Pre-Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Write $- (- \frac{9}{8} - 9)$ as a fraction with denominator $1$ .

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

Step 1.6

Multiply $\frac{- (- \frac{9}{8} - 9)}{1}$ by $\frac{72}{72}$ .

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

Step 1.7

Multiply $\frac{- (- \frac{9}{8} - 9)}{1}$ by $\frac{72}{72}$ .

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

Step 1.8

Multiply $8$ by $9$ .

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

Step 1.9

Reorder the factors of $9 \cdot 8$ .

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

Step 1.10

Multiply $8$ by $9$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $- 9$ by $9$ .

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

Step 3.2

Multiply $- 8$ by $8$ .

$\frac{- 81 - 64 - (- \frac{9}{8} - 9) \cdot 72}{72}$

Step 3.3

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

$\frac{- 81 - 64 - (- \frac{9}{8} - 9 \cdot \frac{8}{8}) \cdot 72}{72}$

Step 3.4

Combine $- 9$ and $\frac{8}{8}$ .

$\frac{- 81 - 64 - (- \frac{9}{8} + \frac{- 9 \cdot 8}{8}) \cdot 72}{72}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 81 - 64 - \frac{- 9 - 9 \cdot 8}{8} \cdot 72}{72}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 9$ by $8$ .

$\frac{- 81 - 64 - \frac{- 9 - 72}{8} \cdot 72}{72}$

Step 3.6.2

Subtract $72$ from $- 9$ .

$\frac{- 81 - 64 - \frac{- 81}{8} \cdot 72}{72}$

Step 3.7

Cancel the common factor of $8$ .

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Step 3.7.1

Move the leading negative in $- \frac{- 81}{8}$ into the numerator.

$\frac{- 81 - 64 + \frac{81}{8} \cdot 72}{72}$

Step 3.7.2

Factor $8$ out of $72$ .

$\frac{- 81 - 64 + \frac{81}{8} \cdot (8 (9))}{72}$

Step 3.7.3

Cancel the common factor.

$\frac{- 81 - 64 + \frac{81}{8} \cdot (8 \cdot 9)}{72}$

Step 3.7.4

Rewrite the expression.

$\frac{- 81 - 64 + 81 \cdot 9}{72}$

Step 3.8

Multiply $81$ by $9$ .

$\frac{- 81 - 64 + 729}{72}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $64$ from $- 81$ .

$\frac{- 145 + 729}{72}$

Step 4.2

Add $- 145$ and $729$ .

$\frac{584}{72}$

Step 4.3

Cancel the common factor of $584$ and $72$ .

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Step 4.3.1

Factor $8$ out of $584$ .

$\frac{8 (73)}{72}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $8$ out of $72$ .

$\frac{8 \cdot 73}{8 \cdot 9}$

Step 4.3.2.2

Cancel the common factor.

$\frac{8 \cdot 73}{8 \cdot 9}$

Step 4.3.2.3

Rewrite the expression.

$\frac{73}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{73}{9}$

Decimal Form:

$8.\overline{1}$

Mixed Number Form:

$8 \frac{1}{9}$