add the 2qr. in the question, and divide the amount, 18qr., by 9, and obtain 2qr. for a quotient, which we place under the 2qr. in the dividend. Thus we find the answer to be 14 £. 5s. 8d. 2qr.

RULE.-1. Divide the highest denomination of the dividend by the divisor, and, if there be a remainder, reduce it to the next lower denomination, adding to the number thus found the number in the dividend of the same denomination.

2. Divide the result thus obtained by the divisor; and, if there be a remainder, proceed as before, till all the denominations of the dividend are taken, or till the work is finished. The successive quotients will be of the same denominations with the successive numbers divided, or will correspond with the several denominations of the dividend.

EXAMPLES FOR PRACTICE.

1

8)145 327 24 9)213 2 0 9 10) 98 0 4 2

NOTE. The answers to the following questions are found in the corresponding numbers in Multiplication of Compound Numbers.

14. What costs 1 yard of cloth, when 7yd. can be bought for 6£. 11s. 3d. ?

15. If a man, in 9 days, travel 112m. 1fur. 21rd., how far will he travel in 1 day?

16. If 8 acres produce 21T. 5cwt. 1 qr. 12lb. of hay, what will 1 acre produce?

17. If a family consume in 1 year 598gal. 2qt. of molasses, how much will be necessary for 1 month?

QUESTION. What is the rule for division of compound numbers?

18. John Smith has 12 silver spoons, weighing 3lb. 10oz. 11dwt.; what is the weight of each spoon?

19. Samuel Johnson bought 7 loads of timber, measuring 55T. 19ft.; what was the quantity in each load?

20. If the moon, in 10 days, move in her orbit 4S. 11° 55′ 50", how far does she move in 1 day?

21. If $9 will buy 24tb 83 33 19 10gr. of ipecacuanha, how large a quantity will $1 purchase?

22. When $12 will buy 34A. OR. 32p. Syd. 5ft. 48in. of wild land, how much will $1 buy?

23. Joseph Doe will cut 24 cords 105 feet of wood in 9 days; how much will he cut in 1 day?

24. When 8 acres of land produce 25ch. 17bu. 3pk. 4qt. of grain, what will 1 acre produce?

ART. 110. When the divisor is a composite number, and all its factors are within the table.

Ex. 1. When 24 yards of broadcloth are sold for 57£. 10s. Od., what is the price of 1 yard?

Ans. 2£. 7s. 11d.

In this question we find the component parts, or factors, of 24 are 6 and We therefore first divide the price by one of these numbers, and then the quotient by the other.

RULE. Divide the dividend by one of the component parts, and the quotient thence arising by another, and so on until all the factors have been used as divisors; the last quotient will be the answer.

EXAMPLES FOR PRACTICE.

2. If 360 tons of iron cost 6409£. 10s. Od., what is the cost of 1 ton?

3. If a man travel 117m. 7fur. 20rd. in 30 days, how far will he travel in 1 day?

4. If 84 loads of hay weight 201 tons 4cwt. 2qr. Olb., what will 1 load weigh?

5. When 72 ladies require 567yd. Oqr. Ona. for their dresses, how many yards will be necessary for 1 lady?

QUESTIONS. Art. 110. How does it appear that dividing by 6 in Ex. 1 gives the price of 4 yards? What is the rule for dividing by a composite number?

6. When 132 sailors require 470yd. 1qr. of cloth to make their garments, how many yards will be necessary for 1 sailor?

ART. 111. When the divisor is not a composite number, and is greater than 12, or, if a composite number, when all its factors are not within the table.

Ex. 1. If 23cwt. of iron cost 171£. 1s. 3d., what cost lcwt.? Ans. 7. 8s. 9d.

OPERATION.

£. s. d.

23) 171 1 3 (7£. 161

10
20

23) 201 (8s.

184

17

12

23) 207 (9d. 207

In this question we first divide the pounds by 23, and obtain 7 for the quotient, and 10£. remaining, which we reduce to shillings, and add the 1s., and again divide by 23, and obtain 8s. for the quotient. The remainder, 17s., we reduce to pence, and add the 3d., and again divide by 23, and obtain 9d. for the quotient. Thus, by uniting the several quotients, we find the answer to be 7£. 8s. 9d.

RULE. Divide in the same manner as when the divisor does not exceed 12 (Art. 109), and write down the whole operation as in the preceding example.

2. If $ 62 will buy 1095lb. 14oz. 6dr. of beef, how much may be obtained for $1?

3. Paid £280. 5s. 91d. for 97 tons of lead; what did it cost per ton?

4. If a man travel 662m. 4fur. 28rd. 3yd. 2ft. 2in. in 38 days, how far will he travel in 1 day?

5. When 98 acres produce 2739bu. 1pk. 5qt. of grain, what will 1 acre produce?

6. A tailor made 347 garments from 2732yd. 2qr. 2na. of cloth; what quantity did it take to make 1 garment?

7. When 19 tons of iron will purchase 262A. 3R. 37p. 25yd. 1ft. 40in. of land, how much may be obtained for 1 ton? 8. If 451 tons of copper ore will purchase 8003T. 8cwt. 1qr. Olb. 10oz. of iron ore, how much will 1 ton purchase?

