Solutions for Session 7, Part C

See solutions for Problems: C1 | C2 | C3 | C4

Problem C1

 a. If the numerator is larger than the denominator, the fraction is greater than 1. b. If twice the numerator is larger than the denominator, the fraction is greater than 1/2. If twice the numerator is smaller than the denominator, the fraction is less than 1/2.

Problem C2

Here are the fractions within each range:

 • 0 to 1/2: 17/35, 2/9 • 1/2 to 1: 4/7, 14/15 • Greater than 1: 25/23

Problem C3

 a. These fractions have the same denominator. The order is 4/17, 7/17, 12/17. b. These fractions have the same numerator. The order is 3/8, 3/7, 3/4. c. These fractions all have numerators that are one less than their denominators. The order is 3/4, 5/6, 7/8. d. These fractions all have numerators that are five less than their denominators. The order is 1/6, 8/13, 12/17. e. These fractions all have numerators that are one less than their denominators. The order is 2/3, 5/6, 10/11.

Problem C4

First divide the list into fractions larger and smaller than 1/2:

 • Smaller than 1/2: 2/5, 1/3, 1/4 • Larger than 1/2: 5/8, 3/4, 2/3, 4/7

For those smaller than 1/2, 2/5 is larger than 1/4 (numerators three less than denominators), 1/3 is larger than 1/4 (same numerator), and 2/5 is larger than 1/3 (compare using equivalent fractions 6/15 and 5/15). The order is 1/4, 1/3, 2/5.

For those larger than 1/2, convert 3/4 and 2/3 to fractions where the numerator is three less than the denominator. (Or you may be able to visualize that 3/4 is greater than 2/3.) The list becomes 5/8, 9/12, 6/9, 4/7. This makes it easy to put the list in order: 4/7, 5/8, 6/9, 9/12.

The complete list is 1/4, 1/3, 2/5, 4/7, 5/8, 2/3, 3/4.