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UNIT FRACTIONS

Lesson 20  Section 2


 4.   What kind of fraction does "out of" indicate?
3 out of 5
  A proper fraction. The numerator will be smaller than the denominator.

  3 out of 5 indicates the proper fraction  3
5		 .  3 out of 5 is less than

the whole, which is represented by 1.

*

Rather, 3 out of 5 implies the ratio three fifths. For, to say that 3 out of 5 people responded yes, is equivalent to saying that three fifths responded yes. (Lesson 17.) The word fraction. however, has become confused with the word ratio because 1) the English names of the fractions are the same as the ratios; 2) we do written calculations with fractions; and 3) the formalism of the last century sought to convert even arithmetic into algebra, which is the written manipulations of symbols, and is not verbal. Ratios are verbal, they are expressed in words.

When 3 out of 5 responded yes, we ask, "What fraction responded yes?" It would be very wordy to ask, "What is the ratio of those who responded yes to the total number surveyed?" Yet that is what the former question means. To write a fraction -- "3/5 responded yes" -- is a vulgarism. You will never see it in any newspaper or journal. When we say it, of course, there is no problem.

Fractions, nevertheless, afford a short-handed way of doing ratio problems.

Example 1.   In a class of 20 students, 3 were absent.  What fraction were absent?  What fraction were present?

What percent were absent?  What percent were present?

  Answer.  3 out of 20 students were absent:     Part  
Whole		  =   3 
20
Now, if 3 out of 20 were absent, then the rest, 17 out of 20 --  17
20		  --

were present.

As for the percent, it is so many out of 100.  Proportionally,

 3 
20		  =    ? 
100

"3 out of 20  is  how many out of 100?"

(Lesson 17, Question 5.)

Since 100 = 5 × 20, then the missing term is 5 × 3:

 3 
20		  =   15 
100		  = 15%

15% were absent.  The rest, 100%minus 15% = 85%, were present.

Example 3.  The whole is the sum of the parts.    In a class, there are 17 girls and 12 boys.  What fraction of the class are girls, and what fraction are boys?

Answer.  In this problem, we are not given the whole number of students.  But the whole is the sum of the two parts:

Girls + Boys = 17 + 12 = 29

Therefore, 17 out of 29 are girls:

  Part  
Whole		  =  17
29

And 12 out of 29 are boys:

  Part  
Whole		  =  12
29

Compare Lesson 17, Example 8.

Example 4.  Calculator problem.   In a class election, 135 students voted for candidate A, and 212 voted for candidate B.  What percent voted for A, and what percent voted for B?

Solution.  Again, the whole is the sum of the two parts:

135 + 212 = 347

Therefore, 135 out of 347 voted for A, while 212 out of 347 voted for B.

To find the percent that voted for A, press

135 ÷  347 %

(Lesson 10.)  See

 38.90489  

This is approximately

38.9%

(We could anticipate that this would be less than 50%, because 135 is less than half of 347.)

For the percent that voted for B, press

212 ÷  347 %

See

 61.0951 

This is approximately

61.1%

(We could anticipate that this would be more than 50%, because 212 is more than half of 347.)

Or, since 38.9% voted for A, then the number that voted for B is

100% − 38.9%

The student should easily find this to be 61.1%.  (Lesson 6, Question 6.)


Please "turn" the page and do some Problems.

or

Continue on to the next Lesson.

Section 1 on Unit Fractions


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