Basic Math Examples

$\frac{1}{5} - \frac{1}{3} \div \frac{1}{4} - \frac{1}{2}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{5}$ by $\frac{\frac{2}{4}}{\frac{2}{4}}$ .

$\frac{1}{5} \cdot \frac{\frac{2}{4}}{\frac{2}{4}} - \frac{1}{3} \div \frac{1}{4} - \frac{1}{2}$

Step 1.2

Multiply $\frac{1}{5}$ by $\frac{\frac{2}{4}}{\frac{2}{4}}$ .

$\frac{\frac{2}{4}}{5 (\frac{2}{4})} - \frac{1}{3} \div \frac{1}{4} - \frac{1}{2}$

Step 1.3

Multiply $\frac{1}{3} \div \frac{1}{4}$ by $\frac{10}{10}$ .

$\frac{\frac{2}{4}}{5 (\frac{2}{4})} - (\frac{1}{3} \div \frac{1}{4} \cdot \frac{10}{10}) - \frac{1}{2}$

Step 1.4

Multiply $\frac{1}{3} \div \frac{1}{4}$ by $\frac{10}{10}$ .

$\frac{\frac{2}{4}}{5 (\frac{2}{4})} - \frac{\frac{1}{3} \cdot 10}{\frac{1}{4} \cdot 10} - \frac{1}{2}$

Step 1.5

Multiply $\frac{1}{2}$ by $\frac{\frac{5}{4}}{\frac{5}{4}}$ .

$\frac{\frac{2}{4}}{5 (\frac{2}{4})} - \frac{\frac{1}{3} \cdot 10}{\frac{1}{4} \cdot 10} - (\frac{1}{2} \cdot \frac{\frac{5}{4}}{\frac{5}{4}})$

Step 1.6

Multiply $\frac{1}{2}$ by $\frac{\frac{5}{4}}{\frac{5}{4}}$ .

$\frac{\frac{2}{4}}{5 (\frac{2}{4})} - \frac{\frac{1}{3} \cdot 10}{\frac{1}{4} \cdot 10} - \frac{\frac{5}{4}}{2 (\frac{5}{4})}$

Step 1.7

Combine $5$ and $\frac{2}{4}$ .

$\frac{\frac{2}{4}}{\frac{5 \cdot 2}{4}} - \frac{\frac{1}{3} \cdot 10}{\frac{1}{4} \cdot 10} - \frac{\frac{5}{4}}{2 (\frac{5}{4})}$

Step 1.8

Multiply $5$ by $2$ .

$\frac{\frac{2}{4}}{\frac{10}{4}} - \frac{\frac{1}{3} \cdot 10}{\frac{1}{4} \cdot 10} - \frac{\frac{5}{4}}{2 (\frac{5}{4})}$

Step 1.9

Reorder the factors of $\frac{1}{4} \cdot 10$ .

$\frac{\frac{2}{4}}{\frac{10}{4}} - \frac{\frac{1}{3} \cdot 10}{10 (\frac{1}{4})} - \frac{\frac{5}{4}}{2 (\frac{5}{4})}$

Step 1.10

Combine $10$ and $\frac{1}{4}$ .

$\frac{\frac{2}{4}}{\frac{10}{4}} - \frac{\frac{1}{3} \cdot 10}{\frac{10}{4}} - \frac{\frac{5}{4}}{2 (\frac{5}{4})}$

Step 1.11

Combine $2$ and $\frac{5}{4}$ .

$\frac{\frac{2}{4}}{\frac{10}{4}} - \frac{\frac{1}{3} \cdot 10}{\frac{10}{4}} - \frac{\frac{5}{4}}{\frac{2 \cdot 5}{4}}$

Step 1.12

Multiply $2$ by $5$ .

$\frac{\frac{2}{4}}{\frac{10}{4}} - \frac{\frac{1}{3} \cdot 10}{\frac{10}{4}} - \frac{\frac{5}{4}}{\frac{10}{4}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\frac{2}{4} - \frac{1}{3} \cdot 10 - \frac{5}{4}}{\frac{10}{4}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- \frac{1}{3} \cdot 10 + \frac{2 - 5}{4}}{\frac{10}{4}}$

Step 2.3

Subtract $5$ from $2$ .

$\frac{- \frac{1}{3} \cdot 10 + \frac{- 3}{4}}{\frac{10}{4}}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- \frac{1}{3} \cdot 10$ .

