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

By Susan J. Lamon | Go to book overview

Chapter 10
Reasoning With Fractions
1. Fifths are shown using horizontal divisions and sixths are shown using vertical divisions. Essentially, this double partitioning process produces a common denominator. When 4/5 is shaded, 24/30 of the unit is shaded, and when 5/6 is shaded, 25/30 of the unit is shaded. Thus, 5/6 is greater.
2. CRP 8/14 is greater than 1/2 and 4/9 is less than 1/2. So 8/14 > 4/9.
 a. SNP 3/17 and 3/19 each have the same number of pieces, and so the critical question becomes "What size are the pieces?" Seventeenths are larger than nineteenths, so 3/17 > 3/9. b. SSP Because both fractions involve thirteenths, the decision about which is larger can be made by asking how many of those identical pieces each fraction contains. 5/13 > 8/13. c. SNP 3/2 = 1 1/2, while 3/4 = 1 1/3. Both mixed numbers are between 1 unit and 2 units and we need only compare their fractional parts. Because numerators are the same, we need to compare the size of the pieces. Because 1/2 > 1/3, 1 1/2 > 1 1/3 and 3/2 > 4/3.
3. , so to find fractions between 7/14 and choose numerators greater than 7 and less than 7 7/13. For example, choose 7 6/13, 7 5/13, and 7 4/13. Then and and between the given fractions.

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