Basic Math Examples

$(- \frac{9}{8} - \frac{8}{9}) - (- \frac{11}{10} - 9)$

Step 1

Find the common denominator.

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Step 1.1

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

$- (\frac{9}{8} \cdot \frac{9}{9}) - \frac{8}{9} - (- \frac{11}{10} - 9)$

Step 1.2

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

$- \frac{9 \cdot 9}{8 \cdot 9} - \frac{8}{9} - (- \frac{11}{10} - 9)$

Step 1.3

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

$- \frac{9 \cdot 9}{8 \cdot 9} - (\frac{8}{9} \cdot \frac{8}{8}) - (- \frac{11}{10} - 9)$

Step 1.4

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

$- \frac{9 \cdot 9}{8 \cdot 9} - \frac{8 \cdot 8}{9 \cdot 8} - (- \frac{11}{10} - 9)$

Step 1.5

Write $- (- \frac{11}{10} - 9)$ as a fraction with denominator $1$ .

$- \frac{9 \cdot 9}{8 \cdot 9} - \frac{8 \cdot 8}{9 \cdot 8} + \frac{- (- \frac{11}{10} - 9)}{1}$

Step 1.6

Multiply $\frac{- (- \frac{11}{10} - 9)}{1}$ by $\frac{72}{72}$ .

$- \frac{9 \cdot 9}{8 \cdot 9} - \frac{8 \cdot 8}{9 \cdot 8} + \frac{- (- \frac{11}{10} - 9)}{1} \cdot \frac{72}{72}$

Step 1.7

Multiply $\frac{- (- \frac{11}{10} - 9)}{1}$ by $\frac{72}{72}$ .

$- \frac{9 \cdot 9}{8 \cdot 9} - \frac{8 \cdot 8}{9 \cdot 8} + \frac{- (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 1.8

Multiply $8$ by $9$ .

$- \frac{9 \cdot 9}{72} - \frac{8 \cdot 8}{9 \cdot 8} + \frac{- (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 1.9

Reorder the factors of $9 \cdot 8$ .

$- \frac{9 \cdot 9}{72} - \frac{8 \cdot 8}{8 \cdot 9} + \frac{- (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 1.10

Multiply $8$ by $9$ .

$- \frac{9 \cdot 9}{72} - \frac{8 \cdot 8}{72} + \frac{- (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 9 \cdot 9 - 8 \cdot 8 - (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 9$ by $9$ .

$\frac{- 81 - 8 \cdot 8 - (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 3.2

Multiply $- 8$ by $8$ .

$\frac{- 81 - 64 - (- \frac{11}{10} - 9) \cdot 72}{72}$

Step 3.3

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

$\frac{- 81 - 64 - (- \frac{11}{10} - 9 \cdot \frac{10}{10}) \cdot 72}{72}$

Step 3.4

Combine $- 9$ and $\frac{10}{10}$ .

$\frac{- 81 - 64 - (- \frac{11}{10} + \frac{- 9 \cdot 10}{10}) \cdot 72}{72}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 81 - 64 - \frac{- 11 - 9 \cdot 10}{10} \cdot 72}{72}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 9$ by $10$ .

$\frac{- 81 - 64 - \frac{- 11 - 90}{10} \cdot 72}{72}$

Step 3.6.2

Subtract $90$ from $- 11$ .

$\frac{- 81 - 64 - \frac{- 101}{10} \cdot 72}{72}$

Step 3.7

Cancel the common factor of $2$ .

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Step 3.7.1

Move the leading negative in $- \frac{- 101}{10}$ into the numerator.

$\frac{- 81 - 64 + \frac{101}{10} \cdot 72}{72}$

Step 3.7.2

Factor $2$ out of $10$ .

$\frac{- 81 - 64 + \frac{101}{2 (5)} \cdot 72}{72}$

Step 3.7.3

Factor $2$ out of $72$ .

$\frac{- 81 - 64 + \frac{101}{2 \cdot 5} \cdot (2 \cdot 36)}{72}$

Step 3.7.4

Cancel the common factor.

$\frac{- 81 - 64 + \frac{101}{2 \cdot 5} \cdot (2 \cdot 36)}{72}$

Step 3.7.5

Rewrite the expression.

$\frac{- 81 - 64 + \frac{101}{5} \cdot 36}{72}$

Step 3.8

Combine $\frac{101}{5}$ and $36$ .

$\frac{- 81 - 64 + \frac{101 \cdot 36}{5}}{72}$

Step 3.9

Multiply $101$ by $36$ .

$\frac{- 81 - 64 + \frac{3636}{5}}{72}$

Step 4

Find the common denominator.

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Step 4.1

Write $- 81$ as a fraction with denominator $1$ .

$\frac{\frac{- 81}{1} - 64 + \frac{3636}{5}}{72}$

Step 4.2

Multiply $\frac{- 81}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{- 81}{1} \cdot \frac{5}{5} - 64 + \frac{3636}{5}}{72}$

Step 4.3

Multiply $\frac{- 81}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{- 81 \cdot 5}{5} - 64 + \frac{3636}{5}}{72}$

Step 4.4

Write $- 64$ as a fraction with denominator $1$ .

$\frac{\frac{- 81 \cdot 5}{5} + \frac{- 64}{1} + \frac{3636}{5}}{72}$

Step 4.5

Multiply $\frac{- 64}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{- 81 \cdot 5}{5} + \frac{- 64}{1} \cdot \frac{5}{5} + \frac{3636}{5}}{72}$

Step 4.6

Multiply $\frac{- 64}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{- 81 \cdot 5}{5} + \frac{- 64 \cdot 5}{5} + \frac{3636}{5}}{72}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{- 81 \cdot 5 - 64 \cdot 5 + 3636}{5}}{72}$

Step 6

Simplify each term.

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Step 6.1

Multiply $- 81$ by $5$ .

$\frac{\frac{- 405 - 64 \cdot 5 + 3636}{5}}{72}$

Step 6.2

Multiply $- 64$ by $5$ .

$\frac{\frac{- 405 - 320 + 3636}{5}}{72}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Subtract $320$ from $- 405$ .

$\frac{\frac{- 725 + 3636}{5}}{72}$

Step 7.2

Add $- 725$ and $3636$ .

$\frac{\frac{2911}{5}}{72}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{2911}{5} \cdot \frac{1}{72}$

Step 9

Multiply $\frac{2911}{5} \cdot \frac{1}{72}$ .

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Step 9.1

Multiply $\frac{2911}{5}$ by $\frac{1}{72}$ .

$\frac{2911}{5 \cdot 72}$

Step 9.2

Multiply $5$ by $72$ .

$\frac{2911}{360}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{2911}{360}$

Decimal Form:

$8.086\overline{1}$

Mixed Number Form:

$8 \frac{31}{360}$