Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{11}{3}$ by $\frac{6}{6}$ .

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

Step 1.2

Multiply $\frac{11}{3}$ by $\frac{6}{6}$ .

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

Step 1.3

Multiply $\frac{35}{6}$ by $\frac{3}{3}$ .

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

Step 1.4

Multiply $\frac{35}{6}$ by $\frac{3}{3}$ .

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

Step 1.5

Multiply $\frac{51}{9}$ by $\frac{2}{2}$ .

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

Step 1.6

Multiply $\frac{51}{9}$ by $\frac{2}{2}$ .

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

Step 1.7

Multiply $3$ by $6$ .

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

Step 1.8

Reorder the factors of $6 \cdot 3$ .

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

Step 1.9

Multiply $3$ by $6$ .

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

Step 1.10

Reorder the factors of $9 \cdot 2$ .

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

Step 1.11

Multiply $2$ by $9$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $11$ by $6$ .

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

Step 3.2

Multiply $- 35$ by $3$ .

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

Step 3.3

Multiply $51$ by $2$ .

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $105$ from $66$ .

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

Step 4.2

Add $- 39$ and $102$ .

$\frac{63}{18}$

Step 4.3

Cancel the common factor of $63$ and $18$ .

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Step 4.3.1

Factor $9$ out of $63$ .

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

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $9$ out of $18$ .

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

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:

$3 \frac{1}{2}$