To find the quotient of \(\frac{3}{4}\) divided by \(\frac{5}{16}\), we'll use the rule that dividing by a fraction is the same as multiplying by its reciprocal.
So we have:
\[ \frac{3}{4} \div \frac{5}{16} = \frac{3}{4} \times \frac{16}{5} \]
Now, we can multiply these fractions:
\[ \frac{3 \times 16}{4 \times 5} = \frac{48}{20} \]
Next, we simplify \(\frac{48}{20}\) by finding the greatest common divisor (GCD) of 48 and 20, which is 4.
Now, dividing the numerator and the denominator by 4:
\[ \frac{48 \div 4}{20 \div 4} = \frac{12}{5} \]
Finally, we can express \(\frac{12}{5}\) as a mixed number. Since 12 divided by 5 is 2 with a remainder of 2, we can write:
\[ \frac{12}{5} = 2 \frac{2}{5} \]
Thus, the quotient in simplest form is:
\[ 2 \frac{2}{5} \]
The answer is \(2 \frac{2}{5}\).