# 3 Fractions of a group

When completing the following activity think back to the very first example given this week about the number of people in a group of 500 who planned to go on holiday in Yorkshire. You worked out that 375 of these did intend to holiday in their own county. These two numbers give the numerator (375) and the denominator (500) for the fraction, which when simplified results in the reported in the article.

## Activity 2 Group fractions

From a survey of a group of 560 people, 245 say that they have taken a college course during the last year, and 140 say that they have taken a maths course.

(a) What fraction of the total group has taken a college course during the last year?

Hint: what number will give you the denominator and which the numerator? The denominator tells you the total number of parts, and the numerator the number of parts for a particular fraction. Remember to simplify your fraction!

### Answer

The total number in the group is 560, so this gives the denominator for the fraction. Of these, 245 took a college course. This is the numerator (the number of parts of the whole).

Therefore, the fraction who have taken a college course during the last year is .

Both 245 and 560 look as though they can be divided by 5, as they end with a 5 and a 0 respectively. Let’s try it. Yes! That gives . Seven is one of the few numbers that can divide evenly into 49. Does it also divide into 112? It does, so this fraction can be simplified by dividing the top and bottom by 5 and then by 7:

So of the group took a college course in the last year.

(b) What fraction of the total group has taken a maths course?

### Answer

The fraction who have taken a maths course is .

Simplify the fraction by dividing the top and bottom by 10, then by 7, and finally by 2. (A different order, or even a different choice of numbers to cancel with can be used, but many people find it easy to divide by 10 first.)

As the numerator is now 1, you know that we have reached the simplest form of this fraction. No number, other than one, will now divide evenly into both the numerator and the denominator, so you know you have your answer.

The fraction of the group who have taken a maths course is .