Pre-Algebra Examples

\frac{5}{6} - \frac{1}{5}

$\frac{5}{6} - \frac{1}{5}$

Step 1

To write

\frac{5}{6}

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5}{6} \cdot \frac{5}{5} - \frac{1}{5}

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

Step 2

To write

- \frac{1}{5}

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

\frac{6}{6}

$\frac{6}{6}$ .

\frac{5}{6} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{6}{6}

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

Step 3

Write each expression with a common denominator of

30

$30$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5 \cdot 5}{6 \cdot 5} - \frac{1}{5} \cdot \frac{6}{6}

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

Step 3.2

Multiply

6

$6$ by

5

$5$ .

\frac{5 \cdot 5}{30} - \frac{1}{5} \cdot \frac{6}{6}

$\frac{5 \cdot 5}{30} - \frac{1}{5} \cdot \frac{6}{6}$

Step 3.3

Multiply

\frac{1}{5}

$\frac{1}{5}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 3.4

Multiply

5

$5$ by

6

$6$ .

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

5

$5$ .

\frac{25 - 6}{30}

$\frac{25 - 6}{30}$

Step 5.2

Subtract

6

$6$ from

25

$25$ .

\frac{19}{30}

$\frac{19}{30}$

\frac{19}{30}

$\frac{19}{30}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{19}{30}

$\frac{19}{30}$

Decimal Form:

0.6 ¯ 3

$0.6\overline{3}$