Question

What is the quotient in simplest form?

Three-fourths divided by StartFraction 5 Over 16 EndFraction
StartFraction 15 Over 64 EndFraction
StartFraction 15 Over 16 EndFraction
2 and two-fifths
2 and StartFraction 8 Over 20 EndFraction

Answer 1

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 \(2 \frac{2}{5}\).