Evaluate (3/8-3/4)/(2/3-3/5)

$\frac{\frac{3}{8} - \frac{3}{4}}{\frac{2}{3} - \frac{3}{5}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $120$ .

Multiply $\frac{\frac{3}{8} - \frac{3}{4}}{\frac{2}{3} - \frac{3}{5}}$ by $\frac{120}{120}$ .

$\frac{120}{120} \cdot \frac{\frac{3}{8} - \frac{3}{4}}{\frac{2}{3} - \frac{3}{5}}$

Combine.

$\frac{120 (\frac{3}{8} - \frac{3}{4})}{120 (\frac{2}{3} - \frac{3}{5})}$

Step 2

Apply the distributive property.

$\frac{120 (\frac{3}{8}) + 120 (- \frac{3}{4})}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $8$ .

Factor $8$ out of $120$ .

$\frac{8 (15) \frac{3}{8} + 120 (- \frac{3}{4})}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Cancel the common factor.

$\frac{8 \cdot 15 \frac{3}{8} + 120 (- \frac{3}{4})}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Rewrite the expression.

$\frac{15 \cdot 3 + 120 (- \frac{3}{4})}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Multiply $15$ by $3$ .

$\frac{45 + 120 (- \frac{3}{4})}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Cancel the common factor of $4$ .

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

$\frac{45 + 120 (\frac{- 3}{4})}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Factor $4$ out of $120$ .

$\frac{45 + 4 (30) \frac{- 3}{4}}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Cancel the common factor.

$\frac{45 + 4 \cdot 30 \frac{- 3}{4}}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Rewrite the expression.

$\frac{45 + 30 \cdot - 3}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Multiply $30$ by $- 3$ .

$\frac{45 - 90}{120 (\frac{2}{3}) + 120 (- \frac{3}{5})}$

Cancel the common factor of $3$ .

Factor $3$ out of $120$ .

$\frac{45 - 90}{3 (40) \frac{2}{3} + 120 (- \frac{3}{5})}$

Cancel the common factor.

$\frac{45 - 90}{3 \cdot 40 \frac{2}{3} + 120 (- \frac{3}{5})}$

Rewrite the expression.

$\frac{45 - 90}{40 \cdot 2 + 120 (- \frac{3}{5})}$

Multiply $40$ by $2$ .

$\frac{45 - 90}{80 + 120 (- \frac{3}{5})}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{45 - 90}{80 + 120 (\frac{- 3}{5})}$

Factor $5$ out of $120$ .

$\frac{45 - 90}{80 + 5 (24) \frac{- 3}{5}}$

Cancel the common factor.

$\frac{45 - 90}{80 + 5 \cdot 24 \frac{- 3}{5}}$

Rewrite the expression.

$\frac{45 - 90}{80 + 24 \cdot - 3}$

Multiply $24$ by $- 3$ .

$\frac{45 - 90}{80 - 72}$

Step 4

Simplify the expression.

Subtract $90$ from $45$ .

$\frac{- 45}{80 - 72}$

Subtract $72$ from $80$ .

$\frac{- 45}{8}$

Move the negative in front of the fraction.

$- \frac{45}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{45}{8}$

Decimal Form:

$- 5.625$

Mixed Number Form:

$- 5 \frac{5}{8}$

Evaluate (3/8-3/4)/(2/3-3/5)

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