COMPOUND MULTIPLICATION AND DIVISION. MULTIPLICATION. Art. 143.-1. If a bushel of oats cost 3s. 6d., how much will two bushels cost? 3. How much must be paid for 4 books, at 4s. 3d. each? 5. What will 5 yds. of cloth cost at 3s. 8d. per yard? 7. How much beer in 8 bottles, each containing 2 qts. 1 pt. 2 gi.? 9. If 1 gallon of molasses cost 2s. 8d. 3qrs., what will 8 gallons cost? d. qr. 2 83 8 If one gallon cost 2s. 8d. 3qrs., it is ev£1 1 10 0 ident that 8 gallons will cost 8 times as much. We begin to multiply with the lowest denomination, which is farthings. 8 times 3qrs. are 24qrs. 6d. Oqr. Place a cipher in the column of farthings, and proceed to multiply the column of pence, reserving the 6d. found in 24qrs. to be added; 8 times 8d. are 64d., and 6d. added are 70d. 5s. 10d. Write the 10d. in the column of pence, and reserve the 5s. to be added to the column of shillings. | Lastly, 8 times 2s. are 16s., and 5s. added are 21s.£1 1s. and 10d., the answer. Art. 145.-COMPOUND MULTIPLICATION is when the multiplicand consists of different denominations. DIVISION. Art. 144.-2. If 2 bushels of oats cost 7s., how much are they per bushel? 4. If 4 books cost 17s., what will 1 book cost? 6. If 5 yds. of cloth cost 18s, 4d., how much is it per yard? 8. If 8 bottles contain 22 qts., how much does 1 contain ? 10. If 8 gallons of molasses cost £1 1s. 10d., what cost 1 gallon ? £. s. s. d. gr. 8)1 1 10 0 If the price of 8 gallons be di0 2 8 3 vided into 8 parts, it is evident that one of these parts would be the price of one gallon. Thus, 1 pound divided by 8, gives a cipher as a quotient figure, which must be written under the column of pounds, and 1 pound remains, which must be reduced to shillings: 1×20=20s., and 1s. added 21s. Dividing 21s. by 8, we have 2 as a quotient figure, and 5s. remainder, which reduced to pence, 5× 12=60, and 10d. added=70d., which divided by 8=8d. and 6d. over; reduce 6d. to qrs., 6×4=24qrs., divided by 8=3qrs.; we have then, £0 2s. 8d. 3qrs., the answer. Art. 146.-COMPOUND DIVISION is when the dividend consists of different denominations. RULE. RULE. Divide the price by the quanWhen the quantity does not Multiply the price by the quantity. When the quantity does not | tity. exceed 12, set down the price of exceed 12, divide by the whole quanone yard, one pound, or one gal-tity at once. Divide the highest lon, etc., and the quantity under | denomination by the divisor ; then, the lowest for a multiplier, observ- multiply the remainder, if any, by ing to carry as in Compound that number which expresses how Addition. EXAMPLES. 1. What will 9 yds. of cloth cost at 5s. 6d. per yard? 3. What will 8 cwt. of cheese cost, at £1 10s. 5d. per cwt.? 5. What will 24 yards of cloth cost at 15s. 3d. per yard? £ s. d. 15 3 6 4 11 6 4 many of the next lower denomination make one of that, adding to the product the next lower denomination; divide this sum by the given divisor, and so proceed. When the multi- 6)18 plier is greater 4) 3 than 12, and is a composite number, s. d. 6 0 1 0 0 15 3 Ans. When the divisor is greater than 12, and is a composite num 18 6 0 Ans. multiply by its ber, divide by its component parts. component parts, as in the last example, 6×4=24. 7. What is the weight of 56 casks of raisins, each weighing 1 cwt. 2 qrs. 12 lbs. ? 9. How much will 66 acres of land come to, at £7 9s. 6d. per acre? 11. What will 108 boxes of sugar weigh, each weighing 2 cwt. 1 qr. 14 lbs. ? 13. What will 112 yds. of cloth cost, at £1 10s. 6d. per yard? 15. How much cloth will be required to make 121 coats, if, to make one, it requires 3 yds. 3 qrs. 3 na. ? 17. What is the value of 336 8. If 56 casks of raisins weigh 90 cwt., what is the weight of one cask? 10. If 66 acres of land cost £493 7s., what will 1 acre cost? 12. If 108 boxes of sugar weigh 256 cwt. 2 qrs., what is the weight of one box? 14. If 112 yards of cloth cost £170 16s., what is it per yard? 16. If it take 476 yds. 1 qr. 3 na. to make 121 coats, how much will it require to make one? 18. If 336 yards of cloth cost QUESTIONS.-1. What is Compound Multiplication? 2. Compound Division? 3. Rule for Compound Multiplication? 4. Rule for Compound Division? 5. How do you proceed when the multiplier is a composite number? 6. When the divisor is a composite number? 7. How do you proceed when the multiplier is greater than 12, and not a composite number? 8. How, when the divisor is not a composite number? yards of cloth, at 2s. 5d per | £40 12s., what is the cost of one yard? yard? 19. What will 153 barrels of 20. If 153 barrels of sugar sugar weigh, each barrel weigh-weigh 516 cwt. 1 qr. 14 lbs., what ing 3 cwt. 1 qr. 14 lbs. ? is the weight of one barrel? When the divisor is not a com As 153 is not a composite number, we will first find the weightposite number, divide by the whole divisor at once, after the manner of Long Division. of 100, then of 50, then of 3; the several products added will be the answer. Thus : Thus, taking the last question, When the multiplier is not a composite number, and is hundreds, multiply by 10, and this product by 10, which will give the product of 100, and this by the number of hundreds. For tens, multiply the product of ten by the number of tens; for units, multiply the multiplicand. The several products added will be the answer sought. 