Basic Math Examples

$\frac{2}{5} - 2 \div (2 - \frac{3}{2}) - 1 \div \frac{2}{3}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{2}{5}$ by $\frac{(2 - \frac{3}{2}) \frac{2}{3}}{(2 - \frac{3}{2}) \frac{2}{3}}$ .

$\frac{2}{5} \cdot \frac{(2 - \frac{3}{2}) \frac{2}{3}}{(2 - \frac{3}{2}) \frac{2}{3}} - 2 \div (2 - \frac{3}{2}) - 1 \div \frac{2}{3}$

Step 1.2

Multiply $\frac{2}{5}$ by $\frac{(2 - \frac{3}{2}) \frac{2}{3}}{(2 - \frac{3}{2}) \frac{2}{3}}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{5 ((2 - \frac{3}{2}) \frac{2}{3})} - 2 \div (2 - \frac{3}{2}) - 1 \div \frac{2}{3}$

Step 1.3

Multiply $2 \div (2 - \frac{3}{2})$ by $\frac{\frac{5 \cdot 2}{3}}{\frac{5 \cdot 2}{3}}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{5 ((2 - \frac{3}{2}) \frac{2}{3})} - (2 \div (2 - \frac{3}{2}) \cdot \frac{\frac{5 \cdot 2}{3}}{\frac{5 \cdot 2}{3}}) - 1 \div \frac{2}{3}$

Step 1.4

Multiply $2 \div (2 - \frac{3}{2})$ by $\frac{\frac{5 \cdot 2}{3}}{\frac{5 \cdot 2}{3}}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{5 ((2 - \frac{3}{2}) \frac{2}{3})} - \frac{2 \frac{5 \cdot 2}{3}}{(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}} - 1 \div \frac{2}{3}$

Step 1.5

Multiply $1 \div \frac{2}{3}$ by $\frac{5 (2 - \frac{3}{2})}{5 (2 - \frac{3}{2})}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{5 ((2 - \frac{3}{2}) \frac{2}{3})} - \frac{2 \frac{5 \cdot 2}{3}}{(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}} - (1 \div \frac{2}{3} \cdot \frac{5 (2 - \frac{3}{2})}{5 (2 - \frac{3}{2})})$

Step 1.6

Multiply $1 \div \frac{2}{3}$ by $\frac{5 (2 - \frac{3}{2})}{5 (2 - \frac{3}{2})}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{5 ((2 - \frac{3}{2}) \frac{2}{3})} - \frac{2 \frac{5 \cdot 2}{3}}{(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}} - \frac{5 (2 - \frac{3}{2})}{\frac{2}{3} (5 (2 - \frac{3}{2}))}$

Step 1.7

Reorder the factors of $5 ((2 - \frac{3}{2}) \frac{2}{3})$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{5 (\frac{2}{3}) (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}} - \frac{5 (2 - \frac{3}{2})}{\frac{2}{3} (5 (2 - \frac{3}{2}))}$

Step 1.8

Combine $5$ and $\frac{2}{3}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{\frac{5 \cdot 2}{3} (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}} - \frac{5 (2 - \frac{3}{2})}{\frac{2}{3} (5 (2 - \frac{3}{2}))}$

Step 1.9

Multiply $5$ by $2$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}} - \frac{5 (2 - \frac{3}{2})}{\frac{2}{3} (5 (2 - \frac{3}{2}))}$

Step 1.10

Reorder the factors of $(2 - \frac{3}{2}) \frac{5 \cdot 2}{3}$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{\frac{5 \cdot 2}{3} (2 - \frac{3}{2})} - \frac{5 (2 - \frac{3}{2})}{\frac{2}{3} (5 (2 - \frac{3}{2}))}$

Step 1.11

Multiply $5$ by $2$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{5 (2 - \frac{3}{2})}{\frac{2}{3} (5 (2 - \frac{3}{2}))}$

Step 1.12

Reorder the factors of $\frac{2}{3} (5 (2 - \frac{3}{2}))$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{5 (2 - \frac{3}{2})}{5 (\frac{2}{3}) (2 - \frac{3}{2})}$

Step 1.13

Combine $5$ and $\frac{2}{3}$ .

Step 1.14

Multiply $5$ by $2$ .

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3})}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{2 \frac{5 \cdot 2}{3}}{\frac{10}{3} (2 - \frac{3}{2})} - \frac{5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 ((2 - \frac{3}{2}) \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3

Simplify each term.

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Step 3.1

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

$\frac{2 ((2 \cdot \frac{2}{2} - \frac{3}{2}) \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.2

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

$\frac{2 ((\frac{2 \cdot 2}{2} - \frac{3}{2}) \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{2 (\frac{2 \cdot 2 - 3}{2} \cdot \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $2$ by $2$ .

$\frac{2 (\frac{4 - 3}{2} \cdot \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.4.2

Subtract $3$ from $4$ .

$\frac{2 (\frac{1}{2} \cdot \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Cancel the common factor.

$\frac{2 (\frac{1}{2} \cdot \frac{2}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.5.2

Rewrite the expression.

$\frac{2 (\frac{1}{3}) - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.6

Combine $2$ and $\frac{1}{3}$ .

