Pre-Algebra Examples

$\frac{25}{12} \div (\frac{1}{3} - \frac{7}{6})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{25}{12}}{\frac{1}{3} - \frac{7}{6}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{12} \cdot \frac{1}{\frac{1}{3} - \frac{7}{6}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{12} \cdot \frac{1}{\frac{1}{3} \cdot \frac{2}{2} - \frac{7}{6}}$

Step 3.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{25}{12} \cdot \frac{1}{\frac{2}{3 \cdot 2} - \frac{7}{6}}$

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{25}{12} \cdot \frac{1}{\frac{2}{6} - \frac{7}{6}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{25}{12} \cdot \frac{1}{\frac{2 - 7}{6}}$

Step 3.4

Subtract $7$ from $2$ .

$\frac{25}{12} \cdot \frac{1}{\frac{- 5}{6}}$

Step 3.5

Move the negative in front of the fraction.

$\frac{25}{12} \cdot \frac{1}{- \frac{5}{6}}$

Step 4

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

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Step 4.1

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

$\frac{25}{12} \cdot \frac{- 1 (- 1)}{- \frac{5}{6}}$

Step 4.2

Move the negative in front of the fraction.

$\frac{25}{12} (- \frac{1}{\frac{5}{6}})$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{12} (- (1 (\frac{6}{5})))$

Step 6

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

$\frac{25}{12} (- \frac{6}{5})$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{25}{12} \cdot \frac{- 6}{5}$

Step 7.2

Factor $5$ out of $25$ .

$\frac{5 (5)}{12} \cdot \frac{- 6}{5}$

Step 7.3

Cancel the common factor.

$\frac{5 \cdot 5}{12} \cdot \frac{- 6}{5}$

Step 7.4

Rewrite the expression.

$\frac{5}{12} \cdot - 6$

Step 8

Cancel the common factor of $6$ .

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Step 8.1

Factor $6$ out of $12$ .

$\frac{5}{6 (2)} \cdot - 6$

Step 8.2

Factor $6$ out of $- 6$ .

$\frac{5}{6 \cdot 2} \cdot (6 \cdot - 1)$

Step 8.3

Cancel the common factor.

$\frac{5}{6 \cdot 2} \cdot (6 \cdot - 1)$

Step 8.4

Rewrite the expression.

$\frac{5}{2} \cdot - 1$

Step 9

Combine $\frac{5}{2}$ and $- 1$ .

$\frac{5 \cdot - 1}{2}$

Step 10

Simplify the expression.

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Step 10.1

Multiply $5$ by $- 1$ .

$\frac{- 5}{2}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{5}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{2}$

Decimal Form:

$- 2.5$

Mixed Number Form:

$- 2 \frac{1}{2}$