Pre-Algebra Examples

$\frac{1}{6} - \frac{\frac{11}{12}}{\frac{5}{6}} + \frac{5}{3}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{6}$ by $\frac{\frac{5}{6}}{\frac{5}{6}}$ .

$\frac{1}{6} \cdot \frac{\frac{5}{6}}{\frac{5}{6}} - \frac{\frac{11}{12}}{\frac{5}{6}} + \frac{5}{3}$

Step 1.2

Multiply $\frac{1}{6}$ by $\frac{\frac{5}{6}}{\frac{5}{6}}$ .

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

Step 1.3

Multiply $\frac{\frac{11}{12}}{\frac{5}{6}}$ by $\frac{6}{6}$ .

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

Step 1.4

Multiply $\frac{\frac{11}{12}}{\frac{5}{6}}$ by $\frac{6}{6}$ .

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

Step 1.5

Multiply $\frac{5}{3}$ by $\frac{\frac{2 \cdot 5}{6}}{\frac{2 \cdot 5}{6}}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{5}{6} \cdot 6} + \frac{5}{3} \cdot \frac{\frac{2 \cdot 5}{6}}{\frac{2 \cdot 5}{6}}$

Step 1.6

Multiply $\frac{5}{3}$ by $\frac{\frac{2 \cdot 5}{6}}{\frac{2 \cdot 5}{6}}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{5}{6} \cdot 6} + \frac{5 \frac{2 \cdot 5}{6}}{3 \frac{2 \cdot 5}{6}}$

Step 1.7

Reorder the factors of $\frac{5}{6} \cdot 6$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{6 (\frac{5}{6})} + \frac{5 \frac{2 \cdot 5}{6}}{3 \frac{2 \cdot 5}{6}}$

Step 1.8

Combine $6$ and $\frac{5}{6}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{6 \cdot 5}{6}} + \frac{5 \frac{2 \cdot 5}{6}}{3 \frac{2 \cdot 5}{6}}$

Step 1.9

Multiply $6$ by $5$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{30}{6}} + \frac{5 \frac{2 \cdot 5}{6}}{3 \frac{2 \cdot 5}{6}}$

Step 1.10

Multiply $2$ by $5$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{30}{6}} + \frac{5 \frac{2 \cdot 5}{6}}{3 (\frac{10}{6})}$

Step 1.11

Combine $3$ and $\frac{10}{6}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{30}{6}} + \frac{5 \frac{2 \cdot 5}{6}}{\frac{3 \cdot 10}{6}}$

Step 1.12

Multiply $3$ by $10$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} - \frac{\frac{11}{12} \cdot 6}{\frac{30}{6}} + \frac{5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 2

Combine the numerators over the common denominator.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{12} \cdot 6 + 5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $6$ .

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Step 3.1.1

Move the leading negative in $- \frac{11}{12}$ into the numerator.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 11}{12} \cdot 6 + 5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 3.1.2

Factor $6$ out of $12$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 11}{6 (2)} \cdot 6 + 5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 3.1.3

Cancel the common factor.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 11}{6 \cdot 2} \cdot 6 + 5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 3.1.4

Rewrite the expression.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 11}{2} + 5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 3.2

Move the negative in front of the fraction.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + 5 \frac{2 \cdot 5}{6}}{\frac{30}{6}}$

Step 3.3

Cancel the common factor of $2$ and $6$ .

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Step 3.3.1

Factor $2$ out of $2 \cdot 5$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + 5 \frac{2 (5)}{6}}{\frac{30}{6}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $2$ out of $6$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + 5 \frac{2 \cdot 5}{2 \cdot 3}}{\frac{30}{6}}$

Step 3.3.2.2

Cancel the common factor.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + 5 \frac{2 \cdot 5}{2 \cdot 3}}{\frac{30}{6}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + 5 (\frac{5}{3})}{\frac{30}{6}}$

Step 3.4

Multiply $5 (\frac{5}{3})$ .

