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SECTION VIII.

PERCENTAGE.

ORAL EXERCISES.

151.-1. A FARMER planted 200 trees, and 1 out of each hundred died; how many trees died in all? If 2 out of each hundred had died, how many would have died in all? If 3? If 4? If 5? If 6?

2. If 7 trees out of each hundred die, what part of them die? If 9 out of each hundred die? If 11? If 13? If 17? If 25? If 50? If 75? If 100?

These expressions, 7 hundredths, 9 hundredths, 11 hundredths, etc. of a number are called Per Cents., from the Latin per centum, which means by the hundred.

3. What per cent. of a number is 3 hundredths of it? 5 hundredths? 6 hundredths? 8 hundredths? 9 hundredths? 103? 105? 108%? 20? 25? .06? .09? .12? .18? .45? .80? .85? .90? .94?

12

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4. How many hundredths of a number is 6 per cent.? 8 per cent.? 9 per cent.? 10 per cent.? 12 per cent.? 20 per cent.? 90 per cent.?

The symbol % is generally used instead of per cent. Thus, 5% means 5 per cent.

5. How many hundredths of a number is 7%? 14%? 15% 6%? 5%? 50%? 75%? 80%? 100% ?

152. To express a per cent. as a decimal and as a common fraction.

Any per cent. of a number may be expressed as a decimal or as a common fraction.

Thus,

.05

180 26.

=

5%
6% = .06 180 = 8%.

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1. 15%, 40%. 2. 20%, 50%.

3. 25%, 75%.

4. 30%, 80%. 5.9%, 16%.

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WRITTEN EXERCISES.

Express each of the following as a decimal and as a com

mon fraction in its lowest terms:

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6. 12%, 18%.

7. 121%, 16%. 8. 24%, 331%. 9. 61%, 11%. 10. 18%, 28%.

8%
10%.10

1. Express as a per cent.

PROCESS.

153. To express a common fraction as a per cent. Any common fraction may be expressed as a per cent. by reducing it to hundredths. Thus,

.663, or 66%, Ans.

Express each of the

2. 1, 1, 4.

3. 1, 1, 4.
4. 4, 1o, 12.

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WRITTEN EXERCISES.

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7. Po, f, f.

11. 90%, 125%. 12. 66%, 150%. 13. 81%, 37%. 14. 621%, 87%. 15. %, 4%.

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25=180.04 4%. 18 = 18% = .52 = 52%.

52

Dividing 2 by 3 to two places of decimals,

we have = .663, or 66% %.

following fractions as a per cent.:

5. 1, 12, f.

8. f, f, fz.

3

6. Tb. 1. f.

9. THE, 200. 10. 00, f.

The following per cents., with their fractional equivalents, are so frequently used that they should be committed to memory:

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1. What is 10% of 60?

40%

70%

50% = 1.75%

60%

=

62% =
66%

ORAL EXERCISES.

2. What is 163% of 60?

80%

871%
90%

DEFINITIONS.

154. Percentage is that process of computation in which the basis of operation is a hundred.

10% of 60 equals 10%, or, of 60, which is 6, Ans.

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The Base is the number of which the per cent. is taken. The Rate is the number of hundredths of the base taken. The Percentage is the result obtained by taking as many hundredths of the base as are indicated by the rate. ten hundredths of $40

Thus, 10% of $40

$4.

In this problem $40 is the base, 10% is the rate, and $4 is the percentage.

The base plus the percentage is the Amount.

The base minus the percentage is the Difference.

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163% (see table). of 60 is 10, Ans.

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CASE I.

155. Given the base and rate, to find the percentage.

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Find

3. 20% of 50 men. 4. 25% of 120 bu. 5. 50% of 600 yd.

6. 40% of 80 tons. 7. 60% of 300 pupils.

8. 121% of 48 acres. 9. 16% of $600. 10. 331% of 900 feet. 11. 37% of 24 cows.

92

21. What is 24% of $23?

PROCESS.

$23

.24

WRITTEN EXERCISES.

46

$5.52, Ans.

22. What is 555% of 63 bu.?

PROCESS.-55%%

55%

500

900 100

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24% of $23 equals .24 times $23, which by multiplication is $5.52.

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12. 70% of 120 years.

13. 62% of 64 days.

14. 81% of 72 bu.

15. 5% of $40. 16. 30% of $80. 17. 4% of 200 yd. 18. 61% of 96 lb. 19. 90% of $120. 20. 80% of 50 horses.

RULE.

Multiply the base by the rate.

FORMULA.-B x R P.

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NOTE.-The method of Ex. 21 should be used in all written work when the per cent. can be readily expressed as a pure decimal. The method of Ex. 1 and 22 should be used in all other cases.

35 bu., Ans.

23. A owned 750 acres of land, and sold 15% of it; how much did he sell?

24. A merchant bought goods for $520, and sold them at a gain of 22%; how much did he gain?

25. A farmer raised 4280 bushels of grain, and sold 20% of it; how much did he sell?

26. A house was bought for $5240, and sold at a gain of 25%; what was the selling price?

27. A farm was bought for $10,500, and was sold at a loss of 20%; required the selling price.

28. A merchant failed in business, and was able to pay only 35% of his debts; how much would A lose, to whom he owes $4860?

29. A coal-dealer buys coal at $4.25 a ton, and sells it at a gain of 18%; what is the selling price?

30. A man whose salary is $4500 pays 121% for board and 17% for current expenses; how much does he save?

31. A store was sold for $10,800: 41% of the price was paid in cash; how much remained unpaid?

32. Mr. Bitner had $8600 in bank: he drew out 41% of it to purchase a library, and 15% of the remainder for living expenses; how much remained in bank?

33. M bought a horse for $200: he sold him to N at an advance of 35%, and N sold him to P at a loss of 228%; what did the horse cost P?

CASE II.

156. Given the rate and percentage, to find the base.

ORAL EXERCISES.

1. 40 is 25% of what number?

If 40 is 25%, or }, of some number, 4 of that number is 4 times 40, or 160, Ans.

Find the number of which

2. 60 is 10%.

3. 64 is 20%. 4. 30 is 121%.

5. 80 is 40%.

6. 125 is 50%.
7. 20 is 5%.

8. 12 is 163%.

9. 70 is 334%. 10. 200 is 66%.

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