Page 99 - ArithBook5thEd ~ BCC

Solution. LCD{3, 4, 9} =36, and

3 27 2 24 7 28
= = = .
4 36 3 36 9 36
We are asked to arrange the fractions in increasing order, so we list them in increasing order of their
numerators, separated by the inequality symbol <.Thus,
24 27 28
< < .
36 36 36
Now, going back to the equivalent fractions in lowest terms, we have
2 3 7
< < .
3 4 9

3 3 6 11
Example 115. Arrange the numbers 1 ,1 ,1 ,and in decreasing order.
5 4 7 12
Solution. Recall that a proper fraction is less than 1, so 11 is obviously the smallest of the four numbers
12
(the others being mixed numbers greater than 1). To compare the other three numbers, it is enough to
3
3
compare their fractional parts, because each has the same whole number part (1). To compare , ,
4
5
6
and ,we find the LCM{5, 4, 7} = 140, and write equivalent fractions with denominator 140:
7
3 84 3 105 6 120
= = = .
5 140 4 140 7 140
In decreasing order, the numerators are 120 > 105 > 84. The corresponding ordering of the fractions is
6 3 3
> > ,
7 4 5
and it follows that the corresponding order of the mixed numbers (each with whole number part 1) is
6 3 3
1 > 1 > 1 .
7 4 5
Adjoining the smallest (proper) fraction 11 at the end, we have, finally, the decreasing order
12
6 3 3 11
1 > 1 > 1 > .
7 4 5 12

3.9.1 Exercises
4 3 1
1. Arrange in decreasing order: , ,and .
9 8 3
3 3 5
2. Arrange in increasing order: , ,and .
5 4 7
5 7
3. Is of an inch more or less than of an inch?
12 16
5
4. Is 9 inches closer to 9 or 10 inches?
8
5 3
5. A stock price changed from 5 to 5 . Did the price go up or down?
8 4

Page 99