lb. dr. As 62 is not the 17 10 13 17 10 13 product of any two 5 2 numbers in the mul88 6 1 35 5 10 tiplication table, we 12 take some conveni1060 8 12 ent number less than 62, viz. 60. 35 5 10 This we resolve into two factors 5 1095 14 6 and 12, and having found the amount of 60 dollars, we then find the quantity 2 dollars will buy, and add this amount to the former, and the sum is the quantity 62 dollars will buy. 32. What cost 97 tons of lead at £2. 178. 9 d. per ton? 33. If a man travel 17m. 3fur. 19r. 3yd. 2ft. 7in. in one day, how far would he travel in 38 days ? 34. If 1 acre will produce 27bu. 3pk. 6qt. 1 pt. of corn, what will 98 acres produce ? 35. If it require 7yd. 3qr. 2na. to make 1 cloak, what quantity would it require to make 48 cloaks? 36. One ton of iron will buy 13A. 3R. 14p. 18yd. 7ft. 76in. of land ; how many acres will 19 tons buy? Section 17. MENTAL OPERATIONS. 1. If 2 yards of cloth cost 3s., what will 1 yard cost ? 2. If 3 barrels of apples cost 5s., what cost 1 barrel ? 3. If 4hhds. of lime cost 15s., what cost lhhd. ? 4. Divide 9g. equally among 9 boys. 5. Divide 10d. equally among 3 girls. 6. What is a fourth part of 5 gallons ; 17. What is a seventh part of 7 gallons ? 8. What is a sixth part of 9 gallons ? FOR THE SLATE. 1. If 9 acres of land cost £ 128. 11s. 8d. 2qr., what is the value of 1 acre ? Ans. £ 14. 5s. 8d. 2qr. OPERATION. d. qr. Having divided the pounds by £. 9, we find the quotient to be 9) 128 11 4 2 £14, which we write under 14 5 8 2 £ 128, and to the £2. remain ing (40s.) we add the 1ls, in question, and their amount is 5ls. ; and these 5ls. we again divide by 9, and the quotient is 5s., which we write under the 11s. in the question ; and to the remainder, 6s., which are 72d., we add the 4d. in the question, and the sum is 76d. ; having again divided these by 9, we write the quotient, 8, under the 4d. in the question ; and to the remainder, 4d., which is 16qr., we add the 2qr. in the question, and the amount is 18qr., which we again divide by 9, and find the quotient to be 2qr., which we write under the 2qr. in the question. Thus we find our answer to the question to be £ 14. 5s. 8d. 2qr. Hence the following RULE. 8. 8. 8. 5)129 OZ. I. Divide the highest denomination by the quantity; and if any thing remains, reduce it to the next lower denomination, and continue to divide until it is reduced to the lowest denomination. 2. 3. 4. f. 9 7 5 6 8 19 11 7 2 5 17 11 ny. Ton. cwt. qr. 6) 112 14 4 2 6)113 1 21 12 7) 103 11 0 0 18 15 8 3 18 3 17 10 14 15 3 12 8. 9. 10. Cwt. dr. M. fur. rd. ft. 8) 15 4 2 15 8 9) 143 5 5 6) 587 4 8 12 19 1 8 15 15 14 13 11. 12. 13. Rd. Fur. rd. ft. in. 8) 145 32 7 24 9)213 2 0 9 10)98 0 4 2 qr, lb. OZ, Ib. Note. The answers to the following questions are found in the corresponding numbers in Compound Multiplication. 14. What cost 1 yard of cloth, when 7yd. can be bought for £ 6. lls. 3d. ? 15. If a man, in 9 days, travel 112m. lfur. 21rd., how far will he travel in 1 day? 16. If 8 acres produce 21T. 5cwt. lqr. 12lb. of hay, what will 1 acre produce ? +17. If a family consume in 1 year 59&gal. 2qt. of molas ses, how much may be necessary for 1 month ? 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 24]b. 83.33. 18. 10gr. of ipecacuanha, how large a quantity will $ 1 purchase ? 22. When $ 12 will buy 34A. OR. 32p. Byd. 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 ? When the quantity is a composite number, that is, one which is composed of the product of two or more numbers, we proceed as in the following question. 25. 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 com0 ponent parts, or factors, of 24 are 8 6 and 4; that is, 6 multiplied by 4 produces 24. We therefore first 7 11 divide the price by one of these numbers, and then divide the quotient by the other. From the above process we deduce the following d. 6) 57 10 4) 9 11 £2 RULE. II. Divide the idend by one of the component parts, and the quotient thence arising by the other, and the last quotient will be the answer. When the quantity is such, that it cannot be resolved OPERATION d. into two or more factors, the question must be performed by Long Division, as in the following question. 26. If 23cwt. of iron cost £171. ls. 3d. what cost lcwt. ? Ans. £7. 8s. 9d. £. In this question we first divide 23) 171 1 3( £7. the pounds by 23, and obtain 7 for 161 the quotient, and £10 remaining, 10 we reduce to shillings and annex 20 the 1s. and again divide by 23 and 23) 201 (8s. obtain 8s. for the quotient. The 184 remainder, 17s., we reduce to pence 17 and annex the 3d. and again divide 12 by 23, and obtain 9d. for the quo tient. Thus we find the answer to 23) 207 (9d. be £7. 8s. 9d. 207 So in similar cases we should divide the highest denomination by the quantity, and if any thing remains, reduce it to the next lower denomination and continue to divide until it is reduced to the lowest denomination. 27. If a man travel 117m. 7fur. 20rd. in 30 days, how far will he travel in 1 day ? 28. If 84 loads of hay weigh 201 Tons 4cwt. 2qr. Olb., what will 1 load weigh? 29. When 72 ladies require 567yd. Oqr. Ona. for their dresses, how many yards will be necessary for 1 lady? 30. When 132 sailors require 470yd. Iqr. of cloth to make their garments, how many yards will be necessary for 1 sailor? 31. If $ 62 will buy 1095lb. 14oz. 6dr. of beef, how much may be obtained for $ 1 ? 32. Paid £ 280. 5s. 9 d. for 97 tons of lead; what did it cost per ton? 33. If a man travel 662m. 4fur. 28rd. 3yd. 2ft. 2in. in 38 days, how far will he travel in 1 day ? . 34. When 98 acres produce 2739bu. lpk. 5qt. of grain, what will 1 acre produce ? 35. A tailor made 48 garments from 378 yards of cloth; what quantity would it take to make 1 garment ? 36. When 19 tons of iron will purchase 262A. 3R. 37p. 25yd. 1ft. 40in. of land, how much may be obtained for 1 ton ? Section 18. BILLS. 86. Haverhill, March 19, 1842. Mr. William Greenleaf, Bought of Moses Atwood, at $ 0.50. 11.00. 3.50. 14 Hammers, 62. 12 Millsaws, 12.12. 46 Cwt. Iron, 12.00. $ 1105.02. Received payment, Moses Atwood. Lowell, June 5, 1842. Mr. Amos Dow, Bought of Lord & Greenleaf. at $ 23.75. 17.50. 99.00. 12 Crates Liverpool Ware, 175.00. 19 bls. Genessee Flour, 7.00. 23 bu. Rye, 1.52. $8138.71. Received payment, Lord & Greenleaf, by James Clark. |