Basic Math Examples

\frac{3}{5} + \frac{2}{3} - \frac{1}{2}

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

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

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

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

Step 1.4

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

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

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

Step 1.5

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{15}{15}

$\frac{15}{15}$ .

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

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

Step 1.6

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{15}{15}

$\frac{15}{15}$ .

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

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

Step 1.7

Multiply

5

$5$ by

6

$6$ .

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

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

Step 1.8

Multiply

3

$3$ by

10

$10$ .

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

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

Step 1.9

Multiply

2

$2$ by

15

$15$ .

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

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

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

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

Step 2

Combine the numerators over the common denominator.

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

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

Step 3

Simplify each term.

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Step 3.1

Multiply

3

$3$ by

6

$6$ .

\frac{18 + 2 \cdot 10 - 15}{30}

$\frac{18 + 2 \cdot 10 - 15}{30}$

Step 3.2

Multiply

2

$2$ by

10

$10$ .

\frac{18 + 20 - 15}{30}

$\frac{18 + 20 - 15}{30}$

\frac{18 + 20 - 15}{30}

$\frac{18 + 20 - 15}{30}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add

18

$18$ and

20

$20$ .

\frac{38 - 15}{30}

$\frac{38 - 15}{30}$

Step 4.2

Subtract

15

$15$ from

38

$38$ .

\frac{23}{30}

$\frac{23}{30}$

\frac{23}{30}

$\frac{23}{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{23}{30}

$\frac{23}{30}$

Decimal Form:

0.7 ¯ 6

$0.7\overline{6}$