Lesson 20 Section 3 ## "Out of"The word 'fraction,' in everyday speech, has come to mean a part -- half, a third, a fourth, a fifth -- as in the phrase "a fraction of the students," or "3 out of 5 students." 3 out of 5, however, is strictly a ratio. 3 is In this Lesson, however, we defer to the everyday use of a fraction to express "out of." Thus when 3 out of 5 respond 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 |
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than the whole, which is represented by 1. Note that the number that follows "of" must be the denominator. For that number signifies the Also, "3 out of 5" -- a smaller number out of a larger -- makes sense. It would make no sense to say "5 out of 3." 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?
The number that follows "of" -- 20 -- is the denominator.
were present. As for the percent, it is so many out of
"3 out of 20 is how many out of 100?" Since 100 is 5 × 20, then the missing term is 5 × 3:
15% were absent. The rest, 100% − 15% = 85%, were present. Example 2. 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?
Girls + Boys = 17 + 12 = 29. Therefore, 17 out of 29 are girls:
And 12 out of 29 are boys:
Compare Lesson 18, Example 12. Example 3. 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?
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
(Lesson 10.) See
This is approximately 38 (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
See
This is approximately 61 (We could anticipate that this would be more than 50%, because 212 is more than half of 347.) Or, since 38 100% − 38 The student should easily find this to be 61
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