Basic Math Examples

$\frac{1}{14} - \frac{1}{7} \div \frac{1}{4} - \frac{1}{8}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{14}$ by $\frac{\frac{4}{4}}{\frac{4}{4}}$ .

$\frac{1}{14} \cdot \frac{\frac{4}{4}}{\frac{4}{4}} - \frac{1}{7} \div \frac{1}{4} - \frac{1}{8}$

Step 1.2

Multiply $\frac{1}{14}$ by $\frac{\frac{4}{4}}{\frac{4}{4}}$ .

$\frac{\frac{4}{4}}{14 (\frac{4}{4})} - \frac{1}{7} \div \frac{1}{4} - \frac{1}{8}$

Step 1.3

Multiply $\frac{1}{7} \div \frac{1}{4}$ by $\frac{56}{56}$ .

$\frac{\frac{4}{4}}{14 (\frac{4}{4})} - (\frac{1}{7} \div \frac{1}{4} \cdot \frac{56}{56}) - \frac{1}{8}$

Step 1.4

Multiply $\frac{1}{7} \div \frac{1}{4}$ by $\frac{56}{56}$ .

$\frac{\frac{4}{4}}{14 (\frac{4}{4})} - \frac{\frac{1}{7} \cdot 56}{\frac{1}{4} \cdot 56} - \frac{1}{8}$

Step 1.5

Multiply $\frac{1}{8}$ by $\frac{\frac{7}{4}}{\frac{7}{4}}$ .

$\frac{\frac{4}{4}}{14 (\frac{4}{4})} - \frac{\frac{1}{7} \cdot 56}{\frac{1}{4} \cdot 56} - (\frac{1}{8} \cdot \frac{\frac{7}{4}}{\frac{7}{4}})$

Step 1.6

Multiply $\frac{1}{8}$ by $\frac{\frac{7}{4}}{\frac{7}{4}}$ .

$\frac{\frac{4}{4}}{14 (\frac{4}{4})} - \frac{\frac{1}{7} \cdot 56}{\frac{1}{4} \cdot 56} - \frac{\frac{7}{4}}{8 (\frac{7}{4})}$

Step 1.7

Combine $14$ and $\frac{4}{4}$ .

$\frac{\frac{4}{4}}{\frac{14 \cdot 4}{4}} - \frac{\frac{1}{7} \cdot 56}{\frac{1}{4} \cdot 56} - \frac{\frac{7}{4}}{8 (\frac{7}{4})}$

Step 1.8

Multiply $14$ by $4$ .

$\frac{\frac{4}{4}}{\frac{56}{4}} - \frac{\frac{1}{7} \cdot 56}{\frac{1}{4} \cdot 56} - \frac{\frac{7}{4}}{8 (\frac{7}{4})}$

Step 1.9

Reorder the factors of $\frac{1}{4} \cdot 56$ .

$\frac{\frac{4}{4}}{\frac{56}{4}} - \frac{\frac{1}{7} \cdot 56}{56 (\frac{1}{4})} - \frac{\frac{7}{4}}{8 (\frac{7}{4})}$

Step 1.10

Combine $56$ and $\frac{1}{4}$ .

$\frac{\frac{4}{4}}{\frac{56}{4}} - \frac{\frac{1}{7} \cdot 56}{\frac{56}{4}} - \frac{\frac{7}{4}}{8 (\frac{7}{4})}$

Step 1.11

Combine $8$ and $\frac{7}{4}$ .

$\frac{\frac{4}{4}}{\frac{56}{4}} - \frac{\frac{1}{7} \cdot 56}{\frac{56}{4}} - \frac{\frac{7}{4}}{\frac{8 \cdot 7}{4}}$

Step 1.12

Multiply $8$ by $7$ .

$\frac{\frac{4}{4}}{\frac{56}{4}} - \frac{\frac{1}{7} \cdot 56}{\frac{56}{4}} - \frac{\frac{7}{4}}{\frac{56}{4}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\frac{4}{4} - \frac{1}{7} \cdot 56 - \frac{7}{4}}{\frac{56}{4}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- \frac{1}{7} \cdot 56 + \frac{4 - 7}{4}}{\frac{56}{4}}$

Step 2.3

Subtract $7$ from $4$ .

