Question

What is Two-thirds divided by StartFraction 4 Over 5 EndFraction?

A fraction bar labeled 1. Under the 1 are 5 boxes labeled one-fifth. Under the 5 boxes are 3 boxes containing one-third. Under the 3 boxes are 15 boxes labeled StartFraction 1 Over 15 EndFraction.
Two-thirds
StartFraction 5 Over 6 EndFraction
1 and one-fifth
3 and one-third

Answer 1

To solve the problem of dividing two-thirds by \(\frac{4}{5}\), we can follow these steps:

1. **Write the expression**:
\[
\frac{2}{3} \div \frac{4}{5}
\]

2. **Change division to multiplication**:
When dividing by a fraction, you can multiply by its reciprocal. The reciprocal of \(\frac{4}{5}\) is \(\frac{5}{4}\). Thus, we have:
\[
\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}
\]

3. **Multiply the fractions**:
To multiply fractions, multiply the numerators and the denominators:
\[
\frac{2 \times 5}{3 \times 4} = \frac{10}{12}
\]

4. **Simplify if necessary**:
We can simplify \(\frac{10}{12}\) by dividing both the numerator and the denominator by 2:
\[
\frac{10 \div 2}{12 \div 2} = \frac{5}{6}
\]

Therefore, the result of \(\frac{2}{3} \div \frac{4}{5}\) is \(\frac{5}{6}\).

The correct answer is: **\(\frac{5}{6}\)**.