Evaluate (2/3-1/5)/(7/2-5/6)

$\frac{\frac{2}{3} - \frac{1}{5}}{\frac{7}{2} - \frac{5}{6}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $30$ .

Multiply $\frac{\frac{2}{3} - \frac{1}{5}}{\frac{7}{2} - \frac{5}{6}}$ by $\frac{30}{30}$ .

$\frac{30}{30} \cdot \frac{\frac{2}{3} - \frac{1}{5}}{\frac{7}{2} - \frac{5}{6}}$

Combine.

$\frac{30 (\frac{2}{3} - \frac{1}{5})}{30 (\frac{7}{2} - \frac{5}{6})}$

Step 2

Apply the distributive property.

$\frac{30 (\frac{2}{3}) + 30 (- \frac{1}{5})}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $3$ .

Factor $3$ out of $30$ .

$\frac{3 (10) \frac{2}{3} + 30 (- \frac{1}{5})}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Cancel the common factor.

$\frac{3 \cdot 10 \frac{2}{3} + 30 (- \frac{1}{5})}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Rewrite the expression.

$\frac{10 \cdot 2 + 30 (- \frac{1}{5})}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Multiply $10$ by $2$ .

$\frac{20 + 30 (- \frac{1}{5})}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{20 + 30 (\frac{- 1}{5})}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Factor $5$ out of $30$ .

$\frac{20 + 5 (6) \frac{- 1}{5}}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Cancel the common factor.

$\frac{20 + 5 \cdot 6 \frac{- 1}{5}}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Rewrite the expression.

$\frac{20 + 6 \cdot - 1}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Multiply $6$ by $- 1$ .

$\frac{20 - 6}{30 (\frac{7}{2}) + 30 (- \frac{5}{6})}$

Cancel the common factor of $2$ .

Factor $2$ out of $30$ .

$\frac{20 - 6}{2 (15) \frac{7}{2} + 30 (- \frac{5}{6})}$

Cancel the common factor.

$\frac{20 - 6}{2 \cdot 15 \frac{7}{2} + 30 (- \frac{5}{6})}$

Rewrite the expression.

$\frac{20 - 6}{15 \cdot 7 + 30 (- \frac{5}{6})}$

Multiply $15$ by $7$ .

$\frac{20 - 6}{105 + 30 (- \frac{5}{6})}$

Cancel the common factor of $6$ .

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

$\frac{20 - 6}{105 + 30 (\frac{- 5}{6})}$

Factor $6$ out of $30$ .

$\frac{20 - 6}{105 + 6 (5) \frac{- 5}{6}}$

Cancel the common factor.

$\frac{20 - 6}{105 + 6 \cdot 5 \frac{- 5}{6}}$

Rewrite the expression.

$\frac{20 - 6}{105 + 5 \cdot - 5}$

Multiply $5$ by $- 5$ .

$\frac{20 - 6}{105 - 25}$

Step 4

Reduce the expression by cancelling the common factors.

Subtract $6$ from $20$ .

$\frac{14}{105 - 25}$

Subtract $25$ from $105$ .

$\frac{14}{80}$

Cancel the common factor of $14$ and $80$ .

Factor $2$ out of $14$ .

$\frac{2 (7)}{80}$

Cancel the common factors.

Factor $2$ out of $80$ .

$\frac{2 \cdot 7}{2 \cdot 40}$

Cancel the common factor.

$\frac{2 \cdot 7}{2 \cdot 40}$

Rewrite the expression.

$\frac{7}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{40}$

Decimal Form:

$0.175$

Evaluate (2/3-1/5)/(7/2-5/6)

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