Basic Math Examples

$36 + \frac{1}{2} \cdot (\frac{3}{11} + \frac{4}{22} - \frac{5}{33}) - \frac{6 o f \cdot 2}{66}$

Step 1

Simplify each term.

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Step 1.1

Find the common denominator.

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Step 1.1.1

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

$36 + \frac{1}{2} \cdot (\frac{3}{11} \cdot \frac{6}{6} + \frac{4}{22} - \frac{5}{33}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.2

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

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{11 \cdot 6} + \frac{4}{22} - \frac{5}{33}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.3

Multiply $\frac{4}{22}$ by $\frac{3}{3}$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{11 \cdot 6} + \frac{4}{22} \cdot \frac{3}{3} - \frac{5}{33}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.4

Multiply $\frac{4}{22}$ by $\frac{3}{3}$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{11 \cdot 6} + \frac{4 \cdot 3}{22 \cdot 3} - \frac{5}{33}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.5

Multiply $\frac{5}{33}$ by $\frac{2}{2}$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{11 \cdot 6} + \frac{4 \cdot 3}{22 \cdot 3} - (\frac{5}{33} \cdot \frac{2}{2})) - \frac{6 o f \cdot 2}{66}$

Step 1.1.6

Multiply $\frac{5}{33}$ by $\frac{2}{2}$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{11 \cdot 6} + \frac{4 \cdot 3}{22 \cdot 3} - \frac{5 \cdot 2}{33 \cdot 2}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.7

Reorder the factors of $11 \cdot 6$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{6 \cdot 11} + \frac{4 \cdot 3}{22 \cdot 3} - \frac{5 \cdot 2}{33 \cdot 2}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.8

Multiply $6$ by $11$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{66} + \frac{4 \cdot 3}{22 \cdot 3} - \frac{5 \cdot 2}{33 \cdot 2}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.9

Reorder the factors of $22 \cdot 3$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{66} + \frac{4 \cdot 3}{3 \cdot 22} - \frac{5 \cdot 2}{33 \cdot 2}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.10

Multiply $3$ by $22$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{66} + \frac{4 \cdot 3}{66} - \frac{5 \cdot 2}{33 \cdot 2}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.11

Reorder the factors of $33 \cdot 2$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{66} + \frac{4 \cdot 3}{66} - \frac{5 \cdot 2}{2 \cdot 33}) - \frac{6 o f \cdot 2}{66}$

Step 1.1.12

Multiply $2$ by $33$ .

$36 + \frac{1}{2} \cdot (\frac{3 \cdot 6}{66} + \frac{4 \cdot 3}{66} - \frac{5 \cdot 2}{66}) - \frac{6 o f \cdot 2}{66}$

Step 1.2

Combine the numerators over the common denominator.

$36 + \frac{1}{2} \cdot \frac{3 \cdot 6 + 4 \cdot 3 - 5 \cdot 2}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $3$ by $6$ .

$36 + \frac{1}{2} \cdot \frac{18 + 4 \cdot 3 - 5 \cdot 2}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.3.2

Multiply $4$ by $3$ .

$36 + \frac{1}{2} \cdot \frac{18 + 12 - 5 \cdot 2}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.3.3

Multiply $- 5$ by $2$ .

$36 + \frac{1}{2} \cdot \frac{18 + 12 - 10}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.4

Add $18$ and $12$ .

$36 + \frac{1}{2} \cdot \frac{30 - 10}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.5

Subtract $10$ from $30$ .

$36 + \frac{1}{2} \cdot \frac{20}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $20$ .

$36 + \frac{1}{2} \cdot \frac{2 (10)}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.6.2

Cancel the common factor.

$36 + \frac{1}{2} \cdot \frac{2 \cdot 10}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.6.3

Rewrite the expression.

$36 + \frac{10}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.7

Cancel the common factor of $10$ and $66$ .

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Step 1.7.1

Factor $2$ out of $10$ .

$36 + \frac{2 (5)}{66} - \frac{6 o f \cdot 2}{66}$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $2$ out of $66$ .

$36 + \frac{2 \cdot 5}{2 \cdot 33} - \frac{6 o f \cdot 2}{66}$

Step 1.7.2.2

Cancel the common factor.

$36 + \frac{2 \cdot 5}{2 \cdot 33} - \frac{6 o f \cdot 2}{66}$

Step 1.7.2.3

Rewrite the expression.

$36 + \frac{5}{33} - \frac{6 o f \cdot 2}{66}$

Step 1.8

Cancel the common factor of $6$ and $66$ .

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Step 1.8.1

Factor $6$ out of $6 o f \cdot 2$ .

$36 + \frac{5}{33} - \frac{6 (o f \cdot 2)}{66}$

Step 1.8.2

Cancel the common factors.

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Step 1.8.2.1

Factor $6$ out of $66$ .

$36 + \frac{5}{33} - \frac{6 (o f \cdot 2)}{6 \cdot 11}$

Step 1.8.2.2

Cancel the common factor.

$36 + \frac{5}{33} - \frac{6 (o f \cdot 2)}{6 \cdot 11}$

Step 1.8.2.3

Rewrite the expression.

$36 + \frac{5}{33} - \frac{o f \cdot 2}{11}$

Step 1.9

Move $2$ to the left of $o f$ .

$36 + \frac{5}{33} - \frac{2 o f}{11}$

Step 2

To write $36$ as a fraction with a common denominator, multiply by $\frac{33}{33}$ .

$36 \cdot \frac{33}{33} + \frac{5}{33} - \frac{2 o f}{11}$

Step 3

Combine $36$ and $\frac{33}{33}$ .

$\frac{36 \cdot 33}{33} + \frac{5}{33} - \frac{2 o f}{11}$

Step 4

Combine the numerators over the common denominator.

$\frac{36 \cdot 33 + 5}{33} - \frac{2 o f}{11}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $36$ by $33$ .

$\frac{1188 + 5}{33} - \frac{2 o f}{11}$

Step 5.2

Add $1188$ and $5$ .

$\frac{1193}{33} - \frac{2 o f}{11}$