Succeed with maths – Part 1
Succeed with maths – Part 1

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Succeed with maths – Part 1

3 Fractions of a group

When completing the following activity think back to the very first example about the number of people in a group of 500 who felt that wind farms were a necessity. You worked out that 375 of these thought that wind farms were a necessity. These two numbers give the numerator (375) and the denominator (500) for the fraction, which when simplified results in the three divided by four reported in the press release.

Activity 3 Group fractions

Timing: Allow approximately 10 minutes

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?

Comment

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

(a) 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 245 divided by 560.

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 49 divided by 112. 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:

equation sequence 245 super 49 divided by 560 sub 112 equals 49 super seven divided by 112 sub 16 equals seven divided by 16

So seven divided by 16 of the group took a college course in the last year.

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

Answer

(b) The fraction who have taken a maths course is 140 divided by 560.

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.)

equation sequence 140 super 14 divided by 560 sub 56 equals 14 squared divided by 56 sub eight equals two super one divided by eight sub four equals one divided by four

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 one divided by four.

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