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WRITTEN EXERCISES.

MISCELLANEOUS EXAMPLES.

1. What will 5 tons of coal cost, at 3714 a hundred ?

Ans. $37.50. 2. How many guineas in 47 pounds and 5 shillings?

Ans. 45 guine As. 3 How many pounds A voirdupois in 105000 grains ?

Ans. 15 lb. 4. At 6% a pound, what will 5 cwt. 75 lb. of sugar cost?

Ans. $31.50. 5. How much will 6 barrels of flour cost, at the rate of 31 cents a pound?

Ans. $4126. 6. How many suits of clothes, containing 6 yd. each, can be cut out of 93 yd. of cloth ? Ans. 13; 5; yd. over.

7. How many doses of medicine, each weighing 7 grains, can be made out 1 3 2 3 2 11 gr.? Ans. 93 doses.

8. How many cannon-balls, each weighing 41 lb. 103 02., can be made out of a ton of iron ?

Ans. 48 balls. 9. How

many times will a wheel, 15 ft. 4 in. in circumference, revolve in going 50 miles ?

Ans. 1721721 10. Which is greater, and how much, six dozen dozen or a half a dozen dozen ?

Ans. 1st, by 792. 11. How many kegs, each containing 5 gal. 2 qt. 1 pt., can be filled from a tun (4 hhd.) of wine?

12. How many lots of 5 A. 82 P. are there in a field containing 66 A. 24 P.?

Ans. 12 lots. 13. At 13 cents a pound, how much rice can be bought for $81,250 ?

Ans. 3124 tons. 14. How much time will a person lose in 50 years by taking an hour's nap each afternoon ? Ans. 2 yr. 3082 da.

15. If a comet pass through an arc of 7° 5' a day, how long will it be in describing an arc of 270° ? Ans. 383, da.

16. How many minutes longer was January, 1860, than February of the same year?

Ans. 2880 min. 17. If a physician uses on an average 53 73 19 4 gr. of drugs daily, how many did he use during February, 1876?

Ans. 14 th. 33 63 17 16 gr.

Ans. 445

18. How long will it take to count a million at the rate of 80 per minute, working 12 hours a day? Ans. 171: da.

19. How many half-pint bottles will it take to put up 6 gallons of Arnold's writing fluid ?

Ans. 96. 20. How many more seconds were there in 1876 than in a solar year? (See Art. 297.)

Ans. 65470.3 sec 21. How many boards, 12 ft. long, will inclose a lot 50 13. long and 27 rd. wide, the fence being 3 boards high ?

Ans. 6351 22. How many ounces of calomel will it take to make 980 pills of 5 grains each?

Ans. 103 13 29. 23. If a weekly newspaper (one sheet) has 5600 subscribers, how many reams of paper will it require in a year, not allowing for waste?

Ans. 606 reams, 13 quires, 8 sheets. 24. How many minutes more in the spring of every com. mon year than in the autumn ?

Ans. 1140 min. 25. How many pages are there in an octavo book, the printing of which requires 20 fully printed sheets ? Ans. 320.

26. Mr. A's income averages 4 cents a minute; what will it be during the three summer months ? Ans. $5299.20.

27. If 32,400 steel pens are made by a factory in a day, bow many gross will be made in the month of March?

Ans. 6975 gross. 28. If a grocer's weights are of an oz. in a pound below the legal standard, how much does he gain fraudulently from the sale of 2 bags of Rio coffee, 116 lb. each, true weigbt, at 1884 a pound?

Ans. $0.6941 29. I bought 5 T. 14 cwt. of hay in a stack, but before it a as all delivered, 1 T. 3 cwt. 56 lb. were spoiled by the weather. The price originally agreed upon was $88.35; what should I pay for what I received ? Ans. $70.091.

30. A New Jersey truck-raiser sold 15 bu. 3 pk. 1 qt. of strawberries, at 11% a quart, and agreed to take flour in payment at 31% a pound, as far as it would make an exact aumber of barrels, and the rest to be paid in cash ; how many barrels and how much cash did he receive ?

Ans. 8 barrels and 67%.

ADDITION OF COMPOUND NUMBERS. 306. Addition of Compound Numbers is the process of finding the sum of two or more similar compound nom

oers.

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1. Find the sum of £7 6 s. 8 d.; £5 9 8. 3 d. ; £14 13 a 10 d.; and £11 19 8. 11 d.

SOLUTION.-We write the numbers so that similar OPERATON. units shall stand in the same column, and begin at £

d. the right to add. 11 d. plus 10 d., plus 3 d., plus 8 d., 7 6 8 are 32 d., which by reduction we find equals 2 s. and 5 9 3 8 d.; we write the 8 d. in the pence column, and re- 14 13 10 serve the 2s. to add to the column of shillings: 2 s. 11 19 11 plus 19 s., plus 13 s., plus 9s., plus 6 s., are 49 s., which by reduction we find equals £2 and 9 s.; we write the

39 9 s. in the column of shillings, and reserve the £2 to add to the column of pounds; £2 plus £11, plus £14, plus £5, plus £7, equal £39, which we write under the pounds. Hence the following

Rule.-I. Write the compound numbers so that similar units stand in the same column.

