6.1.6 Fractions of a Group

Activity symbol 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?

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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!

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Answer

(a) The fraction who have taken a college course during the last year is 245 divided by 560. Now, both 245 and 560 look as though they can be divided by 5. Let’s try it. Yes! That gives us 49 divided by 112. 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:

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

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

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Discussion

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

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Answer

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

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.)

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

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 one divided by four.

6.1.5 Equivalent Fractions

6.1.7 True or False?