SUPPLEMENT TO COMPOUND MULTIPLI CATION. CASE I. When the given quantity is a fraction, and the price or weight, &c. of one given, to find the value of the fractional quantity. Rule. Multiply the price or weight, &c. of one, by the numerator of the fraction, divide the product by the denominator ; the quotient will be the value of the fractional quantity. Note. If the numerator is 1, then only divide by the denominator. EXAMPLES. * 1. Required the value of 1 of a ship, valued at £ 3576. 3576 7 8)25032 per tun? Ans. £ 3129 2. What is the value of of a tun of wine, at £ 36 Ans. £ 15 8 69. 3. What is of a ton of hay worth, at £ 5 10 6 per ton ? Ans. £ 4 2 10. 14. How much is į of a mile ? Ans. 5 furlongs. 5. How much is of 1 C. 3 qr. 16 lb. ? Ans. 1 C. 1 qr. 81. Ib. CASE II. When the given quantity is a mixed number. RULE. Proceed with the fractional part of the quanti. ty, as in the last case. Then multiply the price, weight, or measure of one, by the integral part of the quantity ; add this product, and the quotient together; their sum will be the value required. NOTE. If the numerator of the fraction is 1, only, divide by its denominator. * To prove this rule multiply the answer by the denominator, and divide the product by the numerator, the quotient will be the first sum given. EXAMPLES 1. Required the value of 2. What is 254 bushels 7 gallons of wine, at of salt worth, at 5s. 9d. 5s. 11 d. per gallon. 5 111 4)5 9 5. 9 74 1 5 per bushel ? S. d. 7 4)1 3 10 1 54 1 89 5 value of 5 = 0 4 9= value of 7 = 2 1 8= value of 25=7 3 9 value of 1 51 Ans. £ 2 6 5,5 Ans. £ 7 5 21 3. What is the value of 39 chaldrons of coals, at £1 18 9 per chaldron ? Ans. £76,5 9. 4. There are 8 men, who agree to furnish the following lots of wood, for the parish priest, viz. seven of them will give each 3 cords, the eighth of 3 cords, how much did they all give ? Ans. 23 cords. DIVISION OF FEDERAL MONEY Teaches how, from the value of several articles given in Federal money, to find the value or price of one. RULE. Consider the given value in its lowest denomination ; and divide it by the quantity given, as in Simple Division; the quotient will be the value or price of one, in the same denomination, and may be reduced to its proper terms, as before taught. EXAMPLES. 1. If any acres of land cost 2. If 26 yards of linen cost $ 72, 52, what is it per acre ? | $ 31,79,8, what is it per yard ? 7)72,52 26)31,79,8($ 1,22,3 Ans. $ 10,36 Ans. 57 26 59 59 52 78 78 per cwt. ? 3. If 37 yards of cloth cost $ 212,75; what is it per yard? Ans. $ 5,75. 4. If 4 of dozen buttons cost $ 2,21,2, what were they. per dozen ? Ans. $ 0,55,3. 5. If 90 gallons of brandy cost $ 96,75, 'what was it per gallon ? Ans. $ 1,07,5. 6. If 536 quintals of fish cost $ 1913,52, how much per quintal ? Ans. $ 3,57. 7. If 26 hogsheads of lime cost $ 94,90, how much per hogshead? Ans. $ 3,65. 8. If 84 pounds of tea cost $ 114,24, how much pet Ib. ? Ans. $ 1,36. 9. If 3 hogsheads of tobacco, each weighing net 5C. 2qr. 17 lb, cost