Drinking Juice, Variation 3
Task
Alisa had some juice in a bottle. Then she drank \frac38 liters of juice. If this was \frac34 of the juice that was originally in the bottle, how much juice was there to start?
IM Commentary
This task builds on a fifth grade fraction multiplication task, “5.NF Drinking Juice.” This task uses the identical context, but asks the corresponding “Group Size Unknown” division problem. See “Drinking Juice, Variation 2” for the “Number of Groups Unknown” version.
Solutions
Solution: Solution
From the question we know that Alisa drank \frac38 liters of juice, which was \frac34 of the amount of juice that was in the bottle.

What we really want to know is how many liters or what fraction of a liter of juice was in the bottle. Therefore we are looking for how many liters are in the whole (\frac44) amount of juice in the bottle. To answer this we will start by breaking the amount of juice in the bottle into three equal pieces.

Since \frac38 of a liter is broken into three equal pieces, each piece represents \frac18 of a liter.

What we are really concerned with is the total amount of juice in the bottle, and because the amount of juice in the bottle is divided up into fourths, we need four of them to make the whole.

Relabeling the picture will make it just a bit easier to see the answer.

Now it is clear that the total amount of juice in the bottle was \frac48=\frac12 of a liter.
Solution: A computational approach
This question is equivalent to asking, "\frac34 of what quantity of juice is \frac38 liter?" We can write this symbolically as \frac34 \times ? = \frac38
Alisa had \frac12 liter of juice in the bottle to start.
Drinking Juice, Variation 3
Alisa had some juice in a bottle. Then she drank \frac38 liters of juice. If this was \frac34 of the juice that was originally in the bottle, how much juice was there to start?