Question

find the quotient.
\\(\frac{1}{4} \div \frac{5}{6}\\)
simplify your answer completely.
?

Explanation:

Step1: Recall fraction division rule

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, $\frac{1}{4} \div \frac{5}{6} = \frac{1}{4} \times \frac{6}{5}$.

Step2: Multiply numerators and denominators

Multiply the numerators: $1 \times 6 = 6$. Multiply the denominators: $4 \times 5 = 20$. So we get $\frac{6}{20}$.

Step3: Simplify the fraction

Divide both numerator and denominator by their greatest common divisor, which is 2. $\frac{6 \div 2}{20 \div 2} = \frac{3}{10}$.

Answer:

$\frac{3}{10}$