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CHAPTER XI

PERCENTAGE

or

217. Per Cent. Another name for hundredths is

per

cent. Thus 0.01, or ido, is the same as 1 per cent; 0.001, or ] of Ito, is the same as 1 per cent; 0.06 is the same as 6 per cent.

That part of arithmetic which treats of per cent is called percentage.

218. Symbol for Per Cent. The symbol for per cent is written thus: %.

We may read 0.06 either " 6 hundredths" 6 per cent." In the same way, we may think of 6% as either " 6 per cent” or " 6 hundredths," although it is read "6 per cent."

The expression 800% means 10% and equals the whole number 8; 225% equals the mixed number 2.25, or 27 ; % means 1 of ito, or zdo, and is read either " 1 per cent” or, quite commonly, " 1 of 1%."

219. Relation to Fractions. Since 6% means 1&o, which equals 0.06, or so, we see that we may express per cent as a decimal fraction or as a common fraction.

It is often convenient to use one form, and often another. Thus, if we are multiplying by 13.5%, it is more convenient to think of the multiplier as 0.135; but if we are multiplying by 333%, it is better to think of it as į instead of 0.33}.

621 220. Per Cents as Common Fractions. Since 621%

100 1/8 = 3, therefore

To express per cent as a common fraction, write the number indicating the per cent for the numerator and 100 for the denominator, and reduce this fraction to lowest terms.

For example, 50% means 0.50, or 5%, and this equals 1. Likewise, 25% means 0.25, or 1, and this equals 1.

EXERCISE 125

Reduce to a common fraction, integer, or mixed number: 1. 10%. 6. 4% 11. 100%

16. 331% 2. 20%

7. 5%.
12. 200%

17. 374% 3. 30%

8. 6%.
13. 300%

18. 663%
4. 40%
9. 8%.
14. 150%

19. 624% 5. 50%

10. 9% 15. 275%. 20. 16%% 21. How much is } of 35? 20% of 35? 20% of 350 ? 22. How much is of 40 ? 25% of 40 ? 25% of 400 ? 23. How much is } of 66 ? 50% of 66 ? 50% of 660 ? 24. How much is of 48? 75% of 48? 75% of 480 ? 25. How much is 4 of 90 ? 80% of 90 ? 80% of 900 ?

221. Per Cents as Decimals. Since 25.5% and 0.255 have the same value, therefore

To express as a decimal a number written with the per cent sign, omit the sign and move the decimal point two places to the left.

Thus 13% = 0.01), or 0.015; 125% = 1.25; 0.6% = 0.006.

EXERCISE 126

Erpress as decimals :

1. 25%. 6. 121%. 11. 125%. 16. 37.5%
2. 30%
7. 331%

12. 150% 17. 16.5% 3. 50%

8. 374% 13. 175%. 18. 34.8% 4. 75%. 9. 66%% 14. 250% 19. 62.5% 5. 80% 10. 87%

15. 375% 20. 78.3% 21. Express } as a decimal. Express 1% as a decimal. 22. Express | as a decimal. Express % as a decimal.

222. Decimals as Per Cents. Since per cent means hundredths, to express a decimal as per cent we have to consider only how many hundredths the decimal represents. Thus 0.3 = 0.30 30 hundredths = 30%.

0.375 = 0.373 = 371 hundredths = 371%, or 37.5%.

1.25 = 1/5 = 125%. Therefore, to express a decimal as per cent, write the per cent sign after the number of hundredths.

EXERCISE 127

Express as per cents :
1. 0.25. 3. 0.5. 5. 1.50. 7. 0.375.

9. 0.3. 2. 0.75. 4. 0.8. 6. 2.5. 8. 0.625.

10. 0.63. 11. A pint is what per cent of a quart ? of a gallon ? 12. A dime is what per cent of a dollar ? of a cent?

223. Common Fractions as Per Cents. Since per cent means hundredths, therefore

To express a common fraction as per cent, reduce it to hundredths, omit the denominator, and write the numerator followed by the per cent sign.

This is easily done by reducing the common fraction to a decimal and proceeding as in § 222.

Thus f = 0,80 = 80%; b = 14 = 1.25 = 125%.

EXERCISE 128

Express as per cents :
1.
5.

9. 33.
2.1.
6. } 8. 25

10. 6. 11. A foot is what per cent of a yard ? of 2 yards ? 12. An ounce is what per cent of a pound ? of 2 pounds ?

3. 4.

50%

=

224. Important Per Cents. Certain per cents are used so frequently that their equivalent common fractions should be remembered. These are as follows: 50% = } 831%

f = 121%

= 25% 25% 20% = }

371% 75% 40%

= 621% 121% = } 60%

75%

871% 64% 16 80% 31% 5%

= 163%

333% 371% = 2 81% 12

50%

= 663% 621% = 5 10% = 10 871% = % 30% = 1

20% 163% = 1 70% = io 33}% = } 90% 16

60%

* = 80% 663 % = 3 100% = 1 To take 873% of 648 is, therefore, the same as to take s of 648.

The similarity of these per cents to the corresponding decimal fractions given on page 87 should be noted.

833%

40%

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EXERCISE 129

Find :

1. 50% of $274. 2. 25% of $372. 3. 12% of $512. 4. 61% of $3376. 5. 373% of $17.76. 6. 62% of $11.92. 7. 871% of $34.48. 8. 31% of $739.20.

9. 663% of $80.07. 10. 83}% of $71.10. 11. 20% of $735.15. 12. 40% of $611.25. 13. 60% of $734.15. 14. 112% of 72 ; of 88. 15. 137}% of 96; of 88. 16. 1163 % of 72; of 96.

17. How much is of $2640 ? 12}% of $2640 ? 18. How much is of $3360 ? 37}% of $3360 ? 19. How much is of $4320 ? 624% of $4320 ? 20. How much is 3 of $5768 ? 871% of $5768 ?

21. An inch is what fraction of a foot ? what per cent of a foot ?

22. A pint is what fraction of a gallon ? what per cent of a gallon ?

23. Five cents is what fraction of a dollar ? what per cent of a dollar ?

24. If you wish to find 33}% of a number, what fractional part of the number do you wish to find ?

25. If a man spends one fifth of his income for rent, what per cent does he spend for this purpose ?

26. What per cent of the perimeter is one side of a square? What per cent are two sides ? three sides ?

27. If there are 30 pupils in a class and 50% are boys, what fraction are boys ? How many boys are there?

28. If there are 450 pupils in a school and 52% are boys, what decimal fraction of the pupils are boys ? How many boys are there? How many girls are there?

29. If a city has a population of 18,400, and 221% are pupils in school, what decimal fraction of the population is in school ? How many are in school ?

30. If a shop employs 1680 workers, of whom 37}% are men, 50% are women, and the rest are boys, 'how many are there of each ?

31. A merchant has $9600 invested in his business. The first year he made a profit of 61%, the second year 121%, and the third year 163 %. How much did he make in the three years?

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