RULE.-When the quantity does not exceed 12 yards, pounds, &c. set down the price of one, and place the quantity under the right hand denomination for a multiplier. Multiply the right hand denomination, and divide the product by as many as it takes of that denomination to make one in the next at the left; set down the remainder, (if any,) under the denomination multiplied, and carry the quotient to the product of the next left hand denomination, and so proceed till you come to the left hand denomination and there set down the product as in simple multiplication. NOTE.-This rule will be found very useful in business; where the price of 1 yard, or 1 pound is given, by it, we find the price of a quantity; by multiplying the price of one yard, or one pound, or a unit of any kind by the quantity, the product will be the price of the quantity. Or if the weight of one hogshead or of one bale is given, we find the weight of the whole by multiplying the weight of one, by the whole number; and in like manner we find the weight of any number of boxes or bags where the weight of one is given. INTRODUCTORY EXAMPLES. 1. If one yard of broadcloth cost 1 pound 3 shillings and 4 pence; what will two yards cost? £ s. d. 1 3 4 2 Ans. 2 6 £ s. d. 1 3 4 1 3 4 2 6 S 8 Ans. £2 6s. 8d. DEM. It is plain, that the price of one yard multiplied by 2. must give the price of two yards because it is repeating every denomination expressing the price of one yard by 2; and it will plainly appear by adding, that this is only a short method of performing addition. DEM.--Here, we find by addition the same result is produced; and the same relation exists when we have three, four, five, or any other number for a multiplier, which may clearly be shown by adding the multiplicand as many times as it has been repeated in multiplication. 2. If one Tun of hay cost £2 12s. 8d.; what will three Tuns cost at that rate? Ans. £7 18s. Od. £ 8. d. 2 12 8 The number of Tuns, 3 Ans. £7 18 0 DEм. Here, we first multiply 8d. by 3, and we have 24 for the product; we then divide this product by 12, because it takes 12 pence to make 1 shilling; and we have 2 for a quotient and nothing for a remainder, so we set down a cipher under the pence, and then say three times twelve are thirty six and add the quotient, two, which we carry from the pence; we then have 38, which we divide by 20, because 203. make a pound; we find 20 contained in 38 once and 18 over, which we set down under shillings and carry 1 pound, which is the quotient, to the product of pounds, by saying three times 2 are 6 and I are 7, which we place under pounds, its proper place. This exam ple we will illustrate by addition, so that the student may not mistake the principles of the rule, or the relation which addition and multiplication bear to each other. £ 8. d. 2 12 8 2 2 12 8 Ans. 7 18 0 Here we again see that the same result is produced by adding the price of one yard instead of multiplying. The student will perceive that we carry in both cases the same; when we multiply the 8 pence by 3, the product is 24 pence, that is 2 shillings, consequently 2 shillings may be added to the product of shillings; and in addition we have 24 pence, that is, 2 shillings which may be added to the shillings, and in multiplying the 12 shillings the product is 36 shillings, and the 2 shillings to carry make 38 shillings, that is, 1 pound and 18 shillings, consequently we set down the 18 shillings and carry the pound to the product of pounds; and by addition we obtain 38 shillings the same as in multiplication, that is, 1 pound and 18 shillings; consequently we set down the 18 shillings and carry the 1 pound, and by adding we obtain 7 pounds, and the same number by multiplying. 3. What will 4 yards of cloth come to, at 3s. 4d. per yard? Ans. 13s. 4d. 4. What cost 5 yards of calico, at 39. 9d. per yard? Ans. 18s. 9d. 5. What will 6 tuns of hay cost, at £2 3s. 6d. per tun? Ans. £13 1s. Od. 6. A man bought 7 sheep at 9s. 6d. per head; what did they cost him? Ans. £3 6s. 6d. 7. A man bought 8 bushels of apples, at 2s. 6d. per bushel; what did they cost him? Ans. £1. 8. Bought 9 pieces of shirting, each containing 28yds. 2qrs. 2na.; how many yards in the 9 pieces? Ans. 257yds. 2qrs. 2na. 9. Bought 10 cwt. of beef at £1 18s. 6d. per cwt.; what did the whole cost? Ans. £19. 