \cdot 3 - 5}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 9$ by $3$ .

$\frac{- 27 - 5}{30}$

Step 6.2

Subtract $5$ from $- 27$ .

$\frac{- 32}{30}$

Step 7

Cancel the common factor of $- 32$ and $30$ .

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Step 7.1

Factor $2$ out of $- 32$ .

$\frac{2 (- 16)}{30}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot - 16}{2 \cdot 15}$

Step 7.2.2

Cancel the common factor.

$\frac{2 \cdot - 16}{2 \cdot 15}$

Step 7.2.3

Rewrite the expression.

$\frac{- 16}{15}$

Step 8

Move the negative in front of the fraction.

$- \frac{16}{15}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{16}{15}$

Decimal Form:

$- 1.0\overline{6}$

Mixed Number Form:

$- 1 \frac{1}{15}$