Question

Every day, Emilio's orange juice stand uses 2/3 of a bag of oranges. How many days will 4 2/3 bags of oranges last?

Write your answer as a fraction or as a whole or mixed number.

Answer 1

To find out how many days 4 2/3 bags of oranges will last when Emilio's orange juice stand uses 2/3 of a bag of oranges per day, we need to divide the total amount of oranges by the daily usage.

First, let's convert 4 2/3 bags into an improper fraction:

\[
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\]

Now, we will divide this amount by the daily usage, which is 2/3 bags per day:

\[
\text{Number of days} = \frac{\frac{14}{3}}{\frac{2}{3}}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{\frac{14}{3}}{\frac{2}{3}} = \frac{14}{3} \times \frac{3}{2}
\]

When we multiply the fractions, we can cancel the 3's:

\[
= \frac{14 \times 1}{1 \times 2} = \frac{14}{2} = 7
\]

Thus, the number of days that 4 2/3 bags of oranges will last is

\[
\boxed{7}
\]