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Step 3.1.1

Multiply $10$ by $- 1$ .

$\frac{- 10 (\frac{1}{3}) + \frac{- 3}{4}}{\frac{10}{4}}$

Step 3.1.2

Combine $- 10$ and $\frac{1}{3}$ .

$\frac{\frac{- 10}{3} + \frac{- 3}{4}}{\frac{10}{4}}$

Step 3.2

Move the negative in front of the fraction.

$\frac{- \frac{10}{3} + \frac{- 3}{4}}{\frac{10}{4}}$

Step 3.3

Move the negative in front of the fraction.

$\frac{- \frac{10}{3} - \frac{3}{4}}{\frac{10}{4}}$

Step 4

To write $- \frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{- \frac{10}{3} \cdot \frac{4}{4} - \frac{3}{4}}{\frac{10}{4}}$

Step 5

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

$\frac{- \frac{10}{3} \cdot \frac{4}{4} - \frac{3}{4} \cdot \frac{3}{3}}{\frac{10}{4}}$

Step 6

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{10}{3}$ by $\frac{4}{4}$ .

$\frac{- \frac{10 \cdot 4}{3 \cdot 4} - \frac{3}{4} \cdot \frac{3}{3}}{\frac{10}{4}}$

Step 6.2

Multiply $3$ by $4$ .

$\frac{- \frac{10 \cdot 4}{12} - \frac{3}{4} \cdot \frac{3}{3}}{\frac{10}{4}}$

Step 6.3

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

$\frac{- \frac{10 \cdot 4}{12} - \frac{3 \cdot 3}{4 \cdot 3}}{\frac{10}{4}}$

Step 6.4

Multiply $4$ by $3$ .

$\frac{- \frac{10 \cdot 4}{12} - \frac{3 \cdot 3}{12}}{\frac{10}{4}}$

Step 7

Combine the numerators over the common denominator.

$\frac{\frac{- 10 \cdot 4 - 3 \cdot 3}{12}}{\frac{10}{4}}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 10$ by $4$ .

$\frac{\frac{- 40 - 3 \cdot 3}{12}}{\frac{10}{4}}$

Step 8.2

Multiply $- 3$ by $3$ .

$\frac{\frac{- 40 - 9}{12}}{\frac{10}{4}}$

Step 8.3

Subtract $9$ from $- 40$ .

$\frac{\frac{- 49}{12}}{\frac{10}{4}}$

Step 9

Move the negative in front of the fraction.

$\frac{- \frac{49}{12}}{\frac{10}{4}}$

Step 10

Cancel the common factor of $10$ and $4$ .

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Step 10.1

Factor $2$ out of $10$ .

$\frac{- \frac{49}{12}}{\frac{2 (5)}{4}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $4$ .

$\frac{- \frac{49}{12}}{\frac{2 \cdot 5}{2 \cdot 2}}$

Step 10.2.2

Cancel the common factor.

$\frac{- \frac{49}{12}}{\frac{2 \cdot 5}{2 \cdot 2}}$

Step 10.2.3

Rewrite the expression.

$\frac{- \frac{49}{12}}{\frac{5}{2}}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$- \frac{49}{12} \cdot \frac{2}{5}$

Step 12

Cancel the common factor of $2$ .

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Step 12.1

Move the leading negative in $- \frac{49}{12}$ into the numerator.

$\frac{- 49}{12} \cdot \frac{2}{5}$

Step 12.2

Factor $2$ out of $12$ .

$\frac{- 49}{2 (6)} \cdot \frac{2}{5}$

Step 12.3

Cancel the common factor.

$\frac{- 49}{2 \cdot 6} \cdot \frac{2}{5}$

Step 12.4

Rewrite the expression.

$\frac{- 49}{6} \cdot \frac{1}{5}$

Step 13

Multiply $\frac{- 49}{6}$ by $\frac{1}{5}$ .

$\frac{- 49}{6 \cdot 5}$

Step 14

Simplify the expression.

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Step 14.1

Multiply $6$ by $5$ .

$\frac{- 49}{30}$

Step 14.2

Move the negative in front of the fraction.

$- \frac{49}{30}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$- \frac{49}{30}$

Decimal Form:

$- 1.6\overline{3}$

Mixed Number Form:

$- 1 \frac{19}{30}$