## Carlos’s Method

## Work Time

# Carlos’s Method

Carlos wants to find 3 ÷ $\frac{2}{3}$. He decides to use the same method he used to find $\frac{8}{9}$ ÷ 4 in the previous lesson: multiply by the reciprocal.

At first, Carlos isn’t sure what to do with $\frac{2}{3}$. What is the reciprocal of $\frac{2}{3}$? He thinks back to a rule he learned: the multiplicative inverse, or reciprocal, of $\frac{a}{b}$ is $\frac{b}{a}$. For example, the reciprocal of 4 is $\frac{1}{4}$; the reciprocal of $\frac{1}{5}$ is 5. So, Carlos determines that the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. He then solves the problem as follows: 3 ÷ $\frac{2}{3}$ = 3 • $\frac{3}{2}$ = $\frac{9}{2}$.

Thus, 3 ÷ $\frac{2}{3}$ = $\frac{9}{2}$.

- Use Carlos’s method to find 6 ÷ $\frac{2}{5}$.
- Describe and explain each step of your solution.

Ask yourself:

Will the answer be greater than or less than 3? How can you use the reciprocal of 25 to solve the problem?