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, “5.NF Drinking Juice.” This task uses the identical context, but asks the corresponding “Number of Groups Unknown” division problem. See “Drinking Juice, Variation 3” for the “Group Size Unknown” 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.