CASE I. § 73. When the simple number does not exceed 12. RULE. I. Write down the denominate number and set the multiplier under the lowest denomination. II. Multiply the lowest denomination by the multiplier, and see how many units of the next higher denomination are contained in the product, and set down the excess as in addition. III. Multiply the next higher denomination by the multiplier and add the units to be carried from the last product; then reduce the sum to units of the next higher denomination, write down the excess and proceed in the same way for all the denominations, setting down the entire product when you come to the last. Q. What is required when you multiply a denominate number by a simple one? When the simple number does not exceed 12, how do you write it down? How do you begin to multiply? How do you carry? 3. Multiply 9s 6d by 3? 4. What will 12 gallons of brandy cost at 9s 6d per gallon? 5. What will 9cwt. of butter cost at £1 APPLICATIONS. Ans. £5 14s. 11s 5d per cwt. Ans. £14 2s 9d. 1. What is the cost of 4 yards of cloth at £1 3s 6d per yard? 2. What will be the cost of 9 hats, at 9s 9d each? Ans. £4 7s 9d. 3. A farmer has 11 bags of corn each containing 2bu. 1pk. 3qt.: how much corn in all the bags ? Ans. 25bu. 3pk 1qt. 4. What is the cost of 12 bushels of wheat at 9s 6d per bushel? Ans. £ S. 5. How much sugar in 12 barrels, each containing 3cwt. 2qr. 27lb.? 6. In 7 loads of wood, each cord feet, how many cords? CASE II. Ans. 2 T. 4cwt. 3qr. 16lb. containing 1 cord and 2 Ans. 8 cords 6 cord feet. § 74. When the simple number is greater than 12 and a composite number. RULE. Multiply the denominate number by one of the component parts, or factors, and then multiply the product by the other factors in succession: the last product is the one required. EXAMPLES. 1. Multiply £6 2s 9d by 48=6x8. Ans. £294 12s. 2. What will 24 barrels of flour cost, at £2 11s 8d per barrel? Ans. £62. 3. What is the cost of 42cwt. of tallow, at £1 14s 6d per cwt? 4. What is the cost of 120 dozen of candles at 5s 9d per dozen? Ans. £34 10s. 5. How much water will be contained in 96 hogsheads, each containing 62gal. 1qt. 1pt. 1gi.? Ans. 5991 gallons. CASE III. § 75. When the simple number exceeds 12 and is not a composite number. RULE. Multiply the simple number by each of the denominations separately, and reduce each product to the highest denomination named. Then add the several products together, and their sum will be the answer sought. 2. Multiply £6 8s 9d by 139. 139x9d 1251d=£ 5 4s 3d 4. What is the cost of 46 bushel of wheat at 48 71d bushel? per 5. What is the cost of 117cwt. of raisins at £1 2s 3d per cwt.? Ans. £130 3s 3d. Q. How do you multiply when the simple number is greater than 12 and a composite number? How do you multiply when the simple number exceeds 12 and is not a composite number? DIVISION OF DENOMINATE NUMBERS. 1. Charles has 3s and wishes to divide it equally between himself and two brothers: how much must he give to each? If he divides 2s 6d, how much? If he divides 2s, how much? If he divides 1s 6d, how much? If he divides 1s, how much? 2. John has a bushel of nuts and wishes to divide them equally among himself and three brothers: how much will each have? If he divides 3pks., how much? If he divides 2pks. 4 qt.? If he divides 1pk.? If he divides 2qt. ? If he divides 1qt.? 3. Divide £25 15s 10d equally among In this example we find that 8 is contained in £25, 3 times and £1 over. Now this £1 has yet to be divided by 8, as well as the 15s and 10d. Then by multiplying the £1 by 20 and adding the 15s gives 35s, which contains 8, 4 times and 3s over. Multiplying the 3s by 12 and adding in the 10d, gives 46d, which contains 8, 5 times and 6d over. The 6d being reduced, gives 24 farthings which contains 8, 3 times. Therefore, each of the denominations has been divided by 8. 8 persons. OPERATION. 8)£25 15s 10d(£3 24 £ 1 20 8)35s(48 32 38 12 4 8)24 far.(3far. Ans. £3 4s 53d. § 76. Therefore, a denominate number may be divided into any number of equal parts by dividing each of its denominations by the divisor. RULE. I. Set down the number to be divided in the order of its denominations from the highest to the lowest, and write the divisor on the left. II. Find how often the divisor is contained in the figures of the highest denomination. III. Reduce the remainder, if there be any, to the next lower denomination, and add the figures of the dividend expressing that denomination, and then divide the sum by the divisor. IV. Proceed in the same way for all the denominations to the last, and if there be a remainder place the divisor under it, as in division of simple numbers. Each of the quotients will be of the same denomination as its dividend, and the several quotients connected together will be the entire quotient sought. |