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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $2$ .

$\frac{8 + 20 (- \frac{7}{2})}{20 (\frac{5}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$\frac{8 + 20 (\frac{- 7}{2})}{20 (\frac{5}{2}) + 20 (- \frac{3}{4})}$

Factor $2$ out of $20$ .

$\frac{8 + 2 (10) \frac{- 7}{2}}{20 (\frac{5}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor.

$\frac{8 + 2 \cdot 10 \frac{- 7}{2}}{20 (\frac{5}{2}) + 20 (- \frac{3}{4})}$

Rewrite the expression.

$\frac{8 + 10 \cdot - 7}{20 (\frac{5}{2}) + 20 (- \frac{3}{4})}$

Multiply $10$ by $- 7$ .

$\frac{8 - 70}{20 (\frac{5}{2}) + 20 (- \frac{3}{4})}$

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$\frac{8 - 70}{2 (10) \frac{5}{2} + 20 (- \frac{3}{4})}$

Cancel the common factor.

$\frac{8 - 70}{2 \cdot 10 \frac{5}{2} + 20 (- \frac{3}{4})}$

Rewrite the expression.

$\frac{8 - 70}{10 \cdot 5 + 20 (- \frac{3}{4})}$

Multiply $10$ by $5$ .

$\frac{8 - 70}{50 + 20 (- \frac{3}{4})}$

Cancel the common factor of $4$ .

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

$\frac{8 - 70}{50 + 20 (\frac{- 3}{4})}$

Factor $4$ out of $20$ .

$\frac{8 - 70}{50 + 4 (5) \frac{- 3}{4}}$

Cancel the common factor.

$\frac{8 - 70}{50 + 4 \cdot 5 \frac{- 3}{4}}$

Rewrite the expression.

$\frac{8 - 70}{50 + 5 \cdot - 3}$

Multiply $5$ by $- 3$ .

$\frac{8 - 70}{50 - 15}$

Step 4

Simplify the expression.

Subtract $70$ from $8$ .

$\frac{- 62}{50 - 15}$

Subtract $15$ from $50$ .

$\frac{- 62}{35}$

Move the negative in front of the fraction.

$- \frac{62}{35}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{62}{35}$

Decimal Form:

$- 1.77142857 \dots$

Mixed Number Form:

$- 1 \frac{27}{35}$

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

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