# 6.1.6 Fractions of a Group

## Activity: Fractions of a Group

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 math course.

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

### Discussion

What is the total number of people surveyed? How many of those reported taking a college course during the last year? Remember to reduce your fraction!

### Answer

(a) The fraction who have taken a college course during the last year is . Now, both 245 and 560 look as though they can be divided by 5. Let’s try it. Yes! That gives us . Now, 7 is one of the few numbers that can divide evenly into 49. Does it also divide 112? Yes again! This fraction can be simplified by dividing the top and bottom by 5 and then by 7:

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

### Discussion

How many out of the total number of people interviewed took a math course? Remember to reduce your fraction! |

### Answer

(b) The fraction who have taken a math course is .

Cancel 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 reduce by can be used, but many people find it easy to divide by 10 first.)

Again, there are no more numbers that will divide evenly into both the numerator and the denominator, so we know we have our answer. The fraction who have taken a math course is .

6.1.5 Equivalent Fractions