Basic Math Examples

$- 9 (\frac{1}{36}) + 11 (\frac{11}{36}) + y (\frac{2}{3})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $9$ .

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Step 1.1.1

Factor $9$ out of $- 9$ .

$9 (- 1) \frac{1}{36} + 11 (\frac{11}{36}) + y (\frac{2}{3})$

Step 1.1.2

Factor $9$ out of $36$ .

$9 \cdot - 1 \frac{1}{9 \cdot 4} + 11 (\frac{11}{36}) + y (\frac{2}{3})$

Step 1.1.3

Cancel the common factor.

$9 \cdot - 1 \frac{1}{9 \cdot 4} + 11 (\frac{11}{36}) + y (\frac{2}{3})$

Step 1.1.4

Rewrite the expression.

$- 1 (\frac{1}{4}) + 11 (\frac{11}{36}) + y (\frac{2}{3})$

Step 1.2

Rewrite $- 1 (\frac{1}{4})$ as $- (\frac{1}{4})$ .

$- (\frac{1}{4}) + 11 (\frac{11}{36}) + y (\frac{2}{3})$

Step 1.3

Multiply $11 (\frac{11}{36})$ .

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Step 1.3.1

Combine $11$ and $\frac{11}{36}$ .

$- \frac{1}{4} + \frac{11 \cdot 11}{36} + y (\frac{2}{3})$

Step 1.3.2

Multiply $11$ by $11$ .

$- \frac{1}{4} + \frac{121}{36} + y (\frac{2}{3})$

Step 1.4

Combine $y$ and $\frac{2}{3}$ .

$- \frac{1}{4} + \frac{121}{36} + \frac{y \cdot 2}{3}$

Step 1.5

Move $2$ to the left of $y$ .

$- \frac{1}{4} + \frac{121}{36} + \frac{2 y}{3}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$- (\frac{1}{4} \cdot \frac{9}{9}) + \frac{121}{36} + \frac{2 y}{3}$

Step 2.2

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$- \frac{9}{4 \cdot 9} + \frac{121}{36} + \frac{2 y}{3}$

Step 2.3

Multiply $\frac{2 y}{3}$ by $\frac{12}{12}$ .

$- \frac{9}{4 \cdot 9} + \frac{121}{36} + \frac{2 y}{3} \cdot \frac{12}{12}$

Step 2.4

Multiply $\frac{2 y}{3}$ by $\frac{12}{12}$ .

$- \frac{9}{4 \cdot 9} + \frac{121}{36} + \frac{2 y \cdot 12}{3 \cdot 12}$

Step 2.5

Multiply $4$ by $9$ .

$- \frac{9}{36} + \frac{121}{36} + \frac{2 y \cdot 12}{3 \cdot 12}$

Step 2.6

Multiply $3$ by $12$ .

$- \frac{9}{36} + \frac{121}{36} + \frac{2 y \cdot 12}{36}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 9 + 121 + 2 y \cdot 12}{36}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $12$ by $2$ .

$\frac{- 9 + 121 + 24 y}{36}$

Step 4.2

Add $- 9$ and $121$ .

$\frac{112 + 24 y}{36}$

Step 5

Cancel the common factor of $112 + 24 y$ and $36$ .

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Step 5.1

Factor $4$ out of $112$ .

$\frac{4 (28) + 24 y}{36}$

Step 5.2

Factor $4$ out of $24 y$ .

$\frac{4 (28) + 4 (6 y)}{36}$

Step 5.3

Factor $4$ out of $4 (28) + 4 (6 y)$ .

$\frac{4 (28 + 6 y)}{36}$

Step 5.4

Cancel the common factors.

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Step 5.4.1

Factor $4$ out of $36$ .

$\frac{4 (28 + 6 y)}{4 \cdot 9}$

Step 5.4.2

Cancel the common factor.

$\frac{4 (28 + 6 y)}{4 \cdot 9}$

Step 5.4.3

Rewrite the expression.

$\frac{28 + 6 y}{9}$

Step 6

Factor $2$ out of $28 + 6 y$ .

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Step 6.1

Factor $2$ out of $28$ .

$\frac{2 (14) + 6 y}{9}$

Step 6.2

Factor $2$ out of $6 y$ .

$\frac{2 (14) + 2 (3 y)}{9}$

Step 6.3

Factor $2$ out of $2 (14) + 2 (3 y)$ .

$\frac{2 (14 + 3 y)}{9}$