138

COMPOUND MULTIPLICATION.

9. How long will a man be in sawing 6 cords of wood, if he takes 7 h. 30 min. 45 sec. to saw 1 cord, allowing 10 working hours to each day? Ans. 4 days 5 h. 4 min. 30 sec.

Multiply in the usual way; then reduce the hours to working days by dividing by 10.

10. How much sugar is there in 21 hhd., each containing 11 cwt. 3 qr. 15 lb.? Ans. 12 T. 9 cwt. 3 qr. 15 lb. 11. Bought 15 yd. of broadcloth, at £1 3s. 6d. a yard, and 22 yd. of silk, at 7s. 8d. 2 far. a yd. What was the amount of the bill? Ans. £26 2s. 1d.

Find the cost of each item; then add.

12. The exact time in a year is 365 days 5 h. 48 min. What is the exact time in 50 years?

49,7 sec.

(50=5×10) Ans. 18262 days 2 h. 41 min. 25 sec. 13. How much brandy in 84 pi., each containing 128 gal. 2 qt. 1 pt. 3 gi.? Ans. 10812 gal. 1 qt. 1 pt.

14. If a man owning 5 farms, of 120 A. 1R. 12 sq. rd. each, sells 450 A. 3 R. 25 sq. rd., how much land has he left? Ans. 150 A. 2 R. 35 sq. rd.

15. Bought 17 boxes of raisins, at 12s. 4d. a box; 5 bar. of flour, at £1 10s. 6d. a barrel; and 16 lb. of tea, at 5s. 31d. a lb. Paid on account £19 10s.; how much remains unpaid? Ans. £2 16s. 6d. 16. What will be the yield of 32 acres of wheat, at the rate of 24 bu. 2 pk. 7 qt. per acre? Ans. 791 bu.

17. If 2 gal. 2 qt. 1 pt. 1 gi. leak out of a water pipe in 1 hour, what will be the waste in 1 day? Ans. 63 gal. 3 qt.

18. Suppose a person to walk, on an average, 3 mi. 2 fur. every morning, and 3 mi. 20 rd. I yd. every afternoon; how far will he walk in two weeks? Ans. 88 mi. 3 fur. 2 rd. 3 yd.

19. If from 2 lb. of silver enough is taken to make a dozen spoons, weighing 1 oz. 10 pwt. 2 gr. each, how much will be left? Ans. 5 oz. 19 pwt.

COMPOUND DIVISION.

139

COMPOUND DIVISION.

235. When a compound number is divided, the process is called Compound Division. It combines division and reduction descending.

236. Divide 148 gal. 3 qt. 1 pt. 3 gi. by 23.

Here we must use Long Division. Remember that a quotient is of the same denomination as the dividend from which it arises. Begin to divide at the left.

Divide 148 gal. by 23: quotient, 6 gal.; remainder, 10 gal. Reduce the remainder to qt., and add in the 3 qt. in the dividend. 10x4=40 40+3=43.

Divide 43 qt. by 23: quetient, 1 qt.; remainder, 20 qt. Reduce the remainder to pt., and add in the 1 pt. in the dividend. 20 x 240 = 41.

40+1

Divide 41 pt. by 23: quotient, 1 pt.; remainder, 18 pt. Reduce the remainder to gi., and add in the 3 gi. in the dividend. 18x4=72 72+3=*75.

gal. qt. pt. gi. 23) 148 3 1 3 (6 gal. 138

10 gal.
4

23) 43 qt. (1 qt.
23

20 qt.
2

23) 41 pt. (1 pt.
23

Ans. 6 gal. 1 qt. 1 pt. 3 gi.

23

Divide 75 gi. by 23: quotient, 3 gi; remainder, 6 gi. As there is no lower denomination to reduce this remainder to, write it over the divisor in the form of a fraction, . Collect the several quotients for the answer.

Ᏺ

If in any case there is no remainder, bring down the next denomination of the dividend, and proceed as above.

235. When a compound number is divided, what is the process called? What does Compound Division combine ?-236. Go through the example, explaining the steps.

If the divisor is not contained in any dividend, set 0 în the quotient for that denomination, and reduce the dividend to the next.

237. RULE.-Beginning at the left, divide each denomination in turn. When there is a remainder, reduce it to the next lower denomination, add in the number of that denomination in the given dividend, if any, and continue the division.

When there is a remainder after the last division, place it over the divisor, in the form of a fraction, and annex it to the last quotient. The several quotients, each of the same denomination as its dividend, form the entire quotient.

