Basic Math Examples

\frac{1}{10} + \frac{1}{15}

$\frac{1}{10} + \frac{1}{15}$

Step 1

To write

\frac{1}{10}

$\frac{1}{10}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{1}{10} \cdot \frac{3}{3} + \frac{1}{15}

$\frac{1}{10} \cdot \frac{3}{3} + \frac{1}{15}$

Step 2

To write

\frac{1}{15}

$\frac{1}{15}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{1}{10} \cdot \frac{3}{3} + \frac{1}{15} \cdot \frac{2}{2}

$\frac{1}{10} \cdot \frac{3}{3} + \frac{1}{15} \cdot \frac{2}{2}$

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{1}{10}

$\frac{1}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3}{10 \cdot 3} + \frac{1}{15} \cdot \frac{2}{2}

$\frac{3}{10 \cdot 3} + \frac{1}{15} \cdot \frac{2}{2}$

Step 3.2

Multiply

10

$10$ by

3

$3$ .

\frac{3}{30} + \frac{1}{15} \cdot \frac{2}{2}

$\frac{3}{30} + \frac{1}{15} \cdot \frac{2}{2}$

Step 3.3

Multiply

\frac{1}{15}

$\frac{1}{15}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{30} + \frac{2}{15 \cdot 2}

$\frac{3}{30} + \frac{2}{15 \cdot 2}$

Step 3.4

Multiply

15

$15$ by

2

$2$ .

\frac{3}{30} + \frac{2}{30}

$\frac{3}{30} + \frac{2}{30}$

\frac{3}{30} + \frac{2}{30}

$\frac{3}{30} + \frac{2}{30}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

\frac{3 + 2}{30}

$\frac{3 + 2}{30}$

Step 4.2

Add

3

$3$ and

2

$2$ .

\frac{5}{30}

$\frac{5}{30}$

\frac{5}{30}

$\frac{5}{30}$

Step 5

Cancel the common factor of

5

$5$ and

30

$30$ .

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Step 5.1

Factor

5

$5$ out of

5

$5$ .

\frac{5 (1)}{30}

$\frac{5 (1)}{30}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

5

$5$ out of

30

$30$ .

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{1}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$