Basic Math Examples

\frac{11}{3} - \frac{35}{6} + \frac{51}{9}

$\frac{11}{3} - \frac{35}{6} + \frac{51}{9}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply

\frac{11}{3}

$\frac{11}{3}$ by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{11}{3} \cdot \frac{6}{6} - \frac{35}{6} + \frac{51}{9}

$\frac{11}{3} \cdot \frac{6}{6} - \frac{35}{6} + \frac{51}{9}$

Step 1.2

Multiply

\frac{11}{3}

$\frac{11}{3}$ by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{11 \cdot 6}{3 \cdot 6} - \frac{35}{6} + \frac{51}{9}

$\frac{11 \cdot 6}{3 \cdot 6} - \frac{35}{6} + \frac{51}{9}$

Step 1.3

Multiply

\frac{35}{6}

$\frac{35}{6}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{11 \cdot 6}{3 \cdot 6} - (\frac{35}{6} \cdot \frac{3}{3}) + \frac{51}{9}

$\frac{11 \cdot 6}{3 \cdot 6} - (\frac{35}{6} \cdot \frac{3}{3}) + \frac{51}{9}$

Step 1.4

Multiply

\frac{35}{6}

$\frac{35}{6}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{11 \cdot 6}{3 \cdot 6} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51}{9}

$\frac{11 \cdot 6}{3 \cdot 6} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51}{9}$

Step 1.5

Multiply

\frac{51}{9}

$\frac{51}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{11 \cdot 6}{3 \cdot 6} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51}{9} \cdot \frac{2}{2}

$\frac{11 \cdot 6}{3 \cdot 6} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51}{9} \cdot \frac{2}{2}$

Step 1.6

Multiply

\frac{51}{9}

$\frac{51}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{11 \cdot 6}{3 \cdot 6} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51 \cdot 2}{9 \cdot 2}

$\frac{11 \cdot 6}{3 \cdot 6} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51 \cdot 2}{9 \cdot 2}$

Step 1.7

Multiply

3

$3$ by

6

$6$ .

\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51 \cdot 2}{9 \cdot 2}

$\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{6 \cdot 3} + \frac{51 \cdot 2}{9 \cdot 2}$

Step 1.8

Reorder the factors of

6 \cdot 3

$6 \cdot 3$ .

\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{3 \cdot 6} + \frac{51 \cdot 2}{9 \cdot 2}

$\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{3 \cdot 6} + \frac{51 \cdot 2}{9 \cdot 2}$

Step 1.9

Multiply

3

$3$ by

6

$6$ .

\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{9 \cdot 2}

$\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{9 \cdot 2}$

Step 1.10

Reorder the factors of

9 \cdot 2

$9 \cdot 2$ .

\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{2 \cdot 9}

$\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{2 \cdot 9}$

Step 1.11

Multiply

2

$2$ by

9

$9$ .

\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{18}

$\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{18}$

\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{18}

$\frac{11 \cdot 6}{18} - \frac{35 \cdot 3}{18} + \frac{51 \cdot 2}{18}$

Step 2

Combine the numerators over the common denominator.

\frac{11 \cdot 6 - 35 \cdot 3 + 51 \cdot 2}{18}

$\frac{11 \cdot 6 - 35 \cdot 3 + 51 \cdot 2}{18}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply

11

$11$ by

6

$6$ .

\frac{66 - 35 \cdot 3 + 51 \cdot 2}{18}

$\frac{66 - 35 \cdot 3 + 51 \cdot 2}{18}$

Step 3.2

Multiply

- 35

$- 35$ by

3

$3$ .

\frac{66 - 105 + 51 \cdot 2}{18}

$\frac{66 - 105 + 51 \cdot 2}{18}$

Step 3.3

Multiply

51

$51$ by

2

$2$ .

\frac{66 - 105 + 102}{18}

$\frac{66 - 105 + 102}{18}$

\frac{66 - 105 + 102}{18}

$\frac{66 - 105 + 102}{18}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Subtract

105

$105$ from

66

$66$ .

\frac{- 39 + 102}{18}

$\frac{- 39 + 102}{18}$

Step 4.2

Add

- 39

$- 39$ and

102

$102$ .

\frac{63}{18}

$\frac{63}{18}$

Step 4.3

Cancel the common factor of

63

$63$ and

18

$18$ .

Tap for more steps...

Step 4.3.1

Factor

9

$9$ out of

63

$63$ .

\frac{9 (7)}{18}

$\frac{9 (7)}{18}$

Step 4.3.2

Cancel the common factors.

Tap for more steps...

Step 4.3.2.1

Factor

9

$9$ out of

18

$18$ .

\frac{9 \cdot 7}{9 \cdot 2}

$\frac{9 \cdot 7}{9 \cdot 2}$

Step 4.3.2.2

Cancel the common factor.

$\frac{9 \cdot 7}{9 \cdot 2}$

Step 4.3.2.3

Rewrite the expression.

$\frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{2}$

Decimal Form:

$3.5$

Mixed Number Form:

$3 \frac{1}{2}$