We are asked to choose the reason why \(\frac{3}{5}\) is the exact quotient for \(\frac{1}{2}\) divided by \(\frac{5}{6}\).
We know that divisor is the number that we divide with. The quotient is the answer to any division problem. Dividend is the number that we want to divide.
\(\text{Dividend}=\text{Quotient}\times \text{Divisor}\)
We can see that is our given problem dividend is \(\frac{1}{2}\), quotient is \(\frac{3}{5}\) and divisor is \(\frac{5}{6}\). Upon multiplying quotient with divisor, we will get:
\(\text{Dividend}=\frac{3}{5}\times \frac{5}{6}\)
We can cancel out 5 from numerator and denominator.
\(\frac{1}{2}=\frac{3}{1}\times \frac{1}{6}\)
\(\frac{1}{2}=\frac{3}{6}\)
\(\frac{1}{2}=\frac{3\times 1}{3\times 2}\)
\(\frac{1}{2}=\frac{1}{2}\)
Since both sides are equal, therefore, last option \(\frac{3}{5}\times \frac{5}{6}=\frac{1}{2}\) is the correct choice.
