Basic Math Examples

\frac{3}{10} + \frac{2}{3} - \frac{1}{2}

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

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{3}{10}

$\frac{3}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3}{10} \cdot \frac{3}{3} + \frac{2}{3} - \frac{1}{2}

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

Step 1.2

Multiply

\frac{3}{10}

$\frac{3}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3 \cdot 3}{10 \cdot 3} + \frac{2}{3} - \frac{1}{2}

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

Step 1.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{3 \cdot 3}{10 \cdot 3} + \frac{2}{3} \cdot \frac{10}{10} - \frac{1}{2}

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

Step 1.4

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{3 \cdot 3}{10 \cdot 3} + \frac{2 \cdot 10}{3 \cdot 10} - \frac{1}{2}

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

Step 1.5

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{15}{15}

$\frac{15}{15}$ .

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

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

Step 1.6

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{15}{15}

$\frac{15}{15}$ .

\frac{3 \cdot 3}{10 \cdot 3} + \frac{2 \cdot 10}{3 \cdot 10} - \frac{15}{2 \cdot 15}

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

Step 1.7

Reorder the factors of

10 \cdot 3

$10 \cdot 3$ .

\frac{3 \cdot 3}{3 \cdot 10} + \frac{2 \cdot 10}{3 \cdot 10} - \frac{15}{2 \cdot 15}

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

Step 1.8

Multiply

3

$3$ by

10

$10$ .

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

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

Step 1.9

Multiply

3

$3$ by

10

$10$ .

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

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

Step 1.10

Multiply

2

$2$ by

15

$15$ .

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

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

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

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

Step 2

Combine the numerators over the common denominator.

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

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

Step 3

Simplify each term.

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Step 3.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 + 2 \cdot 10 - 15}{30}

$\frac{9 + 2 \cdot 10 - 15}{30}$

Step 3.2

Multiply

2

$2$ by

10

$10$ .

\frac{9 + 20 - 15}{30}

$\frac{9 + 20 - 15}{30}$

\frac{9 + 20 - 15}{30}

$\frac{9 + 20 - 15}{30}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add

9

$9$ and

20

$20$ .

\frac{29 - 15}{30}

$\frac{29 - 15}{30}$

Step 4.2

Subtract

15

$15$ from

29

$29$ .

\frac{14}{30}

$\frac{14}{30}$

Step 4.3

Cancel the common factor of

14

$14$ and

30

$30$ .

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Step 4.3.1

Factor

2

$2$ out of

14

$14$ .

\frac{2 (7)}{30}

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

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor

$2$ out of

$30$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

$\frac{7}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{15}$

Decimal Form:

$0.4\overline{6}$