Basic Math Examples

\frac{1}{6} + \frac{3}{10}

$\frac{1}{6} + \frac{3}{10}$

Step 1

To write

\frac{1}{6}

$\frac{1}{6}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{1}{6} \cdot \frac{5}{5} + \frac{3}{10}

$\frac{1}{6} \cdot \frac{5}{5} + \frac{3}{10}$

Step 2

To write

\frac{3}{10}

$\frac{3}{10}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{1}{6} \cdot \frac{5}{5} + \frac{3}{10} \cdot \frac{3}{3}

$\frac{1}{6} \cdot \frac{5}{5} + \frac{3}{10} \cdot \frac{3}{3}$

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}{6}

$\frac{1}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5}{6 \cdot 5} + \frac{3}{10} \cdot \frac{3}{3}

$\frac{5}{6 \cdot 5} + \frac{3}{10} \cdot \frac{3}{3}$

Step 3.2

Multiply

6

$6$ by

5

$5$ .

\frac{5}{30} + \frac{3}{10} \cdot \frac{3}{3}

$\frac{5}{30} + \frac{3}{10} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{3}{10}

$\frac{3}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{30} + \frac{3 \cdot 3}{10 \cdot 3}

$\frac{5}{30} + \frac{3 \cdot 3}{10 \cdot 3}$

Step 3.4

Multiply

10

$10$ by

3

$3$ .

\frac{5}{30} + \frac{3 \cdot 3}{30}

$\frac{5}{30} + \frac{3 \cdot 3}{30}$

\frac{5}{30} + \frac{3 \cdot 3}{30}

$\frac{5}{30} + \frac{3 \cdot 3}{30}$

Step 4

Combine the numerators over the common denominator.

\frac{5 + 3 \cdot 3}{30}

$\frac{5 + 3 \cdot 3}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

3

$3$ .

\frac{5 + 9}{30}

$\frac{5 + 9}{30}$

Step 5.2

Add

5

$5$ and

9

$9$ .

\frac{14}{30}

$\frac{14}{30}$

\frac{14}{30}

$\frac{14}{30}$

Step 6

Cancel the common factor of

14

$14$ and

30

$30$ .

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Step 6.1

Factor

2

$2$ out of

14

$14$ .

\frac{2 (7)}{30}

$\frac{2 (7)}{30}$

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 7}{2 \cdot 15}

$\frac{2 \cdot 7}{2 \cdot 15}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 7}{2 \cdot 15}$

Step 6.2.3

Rewrite the expression.

$\frac{7}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{15}$

Decimal Form:

$0.4\overline{6}$