RULE.—Take two figures or factors, whose product ec mes nearesta though short of the multiplier, and multiply by them as in case second. Then multiply the given sum by the number which will make up the deficiency; then add this last product to the sum produced by the two factors, and their sum will be the answer. EXAMPLES. 1. What will 17 bushels of wheat come to, at 10s. 6d. per bushel ? Ans. £8 18s. 60 d. DEM.-It is plain, from 10 6X2 the preceding case, by £ 5 multiplying the price of one by 5, and then that 2 12 6 the price of 2 bu. product by 3, that we have 3 the price of fifteen"; and it is then evident, if we inul. 7 17 6 the price of 15 bu. tiply the price of one by 2, 1 1 O the price of 2 bu. and add the product to the price of fifteen, we must Ans. 8 18 6 the price of 17 bu. have the price of 17 bush els, which was required. 2. What will 23 yards of cloth come to, at 4 shillings 7 pence per yard? Ans. £5 5s. 5d. 3. What is the worth of 47 pounds of butter, at 9 pence 2 farthings per pound? Ans. £1 17s. 2d. 2qrs. 4. How many cwt. are contained in 19 kegs of tobacco, each weighing 561b. ? Ans. 9cwt. 2qrs. 5. What is the weight of 17 hogsheads of sugar, each weighing 8cwt. 3qrs. 141b. ? Ans. 150cwt. 3yrs. 141b. 6. What is the weight of 23 chests of tea, each weighing 3cwt. Iqr. 21lb. ? Ans. 79cwt. Qqrs. 7\b. 7. What will 19 yards of cambrick come to, at ilş. 6d. Ans. $10 18s. 6d. 8. What will 52 pounds of tea come to, at 5 shillings 9 pence per pound ? Ans. £14 19s. 9. If one pound of coffee cost 2 shillings 3 pence; what must be paid for 26 pounds ? Ans. £2 18s. 6d. 10. If one yard of lasting cost 7 shillings 10 pence; what will 65 yards cost? Ans. £25 9s. 2d. Case IV.—To find the value of a hundred weight, by having the price of one pound given. RULE.-. If the price be farthings, multiply 2 shillings 4 pence, by the farthings in the price of one pound, and the product will be the per yard ? price of lcwt., or 112 pounds. If the price be in, pence, multiply 3 shillings 4 pence by the price of one pound, and the product will be the price of lcwt. or 112 pounds. EXAMPLES. 1. If one poúnd cost 2 farthings, what cosť lcwt? d. Ans, 4s. 8d. 2 4 Dem.—The reason of our taking 2 shillings 4 2 pence for a multiplicand, is evident, when we re collect that in 112 farthings there are 2 shillings 4 Ans: 4s. 8d. pence, the prict of lcwt., at onë farthing a pound; then it is plain, at 2 farthings a pound, it must be twice as much; consequently we multiply the price, at one farthing, by 2, which gives us the price of lcwt., at 2 farthings per pound ? 2. What will lcwt. of rice cost, at 21d. per pound? Ans. £1:3s. Ad. S. d. 2 4 10 farthings=2ja: Åns. £1 3s. 4d. 3. What will l'cwt. cost; at 11d. per pound? Ans. 11s. 8d. • 4. What will lcwt. cost, at 1:{d. per pound? Ans. 16s. 4d. 5. What will lcwt. come to, 'at 3 farthings per pound? Ans. 7s, 6. What will lcwt. cost, at 4d per pound? Ans. £1 17s. 40, d.' 9 4; DEM.-The reason of our setting down 9s. 4 48. fór a multiplicand is plain, because Is. 4d. is the price of lcwt. or 112 pounds, at 1 Ans. £1 174 penny per pound, for 112 pence make 9s. and 4d. It is then plain, it must be four times as much, at four pence per pound, as at one penny per pound, consequently we multiply the price of lcwt., at 1 penny per pound, by 4, which must give us the price of lcwt., at 4d. per pound; because at 4d. per pound, lcwt. must cost 4 times as much, as at one penny per pound. 7. What is the value of lcwt., at 3 pence per pound? Ans. £1-85. 8. What is the value of Icwt., at 7 pence per pound? Ans. £3 5s. 4d. 9. At 9 pence per pound, what is the value of"1cwt. ? Ans. £4 4s. 10. At 8 pence per pound, what is the value of lcwt. ? Ans. £3 14s. 84 K: PRACTICAL QUESTIONS 1. What is the worth of 42 bushels of peas, at 4 shillings 6d pence per bushel ? Ans. £9 9s. 2. What is the worth of 42 bushels of apples, at 2 shillings 6 pence per bushel ?: Ans. £5 5s. 3. What is the worth of 49 yards of broadcloth, at 18 shil. lings 4 pence per yard? Ans. £44 18s. 4d. 4. What is the weight of 8 hogsheads of sugar, each weighing 7cwt. 3qrs. 1916. ? Ans. 63cwt. Iqr. 121b. 5. What is the weight of 6 chests of tea, each weighing 3cwt. 2qrs. 8lb. Ans. 21ckt. lgi. 2015. 6. How many yards in 12 pieces of cloth, each containing 18 yards, 2qrs. Ina.? Ans. 222yds. 3qrs. 7. What is the weight of 2 dozen silver spoons, each weighing 2oz. 12pwts. 5grs. ? Ans. 5lb. 2oz. 13grs. 8. How many cords of wood in 9 piles, each containing 26 cords, 98 feet? Ans: 240 cords, 114 feet . 9. In 35 pieces of cloth, each measuring 27+ yards; how mary yards in the whole ? Ans. 953 yds. 3qrs. 10. How much land in 4 fields, each of which contains 12 acres, 2 roods, 16 rods? Ans. 50 acres, í rood, 24 rods. 11. What is the value of 20 cords of wood, at 9s. per cord ? Ans. £9. 