128

EXAMPLES IN COMPOUND NUMBERS.

16. How many days are there in the Spring months, March, April, and May?

17. How many days in the Summer months, June, July, and August?

18. How many days in the Autumn or Fall months, September, October, and November?

19. How many days in the Winter months, December, January, and February, when February falls in a leap year? 20. Reduce 19 cu. ft. to cubic inches. Ans. 32832 cu. in. 21. Reduce 5740 pwt. to pounds. Ans. 23 lb. 11 oz.

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22. If from of an ounce of gold a jeweller takes enough to make 6 rings weighing 2 pwt. each, how many pennyweights will he have left?

23. The depth of water at a certain spot is found to be 31 fathoms, 3 ft. How many inches is this? Ans. 2268 in. 24. How many brushes, at 2s. each, can be bought for £8?

25. How long will 12 bushels of oats last a horse, if he is fed 8 quarts a day?

26. At the rate of $4 a cord, what is the value of a pile of wood, 8 feet long, 4 feet wide, and 4 feet high?

27. If sound moves at the rate of 1120 feet in a second, how many miles off is a cannon that is heard 11 seconds after it is discharged? Ans. 2 mi. 1760 ft.

28. If a family use 28 lb. of flour in a week, how long will 2 barrels last them?

29. How many pounds sterling will 6 dozen combs cost, at 9d. apiece? Ans. £2 14s.

30. If a locomotive goes a mile in 2 minutes, how many

hours will it take to go 150 miles?

31. Reduce 15 A. 3 R. 20 sq. rods, to square inches.

Ans. 5 h.

15 sq. yards, 2 sq. ft.

Ans. 99597888 sq. in.

COMPOUND ADDITION.

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COMPOUND ADDITION.

224. Compound numbers may be added, subtracted, multiplied, and divided.

225. When compound numbers are added, the process is called Compound Addition. It combines addition and reduction ascending.

226. A person spends in one store £6 5s. 7d.; in another, £7 1s. 2d. 1 far.; in a third, £1 13s.; and in a fourth, £4 18s. 1d. 3 far. How much does he lay out altogether?

We are here required to find the sum of several compound numbers. We must add things of the same kind; therefore write numbers of the same denomination in the same column. Mark the denominations over the top.

Beginning at the right, add the first column. Its sum is 4 farthings, which, by dividing by 4, we reduce to 1d. Set .0 in the column of farthings, and carry 1 to the next column.

£ S. d. far. 6 5 7 0 7 1 2 1 1 13 0 0 4 18 1

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19 17 11 0

The sum of the next column is 11. 11d. is not reducible to shillings, since it takes 12d. to make 1s. Set down 11, therefore, under the column of pence. The sum of the shillings is 37s. = £1 17s. Set 17 under the column of shillings, and carry £1 to the next column.

The sum of the next column is £19. As pounds can not be reduced to any higher denomination, we set 19 at once under the column added. Answer, £19 17s. 11d. Hence the following rule:

224. What operations may be performed on compound numbers ?—225. When compound numbers are added, what is the process called? What operations does Compound Addition combine?-226. Explain the several steps in the given example.

227. RULE.-To add compound numbers, set them down so that the same denominations may stand in the same column.

Beginning at the right, add the denominations separately. Set each sum under the column added, unless it can be reduced to a higher denomination. If so, divide by the number that it takes to make one of that denomination; set the remainder under the column added, and carry the quotient.

PROOF.-Prove the addition, by adding in the opposite direction.

EXAMPLES FOR THE SLATE.

Add the following compound numbers. Always mark the denominations over the top.

227. Recite the rule for Compound Addition. How may the addition be

proved?

14. Find the sum of 2 hhd. 50 gal. 3 qt. 1 pt. (Beer Measure); 10 hhd. 30 gal. 1 qt.; 11 hhd. 25 gal. 1 pt.; 25 hhd. 1 gal. 1 qt.; and 6 hhd. 52 gal. 3 qt. 1 pt.

Ans. 56 hhd. 52 gal. 1 qt. 1 pt. 15. Add together £7 13s. 3d.; £3 5s. 10d. 2 far.; £6 18s. 7d.; 2s. 5d. 3 far.; £4 3d.; and £17 15s. 4d. 2 far.

Ans. £39 15s. 9d. 3 far.

16. Add together 1 dr. 18 gr.; 2 dr. 1 sc. 15 gr.; 3 dr. 2 sc. Ans. 2 oz. 2 dr. 13 gr.

13 gr.; 4 dr.; and 6 dr. 1 sc. 7 gr.

17. A stable-keeper uses 8 bu. 2 pk. of oats, one day; 7 bu. 3 pk. 7 qt., the next; 7 bu. 6 qt., the third; 6 bu. 2 pk. 1 pt.,

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EXAMPLES IN COMPOUND ADDITION.

the fourth; 8 bu., the fifth; 7 bu. 1 pk. 6 qt. 1 pt., the sixth; and 6 bu. 3 pk. 5 qt., the seventh. How much does he use during the week? Ans. 52 bu. 2 pk. 1 qt.

18. If one piece of cloth contains 40 yd.; another, 397 yd.; a third, 383 yd.; a fourth, 391 yd.; and a fifth, 402 yd.; how many yards are there in all? Ans. 198 yd.

19. What is the weight of four lots of iron, the first weighing 4 cwt. 3 qr. 20 lb.; the second, 2 T. 5 cwt. 14 lb.; the third, 1 T. 2 cwt. 2 qr.; and the fourth, 10 T. 19 cwt. 1 qr. 24 lb. ? Ans. 14 T. 12 cwt. 8 lb.

20. How much paper will a printer use for three jobs, if the first job requires 6 bales, 1 bundle; the second, 4 bundles, 1 ream, 15 quires; and the third, 2 reams, 10 quires, 12 sheets? Ans. 7 bales, 2 bundles, 15 quires, 12 sheets. The first contains 100 A.

21. A person owns five farms. 1 R. 30 sq. rd.; the second, 600 A.

2 R. 10 sq. rd.; the third,

40 A. 1 R. 12 sq. rd.; the fourth, 250 A. 3 R. 2 sq. rd.; the fifth, 144 A. 20 sq. rd. How much land does he own in all? Ans. 1136 A. 34 sq. rd.

22. A manufacturer makes four lots of pens. The first consists of 20 great gross, 7 gross, 5 dozen, and 6; the second, of 9 gross, 10 dozen, and 5; the third, of 15 great gross, 11 dozen; and the fourth, of 17 great gross, 3 gross. What is the whole amount made?

Ans. 53 great gross, 9 gross, 2 dozen, and 11. 23. Find the sum of 1 wk. 2 days 13 h. 40 min. 30 sec.; 2 wk. 6 days 10 h. 8 min. 3 sec.; 5 days 22 h. 55 min. 45 sec.; 4 h. 1 min. 15 sec.; and 1 wk. 2 days 4h. 5 min.

Ans. 6 wk. 3 days 6 h. 50 min. 33 sec. 24. Add together 10 rd. 4 yd. 2 ft. 8 in.; 1 rd. 3 yd. 5 in.;

8 rd. 2 yd. 1 ft. 6 in.; 1 rd. 4 in.; and 2 yd. 1 ft. 9 in.

Ans. 22 rd. 2 yd. 8 in.