Simplify (6/5-5/2)/(3/2-5/4)

$\frac{\frac{6}{5} - \frac{5}{2}}{\frac{3}{2} - \frac{5}{4}}$

Step 1

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

Multiply $\frac{\frac{6}{5} - \frac{5}{2}}{\frac{3}{2} - \frac{5}{4}}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{\frac{6}{5} - \frac{5}{2}}{\frac{3}{2} - \frac{5}{4}}$

Combine.

$\frac{20 (\frac{6}{5} - \frac{5}{2})}{20 (\frac{3}{2} - \frac{5}{4})}$

Step 2

Apply the distributive property.

$\frac{20 (\frac{6}{5}) + 20 (- \frac{5}{2})}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{5 (4) \frac{6}{5} + 20 (- \frac{5}{2})}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Cancel the common factor.

$\frac{5 \cdot 4 \frac{6}{5} + 20 (- \frac{5}{2})}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Rewrite the expression.

$\frac{4 \cdot 6 + 20 (- \frac{5}{2})}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Multiply $4$ by $6$ .

$\frac{24 + 20 (- \frac{5}{2})}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{24 + 20 (\frac{- 5}{2})}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Factor $2$ out of $20$ .

$\frac{24 + 2 (10) \frac{- 5}{2}}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Cancel the common factor.

$\frac{24 + 2 \cdot 10 \frac{- 5}{2}}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Rewrite the expression.

$\frac{24 + 10 \cdot - 5}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Multiply $10$ by $- 5$ .

$\frac{24 - 50}{20 (\frac{3}{2}) + 20 (- \frac{5}{4})}$

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$\frac{24 - 50}{2 (10) \frac{3}{2} + 20 (- \frac{5}{4})}$

Cancel the common factor.

$\frac{24 - 50}{2 \cdot 10 \frac{3}{2} + 20 (- \frac{5}{4})}$

Rewrite the expression.

$\frac{24 - 50}{10 \cdot 3 + 20 (- \frac{5}{4})}$

Multiply $10$ by $3$ .

$\frac{24 - 50}{30 + 20 (- \frac{5}{4})}$

Cancel the common factor of $4$ .

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

$\frac{24 - 50}{30 + 20 (\frac{- 5}{4})}$

Factor $4$ out of $20$ .

$\frac{24 - 50}{30 + 4 (5) \frac{- 5}{4}}$

Cancel the common factor.

$\frac{24 - 50}{30 + 4 \cdot 5 \frac{- 5}{4}}$

Rewrite the expression.

$\frac{24 - 50}{30 + 5 \cdot - 5}$

Multiply $5$ by $- 5$ .

$\frac{24 - 50}{30 - 25}$

Step 4

Simplify the expression.

Subtract $50$ from $24$ .

$\frac{- 26}{30 - 25}$

Subtract $25$ from $30$ .

$\frac{- 26}{5}$

Move the negative in front of the fraction.

$- \frac{26}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{26}{5}$

Decimal Form:

$- 5.2$

Mixed Number Form:

$- 5 \frac{1}{5}$

Simplify (6/5-5/2)/(3/2-5/4)

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