Running to School, Variation 2
Task
The distance between Rosaâs 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, â5.NF Running to School, Variation 1.â This task uses the identical context, but asks the corresponding âNumber of Groups Unknownâ division problem. See â6.NS Running to School, Variation 3â for the âGroup Size Unknownâ version.
Solutions
Solution: Solution
We know that the distance between Rosaâs house and her school is $\frac34$ of a mile.
We also know that Rosa ran $\frac14$ of a mile.
From the first picture we see that Rosaâs 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.
Running to School, Variation 2
The distance between Rosaâs house and her school is $\frac34$ mile. She ran $\frac14$ mile. What fraction of the way to school did she run?