Basic Math Examples

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

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

Step 1

To write

\frac{1}{3}

$\frac{1}{3}$ as a fraction with a common denominator, multiply by

\frac{10}{10}

$\frac{10}{10}$ .

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

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

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

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

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}{3}

$\frac{1}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

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

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

Step 3.2

Multiply

3

$3$ by

10

$10$ .

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

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

Step 3.3

Multiply

\frac{3}{10}

$\frac{3}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3.4

Multiply

10

$10$ by

3

$3$ .

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

3

$3$ .

\frac{10 + 9}{30}

$\frac{10 + 9}{30}$

Step 5.2

Add

10

$10$ and

9

$9$ .

\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

$0.6\overline{3}$