Ans. 17T. 14cwt. 3qr. 18lb. 14oz.

QUESTIONS.-Art. 111. What is the rule when the divisor is large, and not

a composite number?

§ XVI. MISCELLANEOUS EXAMPLES IN MULTIPLICATION AND DIVISION OF COMPOUND NUMBERS.

1. Bought 30 boxes of sugar, each containing 8cwt. 3qr. 20lb., but having lost 67cwt. 3qr. 12lb., I sold the remainder for 1£. 17s. 6d. per cwt.; what sum did I receive?

Ans. 375£.

2. A company of 144 persons purchased a tract of land containing 11067A. 1R. 8p. John Smith, who was one of the company and owned an equal share with the others, sold his part of the land for 1s. 94d. per square rod; what sum did he receive? Ans. 1101£. 12s. 1d.

3. The exact distance from Boston to the mouth of the Columbia River is 2644m. 3fur. 12rd. A man, starting from Boston, travelled 100 days, going 18m. 7fur. 32rd. each day; required his distance from the mouth of the Columbia at the end of that time. Ans. 746m. 7fur. 12rd.

4. James Bent was born July 4, 1798, at 3h. 17m. A. M.; how long had he lived Sept. 9, 1807, at 11h. 19m. P. M., reckoning 365 days for each year, excepting the leap year 1804, which has 366 days? Ans. 3353da. 20h. 2m.

5. The distance from Vera Cruz, in a straight line, to the city of Mexico, is 121m. 5fur. If a man set out from Vera Cruz to travel this distance, on the first day of January, 1848, which was Saturday, and travelled 3124rd. per day until the eleventh day of January, omitting, however, as in duty bound, to travel on the Lord's Day, how far would he be from the city of Mexico on the morning of that day?

Ans. 43m. 4fur. 8rd. 6. Bought 16 casks of potash, each containing 7ewt. 3qr. 18lb., at 5 cents per pound. I disposed of 9 casks at 6 cents per pound, and sold the remainder at 7 cents per pound; what did I gain? Ans. $203.78.

7. A merchant purchased in London 17 bales of cloth for 17£. 18s. 10d. per bale. He disposed of the cloth at Havana for sugar at 1£. 17s. 6d. per cwt. Now, if he purchased 144cwt. of sugar, what balance did he receive?

Ans. 35. Os. 2d. 8. A and B commenced travelling, the same way, round an island 50 miles in circumference. A travels 17m. 4fur. 30rd. a day, and B travels 12m. 3fur. 20rd. a day; required how far they are apart at the end of 10 days.

Ans. 1m. 4fur. 20rd.

9. Bought 760 barrels of flour at $5.75 per barrel, which I paid for in iron at 2 cents per pound. The purchaser afterwards sold one half of the iron to an axe-manufacturer; what quantity did he sell? Ans. 48 tons 15cwt. 1qr. 22lb.

10. Bought 17 house-lots, each containing 44 perches, 200 square feet. From this purchase I sold 2A. 2R. 240ft., and the remaining quantity I disposed of at 1s. 24d. per square foot ; what amount did I receive for the last sale?

Ans. 5914£. 19s. 51d. 11. J. Spofford's farm is 100 rods square. From this he sold to H. Spaulding a fine house-lot and garden, containing 5A. 3R. 17p.; and to D. Fitts a farm 50rd. square; and to R. Thornton a farm containing 3000 square rods; what is the value of the remainder, at $1.75 per square rod?

Ans. $6235.25.

§ XVII. CANCELLATION.

ART. 112. CANCELLATION, as commonly used in arithmetic, signifies erasing or striking out any factor or factors common to the divisor and dividend.

It can be employed in most rules involving multiplication and division of whole numbers, but is more especially important in abridging operations in multiplication and division of vulgar fractions, and in simple and compound proportions.

ART. 113. If the dividend and divisor are both divided by the same number, the quotient is not altered. Thus, if the dividend is 20 and the divisor 4, the quotient will be 5. Now, if we divide the dividend and divisor by some number, as 2, their proportion is not altered, and we obtain 10 and 2 respectively; and 10 ÷ 2 = = 5, the same as the original quotient.

ART. 114. If a factor is cancelled in any number, the number is divided by that factor. Thus, if 15 is the dividend and 5 the divisor, the quotient will be 3. Now, since the divi

QUESTIONS. Art. 112. What does cancellation signify? In what rules is it most advantageously employed? - Art. 113. What is the effect on the quotient when the dividend and divisor are both divided by the same number? -Art. 114. What is the effect of cancelling a factor of any number?