Algebra Examples

$(- \frac{7}{8} - (\frac{3}{4})) - (\frac{3}{2} - \frac{9}{8})$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$- \frac{7}{8} - (\frac{3}{4} \cdot \frac{2}{2}) - (\frac{3}{2} - \frac{9}{8})$

Step 1.2

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$- \frac{7}{8} - \frac{3 \cdot 2}{4 \cdot 2} - (\frac{3}{2} - \frac{9}{8})$

Step 1.3

Write $- (\frac{3}{2} - \frac{9}{8})$ as a fraction with denominator $1$ .

$- \frac{7}{8} - \frac{3 \cdot 2}{4 \cdot 2} + \frac{- (\frac{3}{2} - \frac{9}{8})}{1}$

Step 1.4

Multiply $\frac{- (\frac{3}{2} - \frac{9}{8})}{1}$ by $\frac{8}{8}$ .

$- \frac{7}{8} - \frac{3 \cdot 2}{4 \cdot 2} + \frac{- (\frac{3}{2} - \frac{9}{8})}{1} \cdot \frac{8}{8}$

Step 1.5

Multiply $\frac{- (\frac{3}{2} - \frac{9}{8})}{1}$ by $\frac{8}{8}$ .

$- \frac{7}{8} - \frac{3 \cdot 2}{4 \cdot 2} + \frac{- (\frac{3}{2} - \frac{9}{8}) \cdot 8}{8}$

Step 1.6

Reorder the factors of $4 \cdot 2$ .

$- \frac{7}{8} - \frac{3 \cdot 2}{2 \cdot 4} + \frac{- (\frac{3}{2} - \frac{9}{8}) \cdot 8}{8}$

Step 1.7

Multiply $2$ by $4$ .

$- \frac{7}{8} - \frac{3 \cdot 2}{8} + \frac{- (\frac{3}{2} - \frac{9}{8}) \cdot 8}{8}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 7 - 3 \cdot 2 - (\frac{3}{2} - \frac{9}{8}) \cdot 8}{8}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 3$ by $2$ .

$\frac{- 7 - 6 - (\frac{3}{2} - \frac{9}{8}) \cdot 8}{8}$

Step 3.2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{- 7 - 6 - (\frac{3}{2} \cdot \frac{4}{4} - \frac{9}{8}) \cdot 8}{8}$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{- 7 - 6 - (\frac{3 \cdot 4}{2 \cdot 4} - \frac{9}{8}) \cdot 8}{8}$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{- 7 - 6 - (\frac{3 \cdot 4}{8} - \frac{9}{8}) \cdot 8}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 7 - 6 - \frac{3 \cdot 4 - 9}{8} \cdot 8}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $4$ .

$\frac{- 7 - 6 - \frac{12 - 9}{8} \cdot 8}{8}$

Step 3.5.2

Subtract $9$ from $12$ .

$\frac{- 7 - 6 - \frac{3}{8} \cdot 8}{8}$

Step 3.6

Cancel the common factor of $8$ .

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Step 3.6.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$\frac{- 7 - 6 + \frac{- 3}{8} \cdot 8}{8}$

Step 3.6.2

Cancel the common factor.

$\frac{- 7 - 6 + \frac{- 3}{8} \cdot 8}{8}$

Step 3.6.3

Rewrite the expression.

$\frac{- 7 - 6 - 3}{8}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $6$ from $- 7$ .

$\frac{- 13 - 3}{8}$

Step 4.2

Subtract $3$ from $- 13$ .

$\frac{- 16}{8}$

Step 4.3

Divide $- 16$ by $8$ .

$- 2$