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Step 3.4.1

Combine $5$ and $\frac{5}{3}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + \frac{5 \cdot 5}{3}}{\frac{30}{6}}$

Step 3.4.2

Multiply $5$ by $5$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} + \frac{25}{3}}{\frac{30}{6}}$

Step 4

To write $- \frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} \cdot \frac{3}{3} + \frac{25}{3}}{\frac{30}{6}}$

Step 5

To write $\frac{25}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11}{2} \cdot \frac{3}{3} + \frac{25}{3} \cdot \frac{2}{2}}{\frac{30}{6}}$

Step 6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{11}{2}$ by $\frac{3}{3}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11 \cdot 3}{2 \cdot 3} + \frac{25}{3} \cdot \frac{2}{2}}{\frac{30}{6}}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11 \cdot 3}{6} + \frac{25}{3} \cdot \frac{2}{2}}{\frac{30}{6}}$

Step 6.3

Multiply $\frac{25}{3}$ by $\frac{2}{2}$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11 \cdot 3}{6} + \frac{25 \cdot 2}{3 \cdot 2}}{\frac{30}{6}}$

Step 6.4

Multiply $3$ by $2$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{- \frac{11 \cdot 3}{6} + \frac{25 \cdot 2}{6}}{\frac{30}{6}}$

Step 7

Combine the numerators over the common denominator.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 11 \cdot 3 + 25 \cdot 2}{6}}{\frac{30}{6}}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 11$ by $3$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 33 + 25 \cdot 2}{6}}{\frac{30}{6}}$

Step 8.2

Multiply $25$ by $2$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{- 33 + 50}{6}}{\frac{30}{6}}$

Step 8.3

Add $- 33$ and $50$ .

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{17}{6}}{\frac{30}{6}}$

Step 9

Simplify each term.

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Step 9.1

Cancel the common factor of $\frac{5}{6}$ .

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Step 9.1.1

Cancel the common factor.

$\frac{\frac{5}{6}}{6 (\frac{5}{6})} + \frac{\frac{17}{6}}{\frac{30}{6}}$

Step 9.1.2

Rewrite the expression.

$\frac{1}{6} + \frac{\frac{17}{6}}{\frac{30}{6}}$

Step 9.2

Cancel the common factor of $30$ and $6$ .

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Step 9.2.1

Factor $6$ out of $30$ .

$\frac{1}{6} + \frac{\frac{17}{6}}{\frac{6 \cdot 5}{6}}$

Step 9.2.2

Cancel the common factors.

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Step 9.2.2.1

Factor $6$ out of $6$ .

$\frac{1}{6} + \frac{\frac{17}{6}}{\frac{6 \cdot 5}{6 (1)}}$

Step 9.2.2.2

Cancel the common factor.

$\frac{1}{6} + \frac{\frac{17}{6}}{\frac{6 \cdot 5}{6 \cdot 1}}$

Step 9.2.2.3

Rewrite the expression.

$\frac{1}{6} + \frac{\frac{17}{6}}{\frac{5}{1}}$

Step 9.2.2.4

Divide $5$ by $1$ .

$\frac{1}{6} + \frac{\frac{17}{6}}{5}$

Step 9.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{6} + \frac{17}{6} \cdot \frac{1}{5}$

Step 9.4

Multiply $\frac{17}{6} \cdot \frac{1}{5}$ .

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Step 9.4.1

Multiply $\frac{17}{6}$ by $\frac{1}{5}$ .

$\frac{1}{6} + \frac{17}{6 \cdot 5}$

Step 9.4.2

Multiply $6$ by $5$ .

$\frac{1}{6} + \frac{17}{30}$

Step 10

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{6} \cdot \frac{5}{5} + \frac{17}{30}$

Step 11

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 11.1

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{5}{6 \cdot 5} + \frac{17}{30}$

Step 11.2

Multiply $6$ by $5$ .

$\frac{5}{30} + \frac{17}{30}$

Step 12

Simplify the expression.

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Step 12.1

Combine the numerators over the common denominator.

$\frac{5 + 17}{30}$

Step 12.2

Add $5$ and $17$ .

$\frac{22}{30}$

Step 13

Cancel the common factor of $22$ and $30$ .

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Step 13.1

Factor $2$ out of $22$ .

$\frac{2 (11)}{30}$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 11}{2 \cdot 15}$

Step 13.2.2

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 15}$

Step 13.2.3

Rewrite the expression.

$\frac{11}{15}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{15}$

Decimal Form:

$0.7\overline{3}$