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

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

Step 1

Multiply the numerator and denominator of the complex fraction by $60$ .

Multiply $\frac{\frac{2}{3} - \frac{6}{5}}{\frac{3}{4} - \frac{5}{2}}$ by $\frac{60}{60}$ .

$\frac{60}{60} \cdot \frac{\frac{2}{3} - \frac{6}{5}}{\frac{3}{4} - \frac{5}{2}}$

Combine.

$\frac{60 (\frac{2}{3} - \frac{6}{5})}{60 (\frac{3}{4} - \frac{5}{2})}$

Step 2

Apply the distributive property.

$\frac{60 (\frac{2}{3}) + 60 (- \frac{6}{5})}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $3$ .

Factor $3$ out of $60$ .

$\frac{3 (20) \frac{2}{3} + 60 (- \frac{6}{5})}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Cancel the common factor.

$\frac{3 \cdot 20 \frac{2}{3} + 60 (- \frac{6}{5})}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Rewrite the expression.

$\frac{20 \cdot 2 + 60 (- \frac{6}{5})}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Multiply $20$ by $2$ .

$\frac{40 + 60 (- \frac{6}{5})}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{40 + 60 (\frac{- 6}{5})}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Factor $5$ out of $60$ .

$\frac{40 + 5 (12) \frac{- 6}{5}}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Cancel the common factor.

$\frac{40 + 5 \cdot 12 \frac{- 6}{5}}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Rewrite the expression.

$\frac{40 + 12 \cdot - 6}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Multiply $12$ by $- 6$ .

$\frac{40 - 72}{60 (\frac{3}{4}) + 60 (- \frac{5}{2})}$

Cancel the common factor of $4$ .

Factor $4$ out of $60$ .

$\frac{40 - 72}{4 (15) \frac{3}{4} + 60 (- \frac{5}{2})}$

Cancel the common factor.

$\frac{40 - 72}{4 \cdot 15 \frac{3}{4} + 60 (- \frac{5}{2})}$

Rewrite the expression.

$\frac{40 - 72}{15 \cdot 3 + 60 (- \frac{5}{2})}$

Multiply $15$ by $3$ .

$\frac{40 - 72}{45 + 60 (- \frac{5}{2})}$

Cancel the common factor of $2$ .

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

$\frac{40 - 72}{45 + 60 (\frac{- 5}{2})}$

Factor $2$ out of $60$ .

$\frac{40 - 72}{45 + 2 (30) \frac{- 5}{2}}$

Cancel the common factor.

$\frac{40 - 72}{45 + 2 \cdot 30 \frac{- 5}{2}}$

Rewrite the expression.

$\frac{40 - 72}{45 + 30 \cdot - 5}$

Multiply $30$ by $- 5$ .

$\frac{40 - 72}{45 - 150}$

Step 4

Reduce the expression by cancelling the common factors.

Subtract $72$ from $40$ .

$\frac{- 32}{45 - 150}$

Subtract $150$ from $45$ .

$\frac{- 32}{- 105}$

Dividing two negative values results in a positive value.

$\frac{32}{105}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{32}{105}$

Decimal Form:

$0.3\overline{047619}$

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

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