Basic Math Examples

\frac{5}{6} - \frac{5}{9} \div \frac{4}{5}

$\frac{5}{6} - \frac{5}{9} \div \frac{4}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

\frac{5}{6} - (\frac{5}{9} \cdot \frac{5}{4})

$\frac{5}{6} - (\frac{5}{9} \cdot \frac{5}{4})$

Step 1.2

Multiply

\frac{5}{9} \cdot \frac{5}{4}

$\frac{5}{9} \cdot \frac{5}{4}$ .

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Step 1.2.1

Multiply

\frac{5}{9}

$\frac{5}{9}$ by

\frac{5}{4}

$\frac{5}{4}$ .

\frac{5}{6} - \frac{5 \cdot 5}{9 \cdot 4}

$\frac{5}{6} - \frac{5 \cdot 5}{9 \cdot 4}$

Step 1.2.2

Multiply

5

$5$ by

5

$5$ .

\frac{5}{6} - \frac{25}{9 \cdot 4}

$\frac{5}{6} - \frac{25}{9 \cdot 4}$

Step 1.2.3

Multiply

9

$9$ by

4

$4$ .

\frac{5}{6} - \frac{25}{36}

$\frac{5}{6} - \frac{25}{36}$

\frac{5}{6} - \frac{25}{36}

$\frac{5}{6} - \frac{25}{36}$

\frac{5}{6} - \frac{25}{36}

$\frac{5}{6} - \frac{25}{36}$

Step 2

To write

\frac{5}{6}

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

\frac{6}{6}

$\frac{6}{6}$ .

\frac{5}{6} \cdot \frac{6}{6} - \frac{25}{36}

$\frac{5}{6} \cdot \frac{6}{6} - \frac{25}{36}$

Step 3

Write each expression with a common denominator of

36

$36$ , 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{6}{6}

$\frac{6}{6}$ .

\frac{5 \cdot 6}{6 \cdot 6} - \frac{25}{36}

$\frac{5 \cdot 6}{6 \cdot 6} - \frac{25}{36}$

Step 3.2

Multiply

6

$6$ by

6

$6$ .

\frac{5 \cdot 6}{36} - \frac{25}{36}

$\frac{5 \cdot 6}{36} - \frac{25}{36}$

\frac{5 \cdot 6}{36} - \frac{25}{36}

$\frac{5 \cdot 6}{36} - \frac{25}{36}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 6 - 25}{36}

$\frac{5 \cdot 6 - 25}{36}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

6

$6$ .

\frac{30 - 25}{36}

$\frac{30 - 25}{36}$

Step 5.2

Subtract

25

$25$ from

30

$30$ .

\frac{5}{36}

$\frac{5}{36}$

\frac{5}{36}

$\frac{5}{36}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{5}{36}

$\frac{5}{36}$

Decimal Form:

0.13\overline{8}

$0.13\overline{8}$