Algebra Examples

$(1 \frac{1}{8} + 1 \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 1

Convert $1 \frac{1}{8}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(1 + \frac{1}{8} + 1 \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 1.2

Add $1$ and $\frac{1}{8}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{8}{8} + \frac{1}{8} + 1 \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 1.2.2

Combine the numerators over the common denominator.

$(\frac{8 + 1}{8} + 1 \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 1.2.3

Add $8$ and $1$ .

$(\frac{9}{8} + 1 \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 2

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$(\frac{9}{8} + 1 + \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 2.2

Add $1$ and $\frac{1}{2}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{9}{8} + \frac{2}{2} + \frac{1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$(\frac{9}{8} + \frac{2 + 1}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 2.2.3

Add $2$ and $1$ .

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (5 \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 3

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 3.1

A mixed number is an addition of its whole and fractional parts.

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (5 + \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 3.2

Add $5$ and $\frac{1}{2}$ .

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Step 3.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (5 \cdot \frac{2}{2} + \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 3.2.2

Combine $5$ and $\frac{2}{2}$ .

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{5 \cdot 2}{2} + \frac{1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 3.2.3

Combine the numerators over the common denominator.

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{5 \cdot 2 + 1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $5$ by $2$ .

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{10 + 1}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 3.2.4.2

Add $10$ and $1$ .

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{11}{2} - \frac{9}{20} \div 1 \frac{4}{5})$

Step 4

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 4.1

A mixed number is an addition of its whole and fractional parts.

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{11}{2} - \frac{9}{20} \div (1 + \frac{4}{5}))$

Step 4.2

Add $1$ and $\frac{4}{5}$ .

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Step 4.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{11}{2} - \frac{9}{20} \div (\frac{5}{5} + \frac{4}{5}))$

Step 4.2.2

Combine the numerators over the common denominator.

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{11}{2} - \frac{9}{20} \div \frac{5 + 4}{5})$

Step 4.2.3

Add $5$ and $4$ .

$(\frac{9}{8} + \frac{3}{2}) \div 3 \div (\frac{11}{2} - \frac{9}{20} \div \frac{9}{5})$

Step 5

Rewrite the division as a fraction.

$\frac{(\frac{9}{8} + \frac{3}{2}) \div 3}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$(\frac{9}{8} + \frac{3}{2}) \div 3 \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 7

Rewrite the division as a fraction.

$\frac{\frac{9}{8} + \frac{3}{2}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 8

Simplify the numerator.

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Step 8.1

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{9}{8} + \frac{3}{2} \cdot \frac{4}{4}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 8.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.2.1

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{\frac{9}{8} + \frac{3 \cdot 4}{2 \cdot 4}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 8.2.2

Multiply $2$ by $4$ .

$\frac{\frac{9}{8} + \frac{3 \cdot 4}{8}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 8.3

Combine the numerators over the common denominator.

$\frac{\frac{9 + 3 \cdot 4}{8}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 8.4

Simplify the numerator.

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Step 8.4.1

Multiply $3$ by $4$ .

$\frac{\frac{9 + 12}{8}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 8.4.2

Add $9$ and $12$ .

$\frac{\frac{21}{8}}{3} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{21}{8} \cdot \frac{1}{3} \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 10

Cancel the common factor of $3$ .

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Step 10.1

Factor $3$ out of $21$ .

$\frac{3 (7)}{8} \cdot \frac{1}{3} \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 10.2

Cancel the common factor.

$\frac{3 \cdot 7}{8} \cdot \frac{1}{3} \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 10.3

Rewrite the expression.

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - \frac{9}{20} \div \frac{9}{5}}$

Step 11

Simplify the denominator.

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Step 11.1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - (\frac{9}{20} \cdot \frac{5}{9})}$

Step 11.2

Cancel the common factor of $9$ .

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Step 11.2.1

Cancel the common factor.

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - (\frac{9}{20} \cdot \frac{5}{9})}$

Step 11.2.2

Rewrite the expression.

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - (\frac{1}{20} \cdot 5)}$

Step 11.3

Cancel the common factor of $5$ .

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Step 11.3.1

Factor $5$ out of $20$ .

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - (\frac{1}{5 (4)} \cdot 5)}$

Step 11.3.2

Cancel the common factor.

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - (\frac{1}{5 \cdot 4} \cdot 5)}$

Step 11.3.3

Rewrite the expression.

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} - \frac{1}{4}}$

Step 11.4

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

$\frac{7}{8} \cdot \frac{1}{\frac{11}{2} \cdot \frac{2}{2} - \frac{1}{4}}$

Step 11.5

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 11.5.1

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

$\frac{7}{8} \cdot \frac{1}{\frac{11 \cdot 2}{2 \cdot 2} - \frac{1}{4}}$

Step 11.5.2

Multiply $2$ by $2$ .

$\frac{7}{8} \cdot \frac{1}{\frac{11 \cdot 2}{4} - \frac{1}{4}}$

Step 11.6

Combine the numerators over the common denominator.

$\frac{7}{8} \cdot \frac{1}{\frac{11 \cdot 2 - 1}{4}}$

Step 11.7

Simplify the numerator.

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Step 11.7.1

Multiply $11$ by $2$ .

$\frac{7}{8} \cdot \frac{1}{\frac{22 - 1}{4}}$

Step 11.7.2

Subtract $1$ from $22$ .

$\frac{7}{8} \cdot \frac{1}{\frac{21}{4}}$

Step 12

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{8} (1 (\frac{4}{21}))$

Step 13

Multiply $\frac{4}{21}$ by $1$ .

$\frac{7}{8} \cdot \frac{4}{21}$

Step 14

Cancel the common factor of $7$ .

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Step 14.1

Factor $7$ out of $21$ .

$\frac{7}{8} \cdot \frac{4}{7 (3)}$

Step 14.2

Cancel the common factor.

$\frac{7}{8} \cdot \frac{4}{7 \cdot 3}$

Step 14.3

Rewrite the expression.

$\frac{1}{8} \cdot \frac{4}{3}$

Step 15

Cancel the common factor of $4$ .

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Step 15.1

Factor $4$ out of $8$ .

$\frac{1}{4 (2)} \cdot \frac{4}{3}$

Step 15.2

Cancel the common factor.

$\frac{1}{4 \cdot 2} \cdot \frac{4}{3}$

Step 15.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{3}$

Step 16

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

$\frac{1}{2 \cdot 3}$

Step 17

Multiply $2$ by $3$ .

$\frac{1}{6}$

Step 18

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$