Basic Math Examples

$\frac{1}{5} + \frac{3}{10} + \frac{6}{15}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{1}{5} \cdot \frac{6}{6} + \frac{3}{10} + \frac{6}{15}$

Step 1.2

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{6}{5 \cdot 6} + \frac{3}{10} + \frac{6}{15}$

Step 1.3

Multiply $\frac{3}{10}$ by $\frac{3}{3}$ .

$\frac{6}{5 \cdot 6} + \frac{3}{10} \cdot \frac{3}{3} + \frac{6}{15}$

Step 1.4

Multiply $\frac{3}{10}$ by $\frac{3}{3}$ .

$\frac{6}{5 \cdot 6} + \frac{3 \cdot 3}{10 \cdot 3} + \frac{6}{15}$

Step 1.5

Multiply $\frac{6}{15}$ by $\frac{2}{2}$ .

$\frac{6}{5 \cdot 6} + \frac{3 \cdot 3}{10 \cdot 3} + \frac{6}{15} \cdot \frac{2}{2}$

Step 1.6

Multiply $\frac{6}{15}$ by $\frac{2}{2}$ .

$\frac{6}{5 \cdot 6} + \frac{3 \cdot 3}{10 \cdot 3} + \frac{6 \cdot 2}{15 \cdot 2}$

Step 1.7

Multiply $5$ by $6$ .

$\frac{6}{30} + \frac{3 \cdot 3}{10 \cdot 3} + \frac{6 \cdot 2}{15 \cdot 2}$

Step 1.8

Reorder the factors of $10 \cdot 3$ .

$\frac{6}{30} + \frac{3 \cdot 3}{3 \cdot 10} + \frac{6 \cdot 2}{15 \cdot 2}$

Step 1.9

Multiply $3$ by $10$ .

$\frac{6}{30} + \frac{3 \cdot 3}{30} + \frac{6 \cdot 2}{15 \cdot 2}$

Step 1.10

Reorder the factors of $15 \cdot 2$ .

$\frac{6}{30} + \frac{3 \cdot 3}{30} + \frac{6 \cdot 2}{2 \cdot 15}$

Step 1.11

Multiply $2$ by $15$ .

$\frac{6}{30} + \frac{3 \cdot 3}{30} + \frac{6 \cdot 2}{30}$

Step 2

Combine the numerators over the common denominator.

$\frac{6 + 3 \cdot 3 + 6 \cdot 2}{30}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $3$ .

$\frac{6 + 9 + 6 \cdot 2}{30}$

Step 3.2

Multiply $6$ by $2$ .

$\frac{6 + 9 + 12}{30}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $6$ and $9$ .

$\frac{15 + 12}{30}$

Step 4.2

Add $15$ and $12$ .

$\frac{27}{30}$

Step 4.3

Cancel the common factor of $27$ and $30$ .

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Step 4.3.1

Factor $3$ out of $27$ .

$\frac{3 (9)}{30}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $3$ out of $30$ .

$\frac{3 \cdot 9}{3 \cdot 10}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 \cdot 9}{3 \cdot 10}$

Step 4.3.2.3

Rewrite the expression.

$\frac{9}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{10}$

Decimal Form:

$0.9$