## Simple Fractions

#### Problem

A fraction whose numerator (top number) is less than its denominator (bottom number) is called a simple fraction.

1 9 | 2 9 | 4 9 | 5 9 | 7 9 | 8 9 |

There are six simple fractions involving ninths that cannot be cancelled down. How many simple fractions with a denominator equal to 24 cannot be cancelled down?

#### Solution

We are looking for the set of integers less than 24 that are co-prime (have no factors in common) with 24: 1, 5, 7, 11, 13, 17, 19 and 23.

So there are 8 simple fractions with a denominator of 24 that cannot be cancelled down.

Investigate difference fractions.

(Hint: look at the numbers that are not co-prime to begin with.)

Problem ID: 72 (Apr 2002) Difficulty: 1 Star