# More: In-Depth Discussion of the Reasoning Activities in "Teaching Fractions and Ratios for Understanding"

By Susan J. Lamon | Go to book overview

Chapter 8
Rational Numbers as Measures
1. By successively partitioning until you have thirty-seconds, you can see that you have about 23/32 of an hour, or 43 minutes. (You should get something close to .72.)
2. By partitioning the quarter-hour interval into 4 equal pieces, you get sixteenths of an hour. Your meter has 1/16 hr. on it and you need 8/16 of an hour, so you must pay for 7/16 of an hour or 26 1/4 minutes. You should deposit 1 quarter and 1 dime.
3. a.If the given interval is 5/9, then partition it into 5 equal pieces, each of which is 1/9. Add another interval that is as long as 4 of those interval to get a unit interval.
 a. Successively partition the given interval until you have 9 equal subintervals. Because 9 subintervals = 9/4, 1 subinterval must be 1/4, and the unit interval must be 4 subintervals.Click for a larger version b. Partition the given interval into 10 subintervals. Then each is 1/17. By adding an interval the length of 7 of them, you get the unit interval.Click for a larger version
4. You get 38 minutes on the meter, which is 38/60 or 19/30 of an hour. Successively partition the hour until you have thirtieths (sixths then

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