## Counting fractions in a range

### Problem 73

Published on Friday, 2nd July 2004, 06:00 pm; Solved by 16105; Difficulty rating: 15%Consider the fraction, *n/d*, where *n* and *d* are positive integers. If *n*<*d* and HCF(*n,d*)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for *d* ≤ 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, **3/8, 2/5, 3/7**, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 3 fractions between 1/3 and 1/2.

How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for *d* ≤ 12,000?