Pre-Algebra Examples

$(\frac{5}{6} - \frac{1}{5}) \div \frac{4}{5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{5}{6} - \frac{1}{5}) \frac{5}{4}$

Step 2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{5}{6} \cdot \frac{5}{5} - \frac{1}{5}) \frac{5}{4}$

Step 3

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(\frac{5}{6} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{6}{6}) \frac{5}{4}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$(\frac{5 \cdot 5}{6 \cdot 5} - \frac{1}{5} \cdot \frac{6}{6}) \frac{5}{4}$

Step 4.2

Multiply $6$ by $5$ .

$(\frac{5 \cdot 5}{30} - \frac{1}{5} \cdot \frac{6}{6}) \frac{5}{4}$

Step 4.3

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

$(\frac{5 \cdot 5}{30} - \frac{6}{5 \cdot 6}) \frac{5}{4}$

Step 4.4

Multiply $5$ by $6$ .

$(\frac{5 \cdot 5}{30} - \frac{6}{30}) \frac{5}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 6}{30} \cdot \frac{5}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $5$ .

$\frac{25 - 6}{30} \cdot \frac{5}{4}$

Step 6.2

Subtract $6$ from $25$ .

$\frac{19}{30} \cdot \frac{5}{4}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Factor $5$ out of $30$ .

$\frac{19}{5 (6)} \cdot \frac{5}{4}$

Step 7.2

Cancel the common factor.

$\frac{19}{5 \cdot 6} \cdot \frac{5}{4}$

Step 7.3

Rewrite the expression.

$\frac{19}{6} \cdot \frac{1}{4}$

Step 8

Multiply $\frac{19}{6}$ by $\frac{1}{4}$ .

$\frac{19}{6 \cdot 4}$

Step 9

Multiply $6$ by $4$ .

$\frac{19}{24}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{24}$

Decimal Form:

$0.791\overline{6}$