Basic Math Examples

$(\frac{3}{8} - \frac{5}{4}) \div (\frac{3}{16} - \frac{1}{8})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{3}{8} - \frac{5}{4}}{\frac{3}{16} - \frac{1}{8}}$

Step 2

Multiply the numerator and denominator of the fraction by $16$ .

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Step 2.1

Multiply $\frac{\frac{3}{8} - \frac{5}{4}}{\frac{3}{16} - \frac{1}{8}}$ by $\frac{16}{16}$ .

$\frac{16}{16} \cdot \frac{\frac{3}{8} - \frac{5}{4}}{\frac{3}{16} - \frac{1}{8}}$

Step 2.2

Combine.

$\frac{16 (\frac{3}{8} - \frac{5}{4})}{16 (\frac{3}{16} - \frac{1}{8})}$

Step 3

Apply the distributive property.

$\frac{16 (\frac{3}{8}) + 16 (- \frac{5}{4})}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $8$ .

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Step 4.1.1

Factor $8$ out of $16$ .

$\frac{8 (2) \frac{3}{8} + 16 (- \frac{5}{4})}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.1.2

Cancel the common factor.

$\frac{8 \cdot 2 \frac{3}{8} + 16 (- \frac{5}{4})}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.1.3

Rewrite the expression.

$\frac{2 \cdot 3 + 16 (- \frac{5}{4})}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{6 + 16 (- \frac{5}{4})}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.3

Cancel the common factor of $4$ .

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Step 4.3.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{6 + 16 (\frac{- 5}{4})}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.3.2

Factor $4$ out of $16$ .

$\frac{6 + 4 (4) \frac{- 5}{4}}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.3.3

Cancel the common factor.

$\frac{6 + 4 \cdot 4 \frac{- 5}{4}}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.3.4

Rewrite the expression.

$\frac{6 + 4 \cdot - 5}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.4

Multiply $4$ by $- 5$ .

$\frac{6 - 20}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.5

Cancel the common factor of $16$ .

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Step 4.5.1

Cancel the common factor.

$\frac{6 - 20}{16 (\frac{3}{16}) + 16 (- \frac{1}{8})}$

Step 4.5.2

Rewrite the expression.

$\frac{6 - 20}{3 + 16 (- \frac{1}{8})}$

Step 4.6

Cancel the common factor of $8$ .

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Step 4.6.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$\frac{6 - 20}{3 + 16 (\frac{- 1}{8})}$

Step 4.6.2

Factor $8$ out of $16$ .

$\frac{6 - 20}{3 + 8 (2) \frac{- 1}{8}}$

Step 4.6.3

Cancel the common factor.

$\frac{6 - 20}{3 + 8 \cdot 2 \frac{- 1}{8}}$

Step 4.6.4

Rewrite the expression.

$\frac{6 - 20}{3 + 2 \cdot - 1}$

Step 4.7

Multiply $2$ by $- 1$ .

$\frac{6 - 20}{3 - 2}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $20$ from $6$ .

$\frac{- 14}{3 - 2}$

Step 5.2

Subtract $2$ from $3$ .

$\frac{- 14}{1}$

Step 5.3

Divide $- 14$ by $1$ .

$- 14$