21. How much will a a man 153)2142(14 lbs. cwt., 1 barrel 153 612 612 weighs 3 cwt., and 57 remain der, which are parts of a cwt. and must be reduced to quarters, the next lower denomination; therefore, multiply 57 by 4, and to the product add the one quarter, and divide the amount, 229, by 153. We now have 1 qr. as the quotient, and a remainder of 76, which must be reduced to pounds by multiplying it by 28, and adding the 14 lbs. to the product. Again, dividing by 153, we have 14 lbs. as the quotient. The several quotients, 3 cwt. 1 qr. 14 lbs., are the answer. 22. If a man in one year spend spend in a year, if he spend 4d. a £6 1s. 8d. how much will he day? 23. What is the value of 1900 yards of linen at 5s. 8d. per yard ? spend in a day? 24. If 1900 yards of linen cost £542 5s. 10d., what will one yard cost? 25. What will 68 hogsheads of lime cost, at £1 1s. 6d. per hhd. ? 27. What is the value of 26 yards of silk, at 9s. 6d. per yard? 29. How many gallons of beer in 14 bottles, each containing 3 qts. 1 pt. 1 gill ? 26. If 68 hhds. of lime cost £73 3s. 5d., what is it per hhd. ? 28. If 26 yards of silk be worth £12 8s. 1d., what will 1 yard be worth? 30. If 14 bottles of beer contain 12 gal. 2 qts. 1 pt. 2 gills, how much does 1 bottle contain? 32. If 6 chests of tea weigh 31. What is the weight of 6 chests of tea, each weighing 321 cwt. 1 qr. 26 lbs., what is the cwt. 2 qrs. 9 lbs. ? weight of 1 chest? 33. How many acres in 9 fields, each containing 12 acr. 2 ro. 25 rds.? 35. How many cords of wood in 37 piles, each containing 8 cords, 28 ft. ? 37. How much will 17 casks of nails weigh, each weighing 1 cwt. 2 qrs. 16 lbs. 3 oz.? 39. How many bushels of apples can be put into 125 barrels, each containing 3 bu. 1 pk. 5 qts.? 41. If a ship sail 2 deg. 30 m. 10 sec. in 1 day, how far will she sail in 30 days? 43. If 3 men build 14 rds. 8 feet of wall in one day, how much will they build in 26 days? 45. If 1 yard of cloth cost £2 2s. 6d., what will 229 yards cost? 47. The moon passes through I sign of the zodiac in 2 days, 6 h. 38 m. 34 sec. In what time does it pass through 12 signs? 49. If one gallon of molasses cost 4s. 2d. 2qrs., what will 1000 gallons cost? 51. If 1 pound of tea cost 8s. 5d. 2qrs., what will 108 lbs. cost? 53. If 1 quintal of fish cost 23s. 9d., what will 345 quintals cost? 34. If in 9 fields there are 113 acr. 3 ro. 25 rds., how many in 1 field? 36. If 37 piles of wood contain 304 cords and 12 ft., how much in 1 pile? 38. If 17 casks of nails weigh 27 cwt. 3 qrs. 23 lbs. 3 oz., what will 1 cask weigh? 40. If 125 barrels contain 425 bush. 3 pks. 1 qt., how much does 1 contain? 42. If a ship sail 75 deg. 5 m. in 30 days, how far will she sail in 1 day? 44. If 3 men build 376 rods, 10 feet, in 26 days, how much do they build in 1 day? 46. Bought 229 yards of cloth for £486 12s. 6d.; what did it cost per yard? 48. If the moon pass through 12 signs of the zodiac in 27 days, 7 h. 42 m. 48 sec., in what time does it pass through 1 sign? 50. If 1000 gallons of molasses cost £210 8s. 4d., what is it per gallon? 52. If 108 pounds of tea cost £45 13s. 6d., what will 1 pound cost? 54. If 345 quintals of fish cost £409 13s. 9d., what was it per quintal ? Art. 147.-A concise view of the application of the prin ciple employed in the addition of simple numbers to compound numbers and fractions : In each case it appears that the numbers to be added must be reduced to the lowest denomination mentioned; and also, that they are reduced by multiplying the higher by that number which expresses how many of the lower make one of the higher. SUPPLEMENT TO COMPOUND NUMBERS. Art. 148.-1. What is the weight of two pieces of gold, one weighing 1 lb. 0 oz. 6 pwt. 4 grs.; the other, 2 lbs. 3 oz. 8 pwt. 16 grs.? Ans. 3 lbs. 3 oz. 14 pwt. 20 grs. 2. A man has one wedge of gold, weighing 25 lbs. 3 oz. 12 pwt., and another weighing 1 lb. 11 oz. 12 pwt. 7 grs. What is the weight of the two? Ans. 27 lbs. 3 oz. 4 pwt. 7 grs. 3. A silversmith had a quantity of silver, weighing 21 lbs. After refining it by melting, it weighed 15 lbs. 10 oz. 9 oz. 11 pwt. 19 grs. What was lost by melting? Ans. 5 lbs. 10 oz. 8 pwt. 5 grs. 4. What is the sum and difference of 3 lbs. 10 oz., and 2 lbs. 11 oz. 7 pwt. 4 grs. ? Ans. Sum: 6 lbs. 9 oz. 7 pwt. 4 grs. Difference: 10 oz. 12 pwt. 20 grs. cost, at 1s. 2d. 3qrs. per 5. What will 13 lbs. of coffee pound? Ans. 15s. 11d. 3qrs. |