Basic Math Examples

\frac{1}{30} + \frac{1}{20}

$\frac{1}{30} + \frac{1}{20}$

Step 1

To write

\frac{1}{30}

$\frac{1}{30}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{1}{30} \cdot \frac{2}{2} + \frac{1}{20}

$\frac{1}{30} \cdot \frac{2}{2} + \frac{1}{20}$

Step 2

To write

\frac{1}{20}

$\frac{1}{20}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{1}{30} \cdot \frac{2}{2} + \frac{1}{20} \cdot \frac{3}{3}

$\frac{1}{30} \cdot \frac{2}{2} + \frac{1}{20} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

60

$60$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{1}{30}

$\frac{1}{30}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2}{30 \cdot 2} + \frac{1}{20} \cdot \frac{3}{3}

$\frac{2}{30 \cdot 2} + \frac{1}{20} \cdot \frac{3}{3}$

Step 3.2

Multiply

30

$30$ by

2

$2$ .

\frac{2}{60} + \frac{1}{20} \cdot \frac{3}{3}

$\frac{2}{60} + \frac{1}{20} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{1}{20}

$\frac{1}{20}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2}{60} + \frac{3}{20 \cdot 3}

$\frac{2}{60} + \frac{3}{20 \cdot 3}$

Step 3.4

Multiply

20

$20$ by

3

$3$ .

\frac{2}{60} + \frac{3}{60}

$\frac{2}{60} + \frac{3}{60}$

\frac{2}{60} + \frac{3}{60}

$\frac{2}{60} + \frac{3}{60}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

\frac{2 + 3}{60}

$\frac{2 + 3}{60}$

Step 4.2

Add

2

$2$ and

3

$3$ .

\frac{5}{60}

$\frac{5}{60}$

\frac{5}{60}

$\frac{5}{60}$

Step 5

Cancel the common factor of

5

$5$ and

60

$60$ .

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Step 5.1

Factor

5

$5$ out of

5

$5$ .

\frac{5 (1)}{60}

$\frac{5 (1)}{60}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

5

$5$ out of

60

$60$ .

\frac{5 \cdot 1}{5 \cdot 12}

$\frac{5 \cdot 1}{5 \cdot 12}$

Step 5.2.2

Cancel the common factor.

$\frac{5 \cdot 1}{5 \cdot 12}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{12}$

Decimal Form:

$0.08\overline{3}$