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

Question

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: $$\frac{2}{3}÷\frac{4}{5}$$

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: $$\frac{2}{3}÷\frac{4}{5}=\frac{2}{3}\times \frac{5}{4}$$

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: $$\frac{10÷2}{12÷2}=\frac{5}{6}$$

Therefore, the result of $\frac{2}{3}÷\frac{4}{5}$ is $\frac{5}{6}$.

The correct answer is: $\frac{5}{6}$.