$\frac{- \frac{1}{7} \cdot 56 + \frac{- 3}{4}}{\frac{56}{4}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $7$ .

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Step 3.1.1

Move the leading negative in $- \frac{1}{7}$ into the numerator.

$\frac{\frac{- 1}{7} \cdot 56 + \frac{- 3}{4}}{\frac{56}{4}}$

Step 3.1.2

Factor $7$ out of $56$ .

$\frac{\frac{- 1}{7} \cdot (7 (8)) + \frac{- 3}{4}}{\frac{56}{4}}$

Step 3.1.3

Cancel the common factor.

$\frac{\frac{- 1}{7} \cdot (7 \cdot 8) + \frac{- 3}{4}}{\frac{56}{4}}$

Step 3.1.4

Rewrite the expression.

$\frac{- 1 \cdot 8 + \frac{- 3}{4}}{\frac{56}{4}}$

Step 3.2

Multiply $- 1$ by $8$ .

$\frac{- 8 + \frac{- 3}{4}}{\frac{56}{4}}$

Step 3.3

Move the negative in front of the fraction.

$\frac{- 8 - \frac{3}{4}}{\frac{56}{4}}$

Step 4

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{- 8 \cdot \frac{4}{4} - \frac{3}{4}}{\frac{56}{4}}$

Step 5

Combine $- 8$ and $\frac{4}{4}$ .

$\frac{\frac{- 8 \cdot 4}{4} - \frac{3}{4}}{\frac{56}{4}}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{- 8 \cdot 4 - 3}{4}}{\frac{56}{4}}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 8$ by $4$ .

$\frac{\frac{- 32 - 3}{4}}{\frac{56}{4}}$

Step 7.2

Subtract $3$ from $- 32$ .

$\frac{\frac{- 35}{4}}{\frac{56}{4}}$

Step 8

Move the negative in front of the fraction.

$\frac{- \frac{35}{4}}{\frac{56}{4}}$

Step 9

Cancel the common factor of $56$ and $4$ .

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Step 9.1

Factor $4$ out of $56$ .

$\frac{- \frac{35}{4}}{\frac{4 \cdot 14}{4}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $4$ out of $4$ .

$\frac{- \frac{35}{4}}{\frac{4 \cdot 14}{4 (1)}}$

Step 9.2.2

Cancel the common factor.

$\frac{- \frac{35}{4}}{\frac{4 \cdot 14}{4 \cdot 1}}$

Step 9.2.3

Rewrite the expression.

$\frac{- \frac{35}{4}}{\frac{14}{1}}$

Step 9.2.4

Divide $14$ by $1$ .

$\frac{- \frac{35}{4}}{14}$

Step 10

Multiply the numerator by the reciprocal of the denominator.

$- \frac{35}{4} \cdot \frac{1}{14}$

Step 11

Cancel the common factor of $7$ .

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Step 11.1

Move the leading negative in $- \frac{35}{4}$ into the numerator.

$\frac{- 35}{4} \cdot \frac{1}{14}$

Step 11.2

Factor $7$ out of $- 35$ .

$\frac{7 (- 5)}{4} \cdot \frac{1}{14}$

Step 11.3

Factor $7$ out of $14$ .

$\frac{7 \cdot - 5}{4} \cdot \frac{1}{7 \cdot 2}$

Step 11.4

Cancel the common factor.

$\frac{7 \cdot - 5}{4} \cdot \frac{1}{7 \cdot 2}$

Step 11.5

Rewrite the expression.

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

Step 12

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

$\frac{- 5}{4 \cdot 2}$

Step 13

Simplify the expression.

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Step 13.1

Multiply $4$ by $2$ .

$\frac{- 5}{8}$

Step 13.2

Move the negative in front of the fraction.

$- \frac{5}{8}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{8}$

Decimal Form:

$- 0.625$