To find the quotient of \(-\frac{5}{6} \div \left(-\frac{3}{2}\right)\), we can rewrite the division of fractions as multiplication by the reciprocal:
\[ -\frac{5}{6} \div \left(-\frac{3}{2}\right) = -\frac{5}{6} \times -\frac{2}{3} \]
Now, when multiplying two negative fractions, the negatives cancel out:
\[ -\frac{5}{6} \times -\frac{2}{3} = \frac{5}{6} \times \frac{2}{3} \]
Next, we multiply the numerators and the denominators:
\[ \frac{5 \times 2}{6 \times 3} = \frac{10}{18} \]
Now, we simplify the fraction \(\frac{10}{18}\) by finding the greatest common divisor (GCD) of 10 and 18, which is 2:
\[ \frac{10 \div 2}{18 \div 2} = \frac{5}{9} \]
Thus, the quotient simplified is:
\[ \frac{5}{9} \]
1 answer