Find all the proper fractions (in reduced form) whose denominators and numerators are single digits. Then
put them in order from smallest to largest. For example, you would not include 3/9 because it is equivalent to 1/3.
People often ask where I come up with the Problems of the Month. This particular problem arose from my daily walk with my wife.
We have a 4.5 mile path that we walk here in the city and that is nine half miles. Using my wife's pedometer
(yes, the pedometer figured into another problem in 2010), we knew where several of the mile markers
were located. So, I could determine when we were 1/3 of the way, 1/2 of the way, 2/3 of the way, ... But on one walk when it
was 8 degrees out, I started telling my wife when we were 1/9 of the way, 1/6 of the way, and then I wondered about the fractions in between.
Hence this problem!
Solution to the Problem:
1/9, 1/8, 1/7, 1/6, 1/5, 2/9, 1/4, 2/7, 1/3. 3/8, 2/5, 3/7, 4/9, 1/2,5/9, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 7/9, 4/5, 5/6, 6/7, 7/8, 8/9
First, I found the least common multiple of 2, 3, 4, 5, 6, 7, 8, and 9, which is 2,520.
Then, I converted each of the unit fractions with single digit denominators to equivalent fractions with 2520 as a denominator and placed them on a number line:
1/9 = 280/2520
1/8 = 315/2520
1/7 = 360/2520
1/6 = 420/2520
1/5 = 504/2520
1/4 = 630/2520
1/3 = 840/2520
1/2 = 1260/2520
Then, I converted each of the remaining fractions to equivalent fractions with 2520 as a denominator and placed them on the number line.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Kalvin Hereford |
Mountain View High School, Mountain View, Wyoming |