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Drinking Juice, Variation 2


Alignments to Content Standards: 6.NS.A.1

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.

Sol_1_260ac57a70ec7501283d58b83f90fbba

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.