Simplify (1/2-6/5)/(3/2-1/6)

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $2$ .

Factor $2$ out of $30$ .

$\frac{2 (15) \frac{1}{2} + 30 (- \frac{6}{5})}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Cancel the common factor.

$\frac{2 \cdot 15 \frac{1}{2} + 30 (- \frac{6}{5})}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Rewrite the expression.

$\frac{15 + 30 (- \frac{6}{5})}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Cancel the common factor of $5$ .

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

$\frac{15 + 30 (\frac{- 6}{5})}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Factor $5$ out of $30$ .

$\frac{15 + 5 (6) \frac{- 6}{5}}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Cancel the common factor.

$\frac{15 + 5 \cdot 6 \frac{- 6}{5}}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Rewrite the expression.

$\frac{15 + 6 \cdot - 6}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Multiply $6$ by $- 6$ .

$\frac{15 - 36}{30 (\frac{3}{2}) + 30 (- \frac{1}{6})}$

Cancel the common factor of $2$ .

Factor $2$ out of $30$ .

$\frac{15 - 36}{2 (15) \frac{3}{2} + 30 (- \frac{1}{6})}$

Cancel the common factor.

$\frac{15 - 36}{2 \cdot 15 \frac{3}{2} + 30 (- \frac{1}{6})}$

Rewrite the expression.

$\frac{15 - 36}{15 \cdot 3 + 30 (- \frac{1}{6})}$

Multiply $15$ by $3$ .

$\frac{15 - 36}{45 + 30 (- \frac{1}{6})}$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{15 - 36}{45 + 30 (\frac{- 1}{6})}$

Factor $6$ out of $30$ .

$\frac{15 - 36}{45 + 6 (5) \frac{- 1}{6}}$

Cancel the common factor.

$\frac{15 - 36}{45 + 6 \cdot 5 \frac{- 1}{6}}$

Rewrite the expression.

$\frac{15 - 36}{45 + 5 \cdot - 1}$

Multiply $5$ by $- 1$ .

$\frac{15 - 36}{45 - 5}$

Step 4

Simplify the expression.

Subtract $36$ from $15$ .

$\frac{- 21}{45 - 5}$

Subtract $5$ from $45$ .

$\frac{- 21}{40}$

Move the negative in front of the fraction.

$- \frac{21}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{21}{40}$

Decimal Form:

$- 0.525$

Simplify (1/2-6/5)/(3/2-1/6)

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