Basic Math Examples

\frac{9}{10} - \frac{5}{6}

$\frac{9}{10} - \frac{5}{6}$

Step 1

To write

\frac{9}{10}

$\frac{9}{10}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{9}{10} \cdot \frac{3}{3} - \frac{5}{6}

$\frac{9}{10} \cdot \frac{3}{3} - \frac{5}{6}$

Step 2

To write

- \frac{5}{6}

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{10} \cdot \frac{3}{3} - \frac{5}{6} \cdot \frac{5}{5}

$\frac{9}{10} \cdot \frac{3}{3} - \frac{5}{6} \cdot \frac{5}{5}$

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{9}{10}

$\frac{9}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{9 \cdot 3}{10 \cdot 3} - \frac{5}{6} \cdot \frac{5}{5}

$\frac{9 \cdot 3}{10 \cdot 3} - \frac{5}{6} \cdot \frac{5}{5}$

Step 3.2

Multiply

10

$10$ by

3

$3$ .

\frac{9 \cdot 3}{30} - \frac{5}{6} \cdot \frac{5}{5}

$\frac{9 \cdot 3}{30} - \frac{5}{6} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9 \cdot 3}{30} - \frac{5 \cdot 5}{6 \cdot 5}

$\frac{9 \cdot 3}{30} - \frac{5 \cdot 5}{6 \cdot 5}$

Step 3.4

Multiply

6

$6$ by

5

$5$ .

\frac{9 \cdot 3}{30} - \frac{5 \cdot 5}{30}

$\frac{9 \cdot 3}{30} - \frac{5 \cdot 5}{30}$

\frac{9 \cdot 3}{30} - \frac{5 \cdot 5}{30}

$\frac{9 \cdot 3}{30} - \frac{5 \cdot 5}{30}$

Step 4

Combine the numerators over the common denominator.

\frac{9 \cdot 3 - 5 \cdot 5}{30}

$\frac{9 \cdot 3 - 5 \cdot 5}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

9

$9$ by

3

$3$ .

\frac{27 - 5 \cdot 5}{30}

$\frac{27 - 5 \cdot 5}{30}$

Step 5.2

Multiply

- 5

$- 5$ by

5

$5$ .

\frac{27 - 25}{30}

$\frac{27 - 25}{30}$

Step 5.3

Subtract

25

$25$ from

27

$27$ .

\frac{2}{30}

$\frac{2}{30}$

\frac{2}{30}

$\frac{2}{30}$

Step 6

Cancel the common factor of

2

$2$ and

30

$30$ .

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Step 6.1

Factor

2

$2$ out of

2

$2$ .

\frac{2 (1)}{30}

$\frac{2 (1)}{30}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

2

$2$ out of

30

$30$ .

\frac{2 \cdot 1}{2 \cdot 15}

$\frac{2 \cdot 1}{2 \cdot 15}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 15}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15}$

Decimal Form:

$0.0\overline{6}$