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

1 answer

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: \(\frac{5}{6}\).