Question

What is the quotient of Three-fourths and StartFraction 5 Over 6 EndFraction?

A fraction bar labeled 1. Under the 1 are 4 boxes labeled one-fourth. Under the 4 boxes are 6 boxes labeled one-sixth. Under the 6 boxes are 12 boxes labeled one-twelfth.
Three-fourths
StartFraction 9 Over 10 EndFraction
mc025-6.jpg
4 and one-half

Answer 1

To find the quotient of \(\frac{3}{4}\) and \(\frac{5}{6}\), you can follow these steps:

1. **Dividing by a fraction** is equivalent to multiplying by its reciprocal. So, we rewrite the expression:
\[
\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5}
\]

2. **Multiply the fractions**:
\[
= \frac{3 \times 6}{4 \times 5} = \frac{18}{20}
\]

3. **Simplify the fraction**: Both the numerator and the denominator can be divided by 2:
\[
= \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\]

Thus, the quotient of \(\frac{3}{4}\) and \(\frac{5}{6}\) is \(\frac{9}{10}\).

The answer is:
\(\frac{9}{10}\)