CHAPTER NINTH.

THE COMPOUND RULES.

SECTION 56.-1. What is a Compound Number? Ans. A number containing different denominations; as, 1 foot 2 inches.

2. What is the addition of compound numbers called? Ans. Compound Addition,

3. What is the sum of £2 17s. 6d. and £3 8s. 4d.?

The sum of

The sum of

MODEL. The sum of the pence is 4d.+6d., or 10d. the shillings is 8s.+17s., or 25s., which equals £1 5s. the pounds is £3+£2, which, with the £1 of the last sum, makes £6. Ans. £6 5s. 10d.

4. What is the sum of 15s. 9d. and 3s. 6d?

5. What is the sum of £1 3s. 10d. and £5 9s. 4d.? 6. A boy throws 3 pk. 6 qt. of potatoes into a barrel already containing 2 pk. 3 qt. How many bushels, &c., are then in the barrel?

7. How much jalap in two bottles, the one containing 4 oz. 3 dr. 2 sc., and the other 8 oz. 2 dr. 1 sc. ?

8. To 3 gal. 1 qt. 1 pt. of alcohol is added 1 gal. 3 qt. 1 pt. of water; how much is there of the mixture?

9. In the morning a person walks 1 mi. 1 fur. 20 rd., in 25 minutes; in the afternoon he walks 4 mi. 3 fur. 30 rd., in 1 h. 35 min. 40 sec. What distance does he walk altogether, and in what time?

10. A grocer mixes three kinds of tea; 5 lb. 11 oz. of the first kind, 6 lb. 7 oz. of the second, and 3 lb. 10 oz. of the third. How many pounds in the mixture?

11. A person, having 53 A. 1 R. 25 sq. rd. of land, bought 7 A. 20 sq. rd. more; how much had he then ?

12. Bought some lace for $3.17, and some calico for $2.85; what was the amount of the bill?

MODEL. The amount of the bill was the sum of $3.17 and $2.85, or $6.02. Ans. $6.02.

NOTE. In the case of Federal Money, add as in simple addition; if the sum is in cents, cut off the two right-hand figures for cents, and what remains on the left will be dollars.

13. If I spend $1.10 for paper, $2.80 for books, and 25 cents for pens, how much do I spend in all?

14. Bought butter for $1.14; cheese for 27c.; lard for 32c.; sugar for $1; what did the bill amount to?

15. A person received three telegrams. The first cost 90c., the second $1.45, and the third 85c. What was the cost of all three ?

16. A carpenter laid out $1.25 for nails, $2.90 for bolts, and 75c. for screws; how much was his bill?

NOTE. Sometimes the items can be combined in a particular order with advantage. Thus, in the last example, the sum of $1.25 and 75c. is $2; $2 and $2.90 make $4.90.

17. A storekeeper took in 40c. in the morning, $5.33 in the afternoon, and $4.60 in the evening; how much did he take in during the day?

18. John Ray bought of T. Kipp a dozen slates for $2.16, some envelopes for $1.72, pencils for 84c., and diaries for $4.28. How much was Ray's bill?

19. A collection having been taken up, the plate was found to contain 18 cents, 21 two-cent pieces, 10 threecent pieces, 10 five-cent stamps, 6 10-cent stamps, and 4 25-cent stamps; how much was collected?

SECTION 57.-1. What is the subtraction of compound numbers called? Ans. Compound Subtraction.

2. A jeweller, who had 1 lb. 11 oz. 4 pwt. 3 gr. of gold, used 10 oz. 15 pwt. 20 gr.; how much had he left?

MODEL. He had left the difference between 1 lb. 11 oz. 4 pwt. 3 gr. and 10 oz. 15 pwt. 20 gr. 20 gr. can not be taken from 3 gr.; we therefore take 1 of the next higher denomination (1 pwt.), reduce it to grains (24), add it to 3 gr., and then subtract. 24 gr.+3 gr.=27 gr. 27 gr.-20 gr. 7 gr.

To balance the pennyweight thus added, we now add 1 pwt. to the 15 pwt. to be subtracted, making 16. pwt. 16 pwt. can not be taken from 4 pwt.; we therefore take 1 of the next higher denomination (1 oz.), reduce it to pennyweights (20), add it to the 4 pwt., and then subtract. 20 pwt.+4 pwt.=24 pwt. 24 pwt.—16 pwt.= 8 pwt.

