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Running to School, Variation 2


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

Task

The distance between Rosa’s house and her school is \frac34 mile. She ran \frac14 mile. What fraction of the way to school did she run?

IM Commentary

This task builds on a fifth grade fraction multiplication task, “5.NF Running to School, Variation 1.” This task uses the identical context, but asks the corresponding “Number of Groups Unknown” division problem. See “6.NS Running to School, Variation 3” for the “Group Size Unknown” version.

Solutions

Solution: Solution

We know that the distance between Rosa’s house and her school is \frac34 of a mile.

Sol_1_ca18942d0475246e3b087401a1c09893

We also know that Rosa ran \frac14 of a mile.

Sol_2_1f479f97b2d381d3b6715d5e9160d3b5
From the first picture we see that Rosa’s trip to school is broken up into three equal pieces, each representing \frac14 of a mile, which is \frac13 of her trip to school. Thus, Rosa ran \frac13 of the way to her school.

Solution: Taking a computational approach

This question is equivalent to asking, "What fraction of \frac34 mile is \frac14 mile?" We can write this symbolically as ? \times \frac34 = \frac14

which is equivalent to the division problem \frac14 \div \frac34=?
Since \frac14 \div \frac34 = \frac14 \times \frac43 = \frac{4}{12} = \frac13
we see we get the same answer as if we did reasoning about the context in the previous solution.

Rosa ran \frac13 of the way to school.