PROOF.-Multiply the quotient by the divisor. If their product is equal to the dividend, the work is right.

238. When the divisor is less than 12, use Short Division.

4. Divide 22 rd. 1 yd. 1 ft. 10 in. by 11. Ans. 2 rd. 5,3 in.

5. Divide £6 15s. 3d. by 10.

6. Divide 86 bu. 1 pk. 1 pt. by 14.

7. Divide 102 A. 1 R. 11 sq. rd. by

8. Divide 4 gal. 2 qt. by 144.

Ans. 13s. 6d. 14 far.

9. Divide 40 cu. yd. 10 cu. ft. by 18.

Ans. 2 A. 1 sq. rd.
Ans. 1 gi.

237. Recite the rule for Compound Division. What is the proof?

EXAMPLES IN COMPOUND DIVISION.

141

10. If 31 clocks cost £113 13s. 4d., how much is that apiece? Ans. £3 13s. 4d. 11. If 6 oz. 7 dr. (Apothecaries' Weight) of magnesia are put up in 60 equal parcels, how much will each weigh?

Ans. 2 sc. 15 gr.

12. A silversmith makes seven teapots, of equal weight, out of 9 lb. 1 oz. 14 pwt. 5 gr. of silver. What is the weight of each? Ans. 1lb. 3 oz. 13 pwt. 11 gr.

13. If 47 casks, of the same size, hold 1686 gall. 1 pt. of beer, how much will each contain? Ans. 35 gal. 3 qt. 1 pt.

8

14. If a traveller goes 600 miles in 1 day 7h. 35 min. 20 sec., what is his average time per mile? Ans. 3 min. 9 sec. 15. Divide 6 bales, 3 bundles, 1 ream, of paper into 8 equal parts. Ans. 4 bundles, 7 quires, 12 sheets. 16. A farmer puts up 1000 bushels of apples in 350 barrels of uniform size. How many bushels, &c., does each barrel contain? Ans. 2 bu. 3 pk. 3 qt.

17. An estate worth £2570 is to be divided as follows: the widow is to have one third of the whole, and the rest is to be divided equally between seven children. What is the widow's share, and what each child's?

Ans.

(Widow's, £856 13s. 4d.

Child's, £244 15s. 2d. 32 far.

18. What is the weight of 13 crowns, each weighing 18 pwt. 4,4 gr.; 14 shillings, each weighing 3 pwt. 15 gr.; and 9 sixpences, each weighing 1pwt. 19,7 gr.?

1 1

Ans. 1 lb. 3 oz. 3pwt. 15 gr.

19. A farmer having 450 bu. 1 pk. 1 qt. of corn, after selling 425 bu. 3 pk. 6 qt., distributed the rest equally among 5 poor families. How much did each receive?

Ans. 4 bu. 3 pk. 3 qt. 13 pt.

20. Divide 182° 5' 12" by 12.

142

MISCELLANEOUS EXAMPLES.

MISCELLANEOUS EXAMPLES.

1. A person has $741.35 in one bank, $350 in another, and $1129.88 in a third; how much has he in bank altogether?

2. At 40 cents a yard, what will be the cost of 5 miles of telegraph cable? Ans. $3520. 3. The silk-worm's thread is about 5 of an inch thick; the spider's web is about as thick. How thick is it?

4. Reduce 21 to its lowest terms.

63

5000

6. Three boys, gathering nuts, agree to divide equally all they get. The first gathers 540, the second 960, the third 720. How many does each receive? Ans. 740 nuts.

7. Cut from a piece of cloth containing 36 yd., enough cloth to make 10 coats, each requiring 24 yd., and how much will be left?

8. The product of two factors is 293. One of the factors is 83; what is the other? Ans. 3.

9. If 1 sovereign is worth $4.84, what are 27 sovereigns worth?

10. A man who has

mile the start of another, gains on him 30 rods more. How many feet is he then ahead of the other?

11. If a boy who has been in the habit of sleeping 9 h., rises an hour earlier every day, how many days will he save in 5 years, allowing for one leap year? Ans. 76 da. 2 h.

12. From 21 subtract 13, and multiply the remainder by 3.

Ans. 23.

13. If a man has 3 small farms, of 8 fields each, and each field contains 2 A. 3 R. 22 sq. rd., how much land has he in all? Ans. 69 A. 1 R. 8 sq. rd.