rooms, how many yards will it take to carpet one of the floors, they being of equal size? Ans. 27yd. 3qr. 2na.

8. If 4doz. spoons weigh 6lbs. 10oz. 16dwt., what will one dozen weigh? Ans. 1lb. 8oz. 14dwt. 9. A farmer put his wheat, consisting of 359bu. 3pk. 2qt., into 12 boxes of equal size; how much did each box contain? Ans. 29bu. 3pk. 7qt. 1pt.

10. If 24hhd. of sugar weigh 4t. 14cwt. 3qr. 5lb., what is the weight of 1hhd.? Ans. 3cwt. 3qr. 20lb. 11. A farmer divided his farm consisting of 446a. 3r. 30 rd., equally among his 8 children; what was the share of each?

MISCELLANEOUS EXAMPLES.

1. A blacksmith bought 5cwt. 2qr. 211b. of iron at one time, 1t. 11cwt. 181b. at another; how much did he buy in all? Ans. 1t. 16cwt. 3qr. 14lb.

2. How many pounds of iron did the above blacksmith buy, and what did it cost him at 5 cents per pound?

3. A farmer raised in one field 302bu. 2pk. 7qt. of oats, in another 290bu. 3pk. 4 qt.; how much more did he raise in one than the other? Ans. 11bu. 3 pk. 3 qt.

4. I have a piece of land containing 50A.; if I sell 25A. 3R. 25rd. of it, how much shall I have left?

5. If a ship sail 2° 2′ 30′′ in one day, how far will she sail in a week? Ans. 14° 17′ 30′′.

6. How much wood in 5 loads, each containing 1c. 3c. ft. 16 cu. ft.?

7. What would be the crop of hay on 10A. if the product of 1A. was 3t. 10 cwt. 2 qr.? Ans. 35 t. 5 cwt.

8. Divide 2t. 7 cwt. 2qr. 10 lb. by 7.

9. If 1 cubic yard of stone weigh 2 tons, 7cwt. 25lb., what is the weight of 1 cubic foot?

Ans. 175lb.

PERCENTAGE.

185. The term PER CENT means by the hundred ; thus, by five per cent of a ton of coal, we mean five one hundredths of it; i. e. five parts out of every one hundred parts; 6 per cent of a sum of money, is six one-hundredths of the sum, i. e. $6 out of every $100.

NOTE. Instead of the words per cent it is quite customary in writing to use the sign %; thus, 6 per cent is written 6 %; 4 per cent 4%.

186. The RATE PER CENT is the number for each hundred; thus, 6 % is 18, or .06, i. e. 6 parts for each hundred parts.

187. The PERCENTAGE is the sum computed on the given. number; thus, the percentage on $200 at 6 per cent is $ 12.

NOTE. The pupil should be cautioned not to confound per cent and percentage. The distinction should clearly be borne in mind. 188. The BASE of percentage is the number on which the percentage is computed; thus, we say the percentage on $500, at 8 per cent is $ 40. Here $500 is the BASE, 8 is the PER CENT and $ 40 is the PERCENTAGE; also, 10 per cent. of 2000 lb. (a ton) of coal is 200lb.; here 2000 lb. is the base, 10 is the per cent and 200lb. is the percentage.

185. Meaning of per cent ? Percentage Illustrate. 188. mentioned terms by an example.

187.

186. Rate per cent? Illustrate. Base of percentage? Explain the three last

189. The rate per cent being a certain number of hundredths, may be expressed either decimally, or by a common fraction, as in the following

NOTE. When the per cent is expressed by a decimal of more than places, the figures after the second decimal place must be regarded as parts of 1 per cent; thus, (in the seventh line of the foregoing table,) .125 is 1215 or 121⁄2 per cent.

Ex. 1. Write the decimal for 6 per cent.

Ans. .06.

2. Write the decimal for 4 per cent; 12 per cent; 8 per cent; 15 per cent; 25 per cent; 16 per cent.

3. Write the common fraction for 5 per cent; 10 per cent;

12 per cent; 61 per cent; 333 per cent.

189. In what ways may the rate be expressed? If expressed decimally by more than two figures, what are the figures after the second decimal place?

NOTE. Too much pains can not be taken to make the pupil thorough in exercises like those in the last two examples.

CASE 1.

190. To find the percentage, the base and rate per cent being given.

Ex. 1. John Dow had $ 360, but lost 5 per cent of it, how many dollars did he lose?

$360

Since 5 per cent is .05= 2, we find the loss, .05 (percentage), by multiplying $360 by .05 or by $18.00. Hence, the

RULE. Multiply the base by the rate per cent expressed decimally or as a common fraction, and the product will be the percentage.

2. What is 20 per cent of $160. ?

Ans. $32.

3. The base is 560 and the rate per cent 40; what is the percentage?

224, Ans.

Or,

560 X

= 224, Ans.

4. What is 16

per cent of 180 barrels of flour?

5. What is 5% of $200?

6. What is 83% of 240 tons of coal?

Ans. 30 bbl.

Ans. $10.

Ans. 20 tons.

7. In a certain school there are 720 pupils, 33 per cent are more than 12 years of age; how many are over 12 years old?

Ans. 240.

190. Rule for finding the percentage when the base and rate are given ?

8. A flour merchant bought 1200 bbls. of flour, but 8 per cent of it was injured by rain; how much was injured?

9. A pupil had a lesson of 40 words, but failed on 10 per cent of them; on how many words did he fail?

10. A city containing 35000 inhabitants, had 15 per cent of the number in school children; how many school children were there? Ans. 5250.

11. A merchant fails in business, owing $12600, and can pay but 35 per cent of his debts; how much will his creditors lose?

100 3 5 = - 6 5

12600 X.65 = $819 0, Ans.

12. Bought 600 boxes of oranges, but on opening them, I find 8 % of them spoiled; how many were lost? Ans. 48.

13. A gentleman sold his house for $6500. $600 he received in cash and took a note for the balance; how much cash did he receive?

14. I have $ 1580 on deposit in the bank. If I draw out 12 per cent of it, what per cent will remain? What amount of money will remain ? Last Ans. $1382.50.

15. In an orchard consisting of 1200 trees, 30 % bear apples, 45 % bear pears, and the remainder bear peaches; how many bear peaches? Ans. 300 trees.

CASE 2.

191. To find the rate per cent when the base and percentage are given.

Ex. 1. What per cent of $ 24 is $ 6. ?