12. What are 18 yards of shirting worth, at 2 shillings 6 pence per yard? Ans. £2 5s. 13. What is the worth of 25 bushels of wheat, at 10 shillings per bushel ? Ans. £12 10s. COMPOUND DIVISION, Is finding how often one number or sum is contained in another of different denominations, or how often it may be subtracted from another. RULE.-Divide the left hand denomination the same as in simple division; and if any thing remains, reduce it to the next inferiour denomination, adding to the product whatever you have in the given sum of the next less denomination; then divide as before, and again reduce the remainder to the next inferiour denomination, and thus continue the work, till the whole is finished. Proved by compound multiplication. Multiply the quotient by the divisor, and if the product equal the multiplicand the work is right.. S. S. CASE I. 1. Divide £32 16s. 88. equally among 4 persons. Ans. £8 4s. 2d. the share of each. £ d. 4)32 16 8 Dem. It is plain, if £32 16s. 8d. be di vided into 4 parts or shares, that one part or Ans. 8 4 share is a fourth part of the whole; and by dividing the whole sum by 4, our quotient must be a fourth part of the whole, which plainly appears from the quotient itself, because each quotient figure is one fourth part of a like denomination in the dividend. 2. If 5 bushels of clover seed cost £11 3s. and 4d. ; what did it cost per bushel ? Ans. £2 45. 8d. £ d. £ d. DEM.It is plain, that the quo5)11 3 4 (2 4 8 tient must be in each place of the kind' or denomination of 10 5 that part of the dividend which I Proof. £11 3 4 produced it, hence by dividing the 20 pounds of the dividend by the divi sor (5) our quotient is 2 pounds; 23 and we have one pound remaining, which we multiply 20 by 20, because it equals 20 shillings, and to the product, we add the 3 shillings of our dividend, and divide the 23 shillings by 5, the divisor, which gives 4 for a quotient; 12 which is shillings, because the shillings of the dividend produced it; we now have 3 shillings for a remainder, 40 which we reduce to pence, by multiplying by 12, and 40 adding the four pence of the dividend to the product; we now have 40 pence, in which we find 5 contained 8 times, which gives us 8 pence in the quotient without a remainder. same NOTE.-The student will recolleet, that compound division is exactly the reverse of compound multiplication. In compound multiplication, we have the price of one pound, one yard, &c. given to find the price of a quantity: In compound division, we have the price of a quantity given to obtain the price of one. And since this rule is exactly the reverse of multiplication, the student will discover, that our remainder, in each place, is produced by the carriage in multiplication; therefore, when any thing remains in pounds, it is as many times 20 in shillings, because in multiplication, we divide the shillings by 20 and carry the quotient to the pounds, which becomes the remainder in division; and for the same reason, when any thing remains in shillings, it is so many times 12 in pence, and so on. 3. A box containing 36 hats cost £48; how much was that per hat? Ans. £1 6s. 8d. 36 216 £ £ s. d. DEM.-It is plain, that one 36) 48 (1 (1 6 8 hat must cost one thirty-sixth 6 part as much as 36, and when we divide the whole sum by 12 8 0 0 20 36, our quotient is one thirty sixth part of the whole sum, as 240 £48-05 0 plainly appears by the proof; because when we repeat the 24 quotient 36 times, we find that the product 12 equals the dividend or whole cost. In the 288 proof, it will be noticed, by multiplying by 288 6, and then that product by 6, is the same as directly multiplying by 36; because the 0 two multipliers are the component parts of 36, for 6 times 6 are 36. Note.- In addition to the illustration of this rule already given, the student has only to keep in mind one thing, that is, to obtain the price of one yard, one pound, &c.; we must divide the price of the quantity by the qnantity, and the quotient will be the price of one yard, one poid, &c." Or if the weight of a number of hogsheads, bales, bags, or boxes, be given, to obtain the weight of one; divide the weight of the whole quantity or number by the number of hogsheads, bales, bags, or boxes, and the quotient will be the weight of one. 4. Three cows cost £22 3s. 9d.; what was the cost of cach? Ans. £7 7s. 11d. 5. If £12 9s. 8d. be divided equally among 4 men; how much will each receive? Ans. £3 2s. 5d. 6. If 7 Ells cost £5 17 shillings 5 pence; what cost 1 ell ? Ans. 16s. 9 d. 7. If 8 horses cost €185 17ş. 6d. ; what was the cost of one horse? Anş. £23 4s. 8d. 1qr. 8. If 10 bushels of wheat cost £3 6s. 8d.; what cost one bushel? Ans. 6s. 8d. 9. A man paid £2 10s. for 15 bushels of corn ; what did he pay per bushel ? Ans, 3s. 4d. 10. À merchant paid £105 for 5n barrels of flour; what did he Ans. £2.2s. CASE II.-- When the divisor. exceeds 12, and is a composite number, it sometimes shortens the work to divide by the component parts of the divisar. pay per barrel? |