Pre-Algebra Examples

$\frac{25}{32} \div (\frac{1}{2} - \frac{9}{8})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{25}{32}}{\frac{1}{2} - \frac{9}{8}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{32} \cdot \frac{1}{\frac{1}{2} - \frac{9}{8}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25}{32} \cdot \frac{1}{\frac{1}{2} \cdot \frac{4}{4} - \frac{9}{8}}$

Step 3.2

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

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Step 3.2.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$\frac{25}{32} \cdot \frac{1}{\frac{4}{2 \cdot 4} - \frac{9}{8}}$

Step 3.2.2

Multiply $2$ by $4$ .

$\frac{25}{32} \cdot \frac{1}{\frac{4}{8} - \frac{9}{8}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{25}{32} \cdot \frac{1}{\frac{4 - 9}{8}}$

Step 3.4

Subtract $9$ from $4$ .

$\frac{25}{32} \cdot \frac{1}{\frac{- 5}{8}}$

Step 3.5

Move the negative in front of the fraction.

$\frac{25}{32} \cdot \frac{1}{- \frac{5}{8}}$

Step 4

Cancel the common factor of $1$ and $- 1$ .

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Step 4.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{25}{32} \cdot \frac{- 1 (- 1)}{- \frac{5}{8}}$

Step 4.2

Move the negative in front of the fraction.

$\frac{25}{32} (- \frac{1}{\frac{5}{8}})$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{32} (- (1 (\frac{8}{5})))$

Step 6

Multiply $\frac{8}{5}$ by $1$ .

$\frac{25}{32} (- \frac{8}{5})$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$\frac{25}{32} \cdot \frac{- 8}{5}$

Step 7.2

Factor $5$ out of $25$ .

$\frac{5 (5)}{32} \cdot \frac{- 8}{5}$

Step 7.3

Cancel the common factor.

$\frac{5 \cdot 5}{32} \cdot \frac{- 8}{5}$

Step 7.4

Rewrite the expression.

$\frac{5}{32} \cdot - 8$

Step 8

Cancel the common factor of $8$ .

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Step 8.1

Factor $8$ out of $32$ .

$\frac{5}{8 (4)} \cdot - 8$

Step 8.2

Factor $8$ out of $- 8$ .

$\frac{5}{8 \cdot 4} \cdot (8 \cdot - 1)$

Step 8.3

Cancel the common factor.

$\frac{5}{8 \cdot 4} \cdot (8 \cdot - 1)$

Step 8.4

Rewrite the expression.

$\frac{5}{4} \cdot - 1$

Step 9

Combine $\frac{5}{4}$ and $- 1$ .

$\frac{5 \cdot - 1}{4}$

Step 10

Simplify the expression.

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Step 10.1

Multiply $5$ by $- 1$ .

$\frac{- 5}{4}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{5}{4}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{4}$

Decimal Form:

$- 1.25$

Mixed Number Form:

$- 1 \frac{1}{4}$