Evaluate (1/5-5/4)/(7/2-3/4)

$\frac{\frac{1}{5} - \frac{5}{4}}{\frac{7}{2} - \frac{3}{4}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $20$ .

Multiply $\frac{\frac{1}{5} - \frac{5}{4}}{\frac{7}{2} - \frac{3}{4}}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{\frac{1}{5} - \frac{5}{4}}{\frac{7}{2} - \frac{3}{4}}$

Combine.

$\frac{20 (\frac{1}{5} - \frac{5}{4})}{20 (\frac{7}{2} - \frac{3}{4})}$

Step 2

Apply the distributive property.

$\frac{20 (\frac{1}{5}) + 20 (- \frac{5}{4})}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{5 (4) \frac{1}{5} + 20 (- \frac{5}{4})}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor.

$\frac{5 \cdot 4 \frac{1}{5} + 20 (- \frac{5}{4})}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Rewrite the expression.

$\frac{4 + 20 (- \frac{5}{4})}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor of $4$ .

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

$\frac{4 + 20 (\frac{- 5}{4})}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Factor $4$ out of $20$ .

$\frac{4 + 4 (5) \frac{- 5}{4}}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor.

$\frac{4 + 4 \cdot 5 \frac{- 5}{4}}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Rewrite the expression.

$\frac{4 + 5 \cdot - 5}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Multiply $5$ by $- 5$ .

$\frac{4 - 25}{20 (\frac{7}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$\frac{4 - 25}{2 (10) \frac{7}{2} + 20 (- \frac{3}{4})}$

Cancel the common factor.

$\frac{4 - 25}{2 \cdot 10 \frac{7}{2} + 20 (- \frac{3}{4})}$

Rewrite the expression.

$\frac{4 - 25}{10 \cdot 7 + 20 (- \frac{3}{4})}$

Multiply $10$ by $7$ .

$\frac{4 - 25}{70 + 20 (- \frac{3}{4})}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{4 - 25}{70 + 20 (\frac{- 3}{4})}$

Factor $4$ out of $20$ .

$\frac{4 - 25}{70 + 4 (5) \frac{- 3}{4}}$

Cancel the common factor.

$\frac{4 - 25}{70 + 4 \cdot 5 \frac{- 3}{4}}$

Rewrite the expression.

$\frac{4 - 25}{70 + 5 \cdot - 3}$

Multiply $5$ by $- 3$ .

$\frac{4 - 25}{70 - 15}$

Step 4

Simplify the expression.

Subtract $25$ from $4$ .

$\frac{- 21}{70 - 15}$

Subtract $15$ from $70$ .

$\frac{- 21}{55}$

Move the negative in front of the fraction.

$- \frac{21}{55}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{21}{55}$

Decimal Form:

$- 0.3\overline{81}$

Evaluate (1/5-5/4)/(7/2-3/4)

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