Basic Math Examples

$\frac{3}{6 y} - \frac{5}{11 y} + \frac{6}{12 y}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{6 y}$ by $\frac{22}{22}$ .

$\frac{3}{6 y} \cdot \frac{22}{22} - \frac{5}{11 y} + \frac{6}{12 y}$

Step 1.2

Multiply $\frac{3}{6 y}$ by $\frac{22}{22}$ .

$\frac{3 \cdot 22}{6 y \cdot 22} - \frac{5}{11 y} + \frac{6}{12 y}$

Step 1.3

Multiply $\frac{5}{11 y}$ by $\frac{12}{12}$ .

$\frac{3 \cdot 22}{6 y \cdot 22} - (\frac{5}{11 y} \cdot \frac{12}{12}) + \frac{6}{12 y}$

Step 1.4

Multiply $\frac{5}{11 y}$ by $\frac{12}{12}$ .

$\frac{3 \cdot 22}{6 y \cdot 22} - \frac{5 \cdot 12}{11 y \cdot 12} + \frac{6}{12 y}$

Step 1.5

Multiply $\frac{6}{12 y}$ by $\frac{11}{11}$ .

$\frac{3 \cdot 22}{6 y \cdot 22} - \frac{5 \cdot 12}{11 y \cdot 12} + \frac{6}{12 y} \cdot \frac{11}{11}$

Step 1.6

Multiply $\frac{6}{12 y}$ by $\frac{11}{11}$ .

$\frac{3 \cdot 22}{6 y \cdot 22} - \frac{5 \cdot 12}{11 y \cdot 12} + \frac{6 \cdot 11}{12 y \cdot 11}$

Step 1.7

Reorder the factors of $6 y \cdot 22$ .

$\frac{3 \cdot 22}{6 \cdot 22 y} - \frac{5 \cdot 12}{11 y \cdot 12} + \frac{6 \cdot 11}{12 y \cdot 11}$

Step 1.8

Multiply $6$ by $22$ .

$\frac{3 \cdot 22}{132 y} - \frac{5 \cdot 12}{11 y \cdot 12} + \frac{6 \cdot 11}{12 y \cdot 11}$

Step 1.9

Reorder the factors of $11 y \cdot 12$ .

$\frac{3 \cdot 22}{132 y} - \frac{5 \cdot 12}{11 \cdot 12 y} + \frac{6 \cdot 11}{12 y \cdot 11}$

Step 1.10

Multiply $11$ by $12$ .

$\frac{3 \cdot 22}{132 y} - \frac{5 \cdot 12}{132 y} + \frac{6 \cdot 11}{12 y \cdot 11}$

Step 1.11

Reorder the factors of $12 y \cdot 11$ .

$\frac{3 \cdot 22}{132 y} - \frac{5 \cdot 12}{132 y} + \frac{6 \cdot 11}{11 \cdot 12 y}$

Step 1.12

Multiply $11$ by $12$ .

$\frac{3 \cdot 22}{132 y} - \frac{5 \cdot 12}{132 y} + \frac{6 \cdot 11}{132 y}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 22 - 5 \cdot 12 + 6 \cdot 11}{132 y}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $22$ .

$\frac{66 - 5 \cdot 12 + 6 \cdot 11}{132 y}$

Step 3.2

Multiply $- 5$ by $12$ .

$\frac{66 - 60 + 6 \cdot 11}{132 y}$

Step 3.3

Multiply $6$ by $11$ .

$\frac{66 - 60 + 66}{132 y}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $60$ from $66$ .

$\frac{6 + 66}{132 y}$

Step 4.2

Add $6$ and $66$ .

$\frac{72}{132 y}$

Step 4.3

Cancel the common factor of $72$ and $132$ .

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Step 4.3.1

Factor $12$ out of $72$ .

$\frac{12 (6)}{132 y}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $12$ out of $132 y$ .

$\frac{12 (6)}{12 (11 y)}$

Step 4.3.2.2

Cancel the common factor.

$\frac{12 \cdot 6}{12 (11 y)}$

Step 4.3.2.3

Rewrite the expression.

$\frac{6}{11 y}$