$\frac{\frac{2}{3} - 2 \frac{5 \cdot 2}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.7

Multiply $5$ by $2$ .

$\frac{\frac{2}{3} - 2 (\frac{10}{3}) - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.8

Multiply $- 2 (\frac{10}{3})$ .

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Step 3.8.1

Combine $- 2$ and $\frac{10}{3}$ .

$\frac{\frac{2}{3} + \frac{- 2 \cdot 10}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.8.2

Multiply $- 2$ by $10$ .

$\frac{\frac{2}{3} + \frac{- 20}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.9

Move the negative in front of the fraction.

$\frac{\frac{2}{3} - \frac{20}{3} - 5 (2 - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.10

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

$\frac{\frac{2}{3} - \frac{20}{3} - 5 (2 \cdot \frac{2}{2} - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.11

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

$\frac{\frac{2}{3} - \frac{20}{3} - 5 (\frac{2 \cdot 2}{2} - \frac{3}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.12

Combine the numerators over the common denominator.

$\frac{\frac{2}{3} - \frac{20}{3} - 5 \frac{2 \cdot 2 - 3}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.13

Simplify the numerator.

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Step 3.13.1

Multiply $2$ by $2$ .

$\frac{\frac{2}{3} - \frac{20}{3} - 5 \frac{4 - 3}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.13.2

Subtract $3$ from $4$ .

$\frac{\frac{2}{3} - \frac{20}{3} - 5 (\frac{1}{2})}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.14

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{\frac{2}{3} - \frac{20}{3} + \frac{- 5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 3.15

Move the negative in front of the fraction.

$\frac{\frac{2}{3} - \frac{20}{3} - \frac{5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 4

Combine fractions.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{\frac{2 - 20}{3} + \frac{- 5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 4.2

Subtract $20$ from $2$ .

$\frac{\frac{- 18}{3} + \frac{- 5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 5

Simplify each term.

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Step 5.1

Divide $- 18$ by $3$ .

$\frac{- 6 + \frac{- 5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 5.2

Move the negative in front of the fraction.

$\frac{- 6 - \frac{5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 6

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- 6 \cdot \frac{2}{2} - \frac{5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 7

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

$\frac{\frac{- 6 \cdot 2}{2} - \frac{5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 8

Combine the numerators over the common denominator.

$\frac{\frac{- 6 \cdot 2 - 5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 6$ by $2$ .

$\frac{\frac{- 12 - 5}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 9.2

Subtract $5$ from $- 12$ .

$\frac{\frac{- 17}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 10

Move the negative in front of the fraction.

$\frac{- \frac{17}{2}}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3} (2 - \frac{3}{2})}$

Step 12

Simplify the denominator.

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Step 12.1

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

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3} (2 \cdot \frac{2}{2} - \frac{3}{2})}$

Step 12.2

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

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3} (\frac{2 \cdot 2}{2} - \frac{3}{2})}$

Step 12.3

Combine the numerators over the common denominator.

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3} \cdot \frac{2 \cdot 2 - 3}{2}}$

Step 12.4

Simplify the numerator.

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Step 12.4.1

Multiply $2$ by $2$ .

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3} \cdot \frac{4 - 3}{2}}$

Step 12.4.2

Subtract $3$ from $4$ .

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3} \cdot \frac{1}{2}}$

Step 13

Simplify terms.

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Step 13.1

Multiply $\frac{10}{3}$ by $\frac{1}{2}$ .

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{3 \cdot 2}}$

Step 13.2

Multiply $3$ by $2$ .

$- \frac{17}{2} \cdot \frac{1}{\frac{10}{6}}$

Step 13.3

Cancel the common factor of $10$ and $6$ .

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Step 13.3.1

Factor $2$ out of $10$ .

$- \frac{17}{2} \cdot \frac{1}{\frac{2 (5)}{6}}$

Step 13.3.2

Cancel the common factors.

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Step 13.3.2.1

Factor $2$ out of $6$ .

$- \frac{17}{2} \cdot \frac{1}{\frac{2 \cdot 5}{2 \cdot 3}}$

Step 13.3.2.2

Cancel the common factor.

$- \frac{17}{2} \cdot \frac{1}{\frac{2 \cdot 5}{2 \cdot 3}}$

Step 13.3.2.3

Rewrite the expression.

$- \frac{17}{2} \cdot \frac{1}{\frac{5}{3}}$

Step 14

Multiply the numerator by the reciprocal of the denominator.

$- \frac{17}{2} (1 (\frac{3}{5}))$

Step 15

Multiply $\frac{3}{5}$ by $1$ .

$- \frac{17}{2} \cdot \frac{3}{5}$

Step 16

Multiply $- \frac{17}{2} \cdot \frac{3}{5}$ .

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Step 16.1

Multiply $\frac{3}{5}$ by $\frac{17}{2}$ .

$- \frac{3 \cdot 17}{5 \cdot 2}$

Step 16.2

Multiply $3$ by $17$ .

$- \frac{51}{5 \cdot 2}$

Step 16.3

Multiply $5$ by $2$ .

$- \frac{51}{10}$

Step 17

The result can be shown in multiple forms.

Exact Form:

$- \frac{51}{10}$

Decimal Form:

$- 5.1$

Mixed Number Form:

$- 5 \frac{1}{10}$