5s. 10. What must a merchant pay you for 11cwt. of pork, at £2 1s. 6d. per cwt.? Ans. £22 16s. 6d. 11. What will twelve horses come to, at £29 16s. 8d. each? Ans. £358. CASE II. When the multiplier exceeds 12, and is a composite number, produced by multiplying together any two figures in the multiplication table, it will often be found more convenient, first, to multiply by one of the component figures, and then that product by the other; the last product will be the answer. EXAMPLES. 1. What will 16 yards of broadcloth come to, at £2 3s. Ans. £34 12s. 3d. per yard? 2 3 3 4 8 13 0 Ans. 34 12 0 4 DEM.-When we multiply the price of one yard by 4, we obtain the price of four yards; because, it is the same as adding the price of one yard 4 times; and when we multiply the price of four yards by 4, it must give the price of sixteen yards, because 4 times 4 are 16; and when we multiply the price of four yards by 4, it is the same as adding as many times, because if we should add the price of four yards to itself once, we would have the price of eight yards, because 2 times 4 are 8; and if we add the price of four twice to itself, we must have the price of twelve, because 3 times 4 are 12, or 4 and 4 are 8 and 4 are 12; then if we multiply the price of four by 4 we have the price of sixteen, because it is the same as adding the price of four 3 times to itself; thus, 4 once added to 4 make 8, and 4 added to 8 make 12, and 4 again added make 16, that is, adding the price of four, 3 times to itself, or putting down the price of four, 4 times and adding. NOTE. It will be recollected that 4 and 4 are the component parts of 16, because 4 times 4 are 16. 2. What will 20 calves come to, at £1 6s. 3d. each? Ans. £26 5s. 3. If one yard of calico cost 2s. 6d. ; what will 24 yards cost? Ans. £3. at 4 pence per Ans. 9s. 4d. 4. What will 28 pounds of beef come to, pound? 5. What must a man pay for 36 sheep, at 9 shillings 4 Ans. £16 16s. pence each ? 6. What is the weight of 48 pipes of wine, each weighing 18cwt. 2qrs. 14lb. Ans. 894cwt., or 44T. 14cwt. 7. What is the weight of 72 boxes, each weighing 1 quarter 14 pounds? Ans. 27cwt. 8. In 21 pieces of cloth, each containing 24yds. 2qrs. 3n. ; how many yards? Ans. 518yds. 1qr. 3na. 9. What will 63 yards of calico come to, at 3 shillings 1 Ans. £9 14s. 3d. penny per yard? 10. What will 56 bushels of corn come to, at 3 shillings 9 pence per bushel ? Ans. £10 10s. CASE III-When the multiplier is not the exact product of any two figures in the multiplication table, and is above 12. N RULE.-Take wo figures or factors, whose product comes nearest, 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. 6d. DEM-It is plain, from the preceding case, by multiplying the price of one by 5, and then that product by 3, that we have the price of fifteen; and it is then evident, if we multiply the price of one by 2, and add the product to the price of fifteen, we must have the price of 17 bushels, 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 56lb.? Ans. 9cwt. 2qrs. 5. What is the weight of 17 hogsheads of sugar, each weighing Scwt. 3qrs. 14lb.? Ans. 150cwt. 3qrs. 14lb. 6. What is the weight of 23 chests of tea, each weighing 3cwt. 1qr. 21lb. ? Ans. 79cwt. Oqrs. 7lb. 7. What will 19 yards of cambrick come to, at 11s. 6d. per yard? 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 price of lcwt., or 112 pounds. If the price be in pence, multiply 9 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 pound cost 2 farthings, what cost 1cwt? Ans. 4s. 8d. 8. d. 2 4 2 Ans. 4s. 8d. DEM. The reason of our taking 2 shillings 4 pence for a multiplicand, is evident when we recollect that in 112 farthings there are shillings 4 pence, the price of lcwt., at one 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 1cwt of. rice cost, at 21d. per pound? 8. d. Ans. £1 3s. 48. 3. What will 1cwt. cost, at 14d. per pound? Ans. 11s. 8d. 4. What will lcwt. cost, at 1d. per pound? Ans. 16s. 4d, 5. What will lcwt. come to, at 3 farthings per pound? 6. What will 1ewt cost, at 4d. per pound? S. d. 9 4 4 Ans. £1 17 4 Ans. 7s. Ans. £1 17s. 4d. DEM.--The reason of our setting down 9s. 4d. for a multiplicand is plain, because 9s. 4d. is the price of 1cwt. or 112 pounds, at 1 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 1cwt., at 3 pence per pound? Ans. £1 8s. 8. What is the value of 1cwt., 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 1cwt. ? Ans. £3 14s. 8d. K |