# Drinking Juice, Variation 2

## Task

Alisa had $\frac12$ liter of juice in a bottle. She drank $\frac38$ liters of juice. What fraction of the juice in the bottle did Alisa drink?

## IM Commentary

This task builds on a fifth grade fraction multiplication task, â€œ5.NF Drinking Juice.â€ This task uses the identical context, but asks the corresponding â€œNumber of Groups Unknownâ€ division problem. See â€œDrinking Juice, Variation 3â€ for the â€œGroup Size Unknownâ€ version.

## Solutions

Solution: Solution

First, draw a rectangle that represents $\frac12$ liter.

We know that Alisa has $\frac12$ liter of juice in a bottle. Now we break the rectangle that represents $\frac12$ liter into four smaller rectangles. Each small rectangle represents $\frac14$ of $\frac12$, which is $$\frac14 \times \frac12 = \frac18 \text{ liter.}$$ Alisa drank $\frac38$ of a liter of juice so 3 of the small rectangles are shaded. We can now see that 3 of the 4 rectangles that make up the juice in the bottle are shaded.

Alisa drank $\frac34$ of the juice that was in the bottle.

Solution: A computational approach

This question is equivalent to asking, "What fraction of $\frac12$ liter is $\frac38$ liter?" We can write this symbolically as $$? \times \frac12 = \frac38$$ which is equivalent to the division problem $$\frac38 \div \frac12=?$$ Since $$\frac38 \div \frac12 = \frac38 \times \frac21 = \frac68 = \frac 34,$$ we see we get the same answer as if we did reasoning about the context in the previous solution.

Alisa drank $\frac34$ of the juice that was in the bottle.

## Drinking Juice, Variation 2

Alisa had $\frac12$ liter of juice in a bottle. She drank $\frac38$ liters of juice. What fraction of the juice in the bottle did Alisa drink?