Basic Math Examples

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

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

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

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

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

Step 1.2

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

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

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

Step 1.3

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.4

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.5

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 1.6

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 1.7

Multiply

3

$3$ by

10

$10$ .

\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{5 \cdot 6} - \frac{5}{6 \cdot 5}

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{5 \cdot 6} - \frac{5}{6 \cdot 5}$

Step 1.8

Multiply

5

$5$ by

6

$6$ .

\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{6 \cdot 5}

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{6 \cdot 5}$

Step 1.9

Reorder the factors of

6 \cdot 5

$6 \cdot 5$ .

\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{5 \cdot 6}

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{5 \cdot 6}$

Step 1.10

Multiply

5

$5$ by

6

$6$ .

\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{30}

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{30}$

\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{30}

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 6}{30} - \frac{5}{30}$

Step 2

Combine the numerators over the common denominator.

\frac{2 \cdot 10 + 3 \cdot 6 - 5}{30}

$\frac{2 \cdot 10 + 3 \cdot 6 - 5}{30}$

Step 3

Simplify each term.

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Step 3.1

Multiply

2

$2$ by

10

$10$ .

\frac{20 + 3 \cdot 6 - 5}{30}

$\frac{20 + 3 \cdot 6 - 5}{30}$

Step 3.2

Multiply

3

$3$ by

6

$6$ .

\frac{20 + 18 - 5}{30}

$\frac{20 + 18 - 5}{30}$

\frac{20 + 18 - 5}{30}

$\frac{20 + 18 - 5}{30}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add

20

$20$ and

18

$18$ .

\frac{38 - 5}{30}

$\frac{38 - 5}{30}$

Step 4.2

Subtract

5

$5$ from

38

$38$ .

\frac{33}{30}

$\frac{33}{30}$

Step 4.3

Cancel the common factor of

33

$33$ and

30

$30$ .

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Step 4.3.1

Factor

3

$3$ out of

33

$33$ .

\frac{3 (11)}{30}

$\frac{3 (11)}{30}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor

3

$3$ out of

30

$30$ .

\frac{3 \cdot 11}{3 \cdot 10}

$\frac{3 \cdot 11}{3 \cdot 10}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 \cdot 11}{3 \cdot 10}$

Step 4.3.2.3

Rewrite the expression.

$\frac{11}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{10}$

Decimal Form:

$1.1$

Mixed Number Form:

$1 \frac{1}{10}$