Pre-Algebra Examples

$\frac{3}{5} - \frac{2}{15} + \frac{1}{10}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{5}$ by $\frac{6}{6}$ .

$\frac{3}{5} \cdot \frac{6}{6} - \frac{2}{15} + \frac{1}{10}$

Step 1.2

Multiply $\frac{3}{5}$ by $\frac{6}{6}$ .

$\frac{3 \cdot 6}{5 \cdot 6} - \frac{2}{15} + \frac{1}{10}$

Step 1.3

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

$\frac{3 \cdot 6}{5 \cdot 6} - (\frac{2}{15} \cdot \frac{2}{2}) + \frac{1}{10}$

Step 1.4

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

$\frac{3 \cdot 6}{5 \cdot 6} - \frac{2 \cdot 2}{15 \cdot 2} + \frac{1}{10}$

Step 1.5

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 6}{5 \cdot 6} - \frac{2 \cdot 2}{15 \cdot 2} + \frac{1}{10} \cdot \frac{3}{3}$

Step 1.6

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

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

Step 1.7

Multiply $5$ by $6$ .

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

Step 1.8

Reorder the factors of $15 \cdot 2$ .

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

Step 1.9

Multiply $2$ by $15$ .

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

Step 1.10

Reorder the factors of $10 \cdot 3$ .

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

Step 1.11

Multiply $3$ by $10$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $6$ .

$\frac{18 - 2 \cdot 2 + 3}{30}$

Step 3.2

Multiply $- 2$ by $2$ .

$\frac{18 - 4 + 3}{30}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Subtract $4$ from $18$ .

$\frac{14 + 3}{30}$

Step 4.2

Add $14$ and $3$ .

$\frac{17}{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{30}$

Decimal Form:

$0.5\overline{6}$