+

5. What are the contents of a granite block that is 6ft. 3′ long, 2ft. 4' wide, and 1ft. 3' thick?

Ans. 18ft. 2' 9". (See Art. 104).

6. How many feet of flag-stone in a walk 15ft. 6′ long and 3ft. 4' wide?

7. How many solid feet of marble in a block that is 8ft. 3' long, 3ft. 6' wide, and 1ft. 4' thick?

8. How many cubic feet of earth must be removed in digging a cellar 15ft. 6' long, 12ft. 8' wide, and 6ft. 8' deep?

9. How many feet in a stock of 8 boards, that are 10ft. 8' long and 10' wide? Ans. 71ft. 1' 4".

10. How many feet of boards 1' thick can be sawed from a a stick of timber that is 12ft. 8′ long, 10′ wide, and ̧ 8′ 4′′ thick, provided no timber is destroyed by the saw-cut?

11. How many cords of wood in a pile that is 18ft. 6′ long, 6ft. 8′ high, and 4ft. wide?

12. How many square yards of carpeting will cover a room that is 18ft. long and 16ft. 6′ wide?

13. Multiply 3ft. 6' 4" by 8ft. 9' 6".

DIVISION.

220. Division of duodecimals is like division of other compound numbers.

Ex. 1. Divide 24ft. 10′ 10′′ 4′′′′ by 7. Also by 9.

NOTE. When both dividend and divisor are expressed as compound numbers, they may be reduced to the smallest denomination in either; after which divide, and the quotient will be units, i. e. feet; thus, 68ft. 10 8// divided by 2ft. 8' equals 9920 ÷ 384′′ : 2512, i. e. 25ft. 10', Ans.

=

220. How is division of duodecimals performed? How when the divisor is compound?

4. The area of a floor is 197ft. 1′ 8′′, and the length of the floor is 15ft. 8'; what is its width? Ans. 12ft. 7'.

5. The area of a garden walk is 89ft. 4' and its width is 2ft. 8'; what is its length?

MISCELLANEOUS EXAMPLES IN COMPOUND NUMBERS.

1. If 152bush. 3pk. 3qt. 1pt. of wheat grow on 9 acres of land, how many bushels grow on 7 acres?

2. A man having 207m. 4fur. 25rd. lyd. to travel in 6 days, goes 30m. 3fur. 25rd. 5yd. on the first day, and 33m. 4fur. 20rd. 4yd. on the second day; how far per day must he travel to finish the journey in the remaining 4 days?

3. Multiply 3£ 15s. 6d. 1qr. by 857, and divide the product by 157.

4. I have a stock of 9 boards, which are 12ft. 8′ long and 10' wide. With these boards I wish to lay a floor 15ft. in length; how wide can I make it?

5. If 1 cubic foot of foot of granite weighs 2

water weighs 621b. 8oz., and if a cubic

times as much, what is the weight of a

block of granite 12ft. long, 1ft. 8′ wide, and 9' thick?

6. From the sum of 3wk. 6d. 16h. 20m. 18sec. and 2wk. 3d. 18h. 50m. 40sec. take the difference between 6wk. 5d. 8h. 25m. 30sec. and 5wk. 2d. 22h. 18m. 15sec.

7. What is the difference in time between Amsterdam 4° 44′ east longitude, and Annapolis 76° 43′ west longitude?

8. When it is noon in Dublin, 6° 7′ 13′′ west longitude, it is 10m. and 1613sec. past 8 o'clock in the evening in Peking; what is the longitude of Peking?

9. How many days, hours, etc., from 30m. 20sec. past 3 o'clock, P. M., Feb. 8, 1864, to 40m. 25sec. past 8 o'clock, A. M., July 4, 1864, reckoning each month at its actual length?

10. Bought 3cwt. 2qr. 18 lb. of sugar at 81c. per pound, and sold of it at 8c. and the remainder at 94c. per pound; what was gained by the transactions?

11. What is the value in Avoirdupois Weight of 24lb. 6oz. 12dwt. 20gr. Troy Weight?

PERCENTAGE.

221. PER CENT. is a contraction of per centum, a Latin phrase which means by the hundred; thus, ten per cent. of a bushel of corn means ten one-hundredths of it; i. e. ten parts out of every hundred parts; six per cent. of a sum of money, is six one-hundredths of the sum, i. e. $6 out of every $100; etc. NOTE. Instead of the words per cent., it is customary to use this sign, %; thus, 6 per cent. is written 6%; 43 per cent., 44%

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

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

224. The BASE of percentage is the number on which the percentage is computed; thus, $200 is the base on which the percentage is computed in Art. 223; a bushel of corn is the first base mentioned in Art. 221.

225. 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 2 places, the figures after the second decimal place must be regarded as parts of 1 per cent.; thus, (in the last line of the foregoing table,) .125 is 12 or 12 per cent.

Ex. 1. Write the decimal for 4 per cent.

Ans. .04.

2. Write the decimal for 8 per cent.; 12 per cent.; 16 per cent.; 25 per cent.; 72 per cent.

3. Write the common fraction for 163 per cent. ; 20 per cent.; 331 per cent.; 75 per cent. 1st Ans.

PROBLEM 1.

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

Ex. 1. B had $175, but lost 8 per cent. of it; how many dollars did he lose?

$175
.08

$14.00, Ans.

Since 8 per cent. is .08 = 2, the loss is found by multiplying $175 by .08 or by. Hence,

RULE 1. Multiply the base by the per cent., written decimally; or,

RULE 2. Find such part of the base as the rate is of 100 (Art. 151).

2. A farmer having 48 sheep, lost 25 per cent. of them; how many did he lose?

By Rule 1.
48

.25

240

96

1 2.0 0, Ans.

221. Meaning of per cent.?

222. Rate per cent.? 223. Percentage?

224. Base of percentage? 225. 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? 226. Rule for finding percentage when the base and rate are given? Second Rule?

3. What is 6 per cent. of $250 ? 4. What is 8 per cent. of $250 ?

5. What is 12 per cent. of $500?

Ans. $15.

Ans. $62.50.

6. What is 8 per cent. of 600bush. of wheat?

Ans. 50bush.

7. What is 163 per cent. of 1200lb. of cheese?

Ans. 2001b.

8. A farmer cultivates 25 acres of corn this year, and intends to cultivate 20 per cent. more next year; how many acres does he intend to cultivate next year ?

Ans. 30.

9. In an orchard of 900 trees, 33 per cent. are peach trees; how many peach trees are there in the orchard?

10. A teacher pronounced 56 words for his pupils to spell, but 14 per cent. were mis-spelled; how many words were misspelled?

11. Only 663 per cent. of a class of 27 pupils solved a problem given them for a lesson; how many of the class failed?

12. The population of a certain city is 18775, what will it be in one year from this time if it gains 8 per cent.?

13. The population of a certain State is 1376875, what will it be in one year if it loses 12 per cent.?

14. A and B commenced business, each with $8456. A gained 25 per cent. and B lost 12 per cent.; how much was A then worth more than B?

15. A speculator paid $56895 for a lot of flour, and lost 9 cent.; for what sum did he sell the flour?

per

16. One acre of corn yields 80 bushels, and another acre 20 per cent. more; how many bushels does the second acre yield?

PROBLEM 2.

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

Ex. 1. One dollar is what per cent. of $4?

4) 100

25, Ans.

reduced

One dollar is of $4, and to a decimal is .25; i. e. $1 is 25 per cent of $4. The same result is obtained by multiplying $1 by 100, and dividing the product by 4. Hence,