8. In an examination the pupils are expected to answer 10 questions. John answers 9 questions correctly. What part does he answer correctly? How many hundredths?

9. In an examination with 5 questions 4 of them are answered correctly. What part is answered correctly? How many hundredths?

If 3 questions are answered correctly, what part is answered correctly? How many hundredths?

10. What fraction

(a) 2 out of 7?
(b) 7 out of 50?

11. How many
take
(a) 11 out of 50?
(b) 37 out of 50?
(c) 8 out of 25?

(c) 9 out of 100?

of a group is taken if we take (c) 9 out of 100? (e) 91 out of a hundred? 47 out of 100? (f) 42 out of 100? hundredths of a group are taken if we

(d)

33. Summary. In computing a pupil's grade on an examination, the standing of a baseball team in a league, and in many business problems it is found convenient to compute according to a certain number out of a hundred. In comparing the scores in examples 6, 7, 8, and 9 it is convenient to have all the scores written as a number of hundredths. But instead of saying so many hundredths, or so many out of a hundred, or so many per hundred, we usually say so many per cent. The expression per cent is a short form of the Latin phrase per centum, which means by the hundred. The symbol % stands for the words per cent. Thus we write 3% for three per cent.

Since 1% means 1 out of a hundred,

1%=.01=100.

These three forms mean exactly the same thing. Similarly, 8%=.08=180, and 125%=1.25=125 100

Exercise 32

1. How many hundredths of 100 is 40? How many per cent?

2. How many hundredths of 100 is each of the following numbers: 6, 18, 16, 121, 24, 8, 100, 120, 500, 842, 1234? 3. Tell how many per cent each is of 100.

What per

4. A man has $100 and gives $6 to his son. cent of the money does the son get? What per cent does the father keep? If the son should receive the same per cent of $200, how much would he receive?

5. In example 4, page 63, what per cent of the class failed? What per cent passed?

34. Changing per cents to decimals. Eight per cent, or 8%, means 8 hundredths and therefore 8% may be written .08, or 18. The fraction may be written in its lowest terms ਗੁੰਨ•

8%=.08=180=28.

Exercise 33

Express as decimals, then as common fractions and reduce to lowest terms the following:

6. 80%. 13. 547%. 20. 12%. 27. .6%.

34. .1%.

7. 22%. 14. 200%. 21. 5%.

28. .08%.

35. .75%

Rule. To change a per cent to a decimal remove the per cent sign and move the decimal point two places to the left.

35. Important equivalents. The following equivalents are very important and should be memorized:

1. Cover the right-hand side of the above equalities and see if you can give them in 20 seconds.

2. Cover the left-hand side of the equalities and see if you can give them in 20 seconds.

3. 50% of a bushel means what part of it?

4. 25% of 36 apples means what part of 36 apples?

5. 33% of the pupils of the seventh grade were absent one day. What part of them were absent? What part were present? What per cent were present?

6. 831% of the pupils in school have been vaccinated. What part have been vaccinated? What part have not? What per cent have not?

7. In a certain year Iowa had half of a full corn crop. What per cent of a full crop did the State have?

8. Of 20 words in a spelling test Harry missed 8. What part of the words did he miss? What per cent of them?

9. Mary solved 4 problems out of 5 correctly. What per cent did she solve correctly? What per cent did she miss?

10. From 2 gallons of whole milk a farmer got a pint of cream. What part of the whole milk was cream? What per cent of it?

11. A man planted 30 acres of corn. Three-fourths of the kernels germinated. What per cent of his crop did the man lose because the seed was poor?

12. One-sixth of a farmer's seed corn failed to germinate. What per cent germinated?

13. A farmer examining an ear of corn found that of the length of the ear was not filled out with kernels. What per cent of the length of the ear was filled out?

14. One-third of the population of a certain city is foreign born. What per cent is native?

15. In the world series baseball game between Brooklyn and Boston, the latter won 4 games and Brooklyn won 1. What part of the games did Boston win? What part did Brooklyn win? What per cent did each win?

16. A teacher sent 50% of her pupils to the playground, 25% of them to the library, and kept the remainder to assist her in putting the room in order. What part of her pupils were sent to the library? What part were kept to assist her? If she had 36 pupils, how many were in each of the three groups?

17. In making a journey a man rode 80 miles by train, then rode 30 miles by automobile, and then drove 10 miles. What part of his journey did he make by automobile? What part did he drive? What per cent of his journey did he make in each way?

18. A recipe for chocolate caramels calls for 1 cup of grated chocolate, 1 cup of brown sugar, cup of molasses, and cup of sweet milk. What part of the mixture is sweet milk? What part is chocolate? What per cent of each?

19. To make raspberry pastils the recipe requires of an ounce of raspberry juice, and 3 ounces of sugar. What part of the mixture is raspberry juice? What part is sugar? What per cent of each?

20. When the housewife buys a round steak she loses about 81% of it in bone and cutting. When she buys porterhouse steak she loses about 121% in bone and cutting. What part of her meat purchase is waste in each case?

36. To find any per cent of a number.

Since 75% of a

number means .75 of it, 75% of 360 may be found by multi