II. Begin with the lowest denomination and add each column separately, placing the sum, when less than a unit of the next higher denomination, under the column added.

III. When the sum equals one or more units of the next higher denomination, reduce it to this denomination, write the remainder under the column added, and add the quotient obtained by reduction to the next column.

IV. Proceed in the same manner with all the columns to the last, under which write the entire sum.

Proof.—The same as in addition of simple numbers.
NOTE.-In writing, if any places are wanting supply them with a cipher.

(2) £ 8. d. 16 12 5 127 13 7 192 18 168 14 11 505

9

WRITTEN EXERCISES.

(3)
£ S. d.
125 16 7
116 13 9
242

17 5
363 15 8

(4) £ 8 d. 672 18 11 149 10 9 941 17 10 876 19 8

10

19

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11. Find the sum of 16 mi. 100 rd. 3 yd. 2 ft. 7 in., 12 mi. 309 rd. 2 yd. 1 ft. 6 in., 15 mi. 274 rd. 5 yd. 2 ft. 9 in., 18 mi. 227 rd. 4 yd. 1 ft. 8 in.

Ans. 63 mi. 273 rd. 1 ft. 12. Find the sum of 132 sq. yd. 8 sq. ft. 120 sq. in.,

246° sq. yd. 7 sq. ft. 137 sq. in., 546 sq. yd. 3 sq. ft. 129 sq. in., 765 sq. yd. 6 sq. ft. 105 sq. in., 382 sq. yd. 5 sq. ft. 126 sq. in.

Ans. 2074 sq. yd. 6 sq. ft. 41 sq. in. 13. Find the sum of 16 A. 104 P. 18 sq. yd. 7 sq. ft., 25A. 116 P. 28 sq. yd. 8 sq. ft., 18 A. 139 P. 17 sq. yd. 6 sq. ft., 27 A. 106 P. 30 sq. yd. 8 sq. ft., 24 A. 155 P. 26 sq. yd. 5 sq. ft.

Ans. 113 A. 144 P. 1 sq..yd. 7 sq. ft. SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed. 14. A vintner sold to A 5 hhd. 59 gal. 3qt. 1 pt. of wine, to B 20 hhd. 45 gal. 2qt., to C 39 hhd.58 gal. 1 pt., and had as much as be sold A remaining; how much had be at first ?

Ans. 72 hhd. 34 gal. 1} qt. 15. What is the sum of 126 yr. 10 mo. 5 wk. 17 hr., 236 yr, 9 mo. wk. 7 da. 18 hr. 41 min., 425 yr. 8 mo. 4 wk. 3 da. 20 hr. 16 min.. 198 yr. 7 mo. 6 wk. 19 hr. 52 min., 385 yr. 5 wk. 40 min.?

Ans. 1373 yr. 3 mo. 3 wk. 6 da. 4 h. 29 min. 16. Find the sum of 144 cu. yd. 18 cu. ft. 1329 cu.in., 275 cu. yd. 25 cu. ft. 1076 cu. in., 382 cu. yd. 17 cu. ft. 1521 cu. in., 420 cu.yd. 20 cu. ft. 1507 cu. in., 367 cu. yd. 21 cu. ft. 1473 cu.in.

Ans. 1591 cu. yd. 23 cu. ft. 1722 ou, in.

OPERATION

OZ.

SUBTRACTION OF COMPOUND NUMBERS. 307. Subtraction of Compound Numbers is the pro cess of finding the difference between two similar compound numbers.

1. From 10 oz. 12 pwt. 20 gr. take 7 oz. 15 pwt. 16 gr. SOLUTION.–We write the subtrahend under the minuend, placing similar units in the same column,

oz. pwt. gr. and begin at the lowest denomination to subtract;

10 12 20 16 gr. subtracted from 20 gr. leaves 4 gr. which we

7 15 16 write under the grains : 15 pwt. from 12 pwt. we can

2 17 not take; we will therefore take 1 oz. from the 10 oz., leaving 9 oz.; loz. equals 20 pwt., which, added to 12 pwt. equals 32 pwt.; 15 pwi. subtracted from 32 pwt. equals 17 pwt., which we write under the pwt. ; 7 oz. from 9 oz. (or, since it will give the same result, we may add 1 oz. to 7 oz., and say 8 oz. from 10 oz.) leaves 2

Hence the following Rule.-I. Write the subtrahend under the minuend, so that similar units stand in the same column.

II. Begin with the lowest denomination and subtract each term of the subtrahend from the corresponding term of the minuend.

III. If any term of the subtrahend exceeds the corresponding term of the minuend, add to the latter as many units of that denomination as make one of the next higher, and then subtract ; add 1 also to the next term of the subtrahend before subtracting.

IV. Proceed in the same manner with each term to the last.

Proof.—The same as in the subtraction of simple nombers.

NOTE.—The pupil will notice that the general principle of addition and Bubtraction is the same as in simple numbers, the difference being in the Irregularity of the scale, the units themselves being expressed in the deci mal scale.

WRITTEN EXERCISES.

(2) £ 8. d. far. 143 11 10 2 115 14 6 3 27 17 3 3

£
930
246

(3)
8. d. far.
17 7 3
19 8 1

(4)
Ib. oz. pwt. gr.
16 10 16 18
13 11 17 15
2 10 19 3

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