To balance the ounce thus added, we now add 1 oz. to the 10 oz. to be subtracted, making 11 oz. 11 oz.-11 oz.=0 oz. 1 lb.-01 lb. Ans. 1 lb. 8 pwt. 7 gr.

a

3. From a bin containing 10 bu. 3 pk. 1 qt. of oats, person took 3 bu. 2 pk. 6 qt. How much was left? 4. If from 1 day we take 19 hours 20 min., how much time will remain ?

5. A person

only £3 7s. 9d.

having a bill of £5 10s. to pay, has How much does he lack?

6. How much of my fence remains to be built, if there is 15 rd. 5 yd. to be built in all, and 11 rd. 2 yd. 1 ft. is completed?

7. To 10 gal. 1 qt. of whiskey a liquor-merchant adds 3 qt. of water, and then sells 7 gal. 2 qt. 1 pt. of

the mixture. How much remains?

8. A hardware-merchant, having on hand 1 cwt. 10 lb. of lead, buys 12 cwt. 20 lb. more, and then sells 10 cwt. 15 lb. How much has he left?

9. How many years, months, and days, from November 9th, 1867, to May 1st, 1868?

NOTE. November is the 11th month, May the 5th. We there. fore take 1867 years 11 months 9 days, which is the earlier date, from 1868 years 5 months 1 day. Allow 30 days to the month. Ans. 5 months 22 days.

10. How many months and days from January 15th to October 3d of the same year?

11. How many months and days from July 20th to December 29th of the same year?

12. How many months and days from July 20th to December 29th of the preceding year?

13. How many years, months, and days, from August 25th, 1865, to March 13th, 1868 ?

14. Some mats were bought for $18.60, and sold at a loss of $3.85; how much did they bring ?

MODEL. If they were bought for $18.60 and sold at a loss of $3.85, they brought $18.60-$3.85, or $14.75. Ans. $14.75.

NOTE. As in the addition of Federal Money, so in subtraction, multiplication, and division; if the result is in cents, cut off the two right-hand figures for cents, and what is left will be dollars.

15. A owes B $25.20, and gives him on account $17.75. If he pays the balance with a ten-dollar bill, how much change should he receive?

16. What is the profit on goods bought for $107.50, and sold for $119.25 ?

17. Some goods, bought for $74.50, are sold for $69.66. Does the owner gain or lose, and how much?

18. On a bill of $48, C has paid $29.25. He now pays the balance with a twenty-dollar bill; how much change should he receive?

SECTION 58.-1. What is the multiplication of a compound number called? Ans. Compound Multiplication.

2. How many pounds, &c., in four packages, each containing 3 lb. 5 oz. 4 dr. ?

MODEL. Four packages, each containing 3 lb. 5 oz. 4 dr., will contain 4 times 3 lb. 5 oz. 4 dr. 4 times 4 dr. is 16 dr., or 1 oz., 4 times 5 oz. is 20 oz., and 1 oz. (the last product) makes 21 oz., or 1 lb. 5 oz. 4 times 3 lb. is 12 lb., and 1 lb. (from the last product)

makes 13 lb. Ans. 13 lb. 5 oz.

3. What cost a dozen Histories, at 3s. 8d. each? 4. If a person gives his five children each £1 10s. 6d., how much does he give them in all?

5. What are the contents of eight pitchers, if each holds 1 qt. 1 pt. 1 gi.?

6. What is the breadth of three strawberry beds, each 1 yd. 1 ft. 10 in. broad?

7. How much land in 7 fields, each containing 1 A. 15 sq. rd.?

8. What cost 8 knives, at $1.38 each? Ans. $11.04. 9. What cost 9 pigs, at $5.30 apiece?

10. What cost 12 caps, at $1.331 apiece?

11. Bought 10 albums, at $2.64 each, and 5 pocketbooks, at 75c. each; what did the bill come to?

12. Bought 3 pair of gloves, at $1.05 each; 4 collars, at $3.60 each; and 11 yards of calico, at 25c. per yd. What was the amount of the bill?

Paid on ac

13. Bought 20 chickens, at 60c. each; 6 ducks, at 75c. each; and 8 turkeys, at $1.60 each. count $16.80; how much remained due? half-dollars will pay the balance?

How many