Algebra Examples

$\frac{11}{15} + \frac{2}{3} \div 1 \frac{1}{2} - \frac{7}{30}$

Step 1

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

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Step 1.1

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

$\frac{11}{15} + \frac{2}{3} \div (1 + \frac{1}{2}) - \frac{7}{30}$

Step 1.2

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

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Step 1.2.1

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

$\frac{11}{15} + \frac{2}{3} \div (\frac{2}{2} + \frac{1}{2}) - \frac{7}{30}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{11}{15} + \frac{2}{3} \div \frac{2 + 1}{2} - \frac{7}{30}$

Step 1.2.3

Add $2$ and $1$ .

$\frac{11}{15} + \frac{2}{3} \div \frac{3}{2} - \frac{7}{30}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{11}{15}$ by $\frac{\frac{2 \cdot 3}{2}}{\frac{2 \cdot 3}{2}}$ .

$\frac{11}{15} \cdot \frac{\frac{2 \cdot 3}{2}}{\frac{2 \cdot 3}{2}} + \frac{2}{3} \div \frac{3}{2} - \frac{7}{30}$

Step 2.2

Multiply $\frac{11}{15}$ by $\frac{\frac{2 \cdot 3}{2}}{\frac{2 \cdot 3}{2}}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{15 \frac{2 \cdot 3}{2}} + \frac{2}{3} \div \frac{3}{2} - \frac{7}{30}$

Step 2.3

Multiply $\frac{2}{3} \div \frac{3}{2}$ by $\frac{30}{30}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{15 \frac{2 \cdot 3}{2}} + \frac{2}{3} \div \frac{3}{2} \cdot \frac{30}{30} - \frac{7}{30}$

Step 2.4

Multiply $\frac{2}{3} \div \frac{3}{2}$ by $\frac{30}{30}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{15 \frac{2 \cdot 3}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{3}{2} \cdot 30} - \frac{7}{30}$

Step 2.5

Multiply $\frac{7}{30}$ by $\frac{\frac{3}{2}}{\frac{3}{2}}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{15 \frac{2 \cdot 3}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{3}{2} \cdot 30} - (\frac{7}{30} \cdot \frac{\frac{3}{2}}{\frac{3}{2}})$

Step 2.6

Multiply $\frac{7}{30}$ by $\frac{\frac{3}{2}}{\frac{3}{2}}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{15 \frac{2 \cdot 3}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{3}{2} \cdot 30} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 2.7

Multiply $2$ by $3$ .

$\frac{11 \frac{2 \cdot 3}{2}}{15 (\frac{6}{2})} + \frac{\frac{2}{3} \cdot 30}{\frac{3}{2} \cdot 30} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 2.8

Combine $15$ and $\frac{6}{2}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{\frac{15 \cdot 6}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{3}{2} \cdot 30} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 2.9

Multiply $15$ by $6$ .

$\frac{11 \frac{2 \cdot 3}{2}}{\frac{90}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{3}{2} \cdot 30} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 2.10

Reorder the factors of $\frac{3}{2} \cdot 30$ .

$\frac{11 \frac{2 \cdot 3}{2}}{\frac{90}{2}} + \frac{\frac{2}{3} \cdot 30}{30 (\frac{3}{2})} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 2.11

Combine $30$ and $\frac{3}{2}$ .

$\frac{11 \frac{2 \cdot 3}{2}}{\frac{90}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{30 \cdot 3}{2}} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 2.12

Multiply $30$ by $3$ .

$\frac{11 \frac{2 \cdot 3}{2}}{\frac{90}{2}} + \frac{\frac{2}{3} \cdot 30}{\frac{90}{2}} - \frac{7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 3

Combine the numerators over the common denominator.

$\frac{11 \frac{2 \cdot 3}{2} + \frac{2}{3} \cdot 30}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Cancel the common factor.

$\frac{11 \frac{2 \cdot 3}{2} + \frac{2}{3} \cdot 30}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4.1.2

Divide $3$ by $1$ .

$\frac{11 \cdot 3 + \frac{2}{3} \cdot 30}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4.2

Multiply $11$ by $3$ .

$\frac{33 + \frac{2}{3} \cdot 30}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Factor $3$ out of $30$ .

$\frac{33 + \frac{2}{3} \cdot (3 (10))}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4.3.2

Cancel the common factor.

$\frac{33 + \frac{2}{3} \cdot (3 \cdot 10)}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4.3.3

Rewrite the expression.

$\frac{33 + 2 \cdot 10}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 4.4

Multiply $2$ by $10$ .

$\frac{33 + 20}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 5

Add $33$ and $20$ .

$\frac{53}{\frac{90}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6

Simplify each term.

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Step 6.1

Cancel the common factor of $90$ and $2$ .

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Step 6.1.1

Factor $2$ out of $90$ .

$\frac{53}{\frac{2 \cdot 45}{2}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Factor $2$ out of $2$ .

$\frac{53}{\frac{2 \cdot 45}{2 (1)}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6.1.2.2

Cancel the common factor.

$\frac{53}{\frac{2 \cdot 45}{2 \cdot 1}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6.1.2.3

Rewrite the expression.

$\frac{53}{\frac{45}{1}} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6.1.2.4

Divide $45$ by $1$ .

$\frac{53}{45} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6.2

Cancel the common factor of $\frac{3}{2}$ .

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Step 6.2.1

Cancel the common factor.

$\frac{53}{45} + \frac{- 7 (\frac{3}{2})}{30 (\frac{3}{2})}$

Step 6.2.2

Rewrite the expression.

$\frac{53}{45} + \frac{- 7}{30}$

Step 6.3

Move the negative in front of the fraction.

$\frac{53}{45} - \frac{7}{30}$

Step 7

To write $\frac{53}{45}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{53}{45} \cdot \frac{2}{2} - \frac{7}{30}$

Step 8

To write $- \frac{7}{30}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{53}{45} \cdot \frac{2}{2} - \frac{7}{30} \cdot \frac{3}{3}$

Step 9

Write each expression with a common denominator of $90$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{53}{45}$ by $\frac{2}{2}$ .

$\frac{53 \cdot 2}{45 \cdot 2} - \frac{7}{30} \cdot \frac{3}{3}$

Step 9.2

Multiply $45$ by $2$ .

$\frac{53 \cdot 2}{90} - \frac{7}{30} \cdot \frac{3}{3}$

Step 9.3

Multiply $\frac{7}{30}$ by $\frac{3}{3}$ .

$\frac{53 \cdot 2}{90} - \frac{7 \cdot 3}{30 \cdot 3}$

Step 9.4

Multiply $30$ by $3$ .

$\frac{53 \cdot 2}{90} - \frac{7 \cdot 3}{90}$

Step 10

Combine the numerators over the common denominator.

$\frac{53 \cdot 2 - 7 \cdot 3}{90}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $53$ by $2$ .

$\frac{106 - 7 \cdot 3}{90}$

Step 11.2

Multiply $- 7$ by $3$ .

$\frac{106 - 21}{90}$

Step 11.3

Subtract $21$ from $106$ .

$\frac{85}{90}$

Step 12

Cancel the common factor of $85$ and $90$ .

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Step 12.1

Factor $5$ out of $85$ .

$\frac{5 (17)}{90}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $5$ out of $90$ .

$\frac{5 \cdot 17}{5 \cdot 18}$

Step 12.2.2

Cancel the common factor.

$\frac{5 \cdot 17}{5 \cdot 18}$

Step 12.2.3

Rewrite the expression.

$\frac{17}{18}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{18}$

Decimal Form:

$0.9\overline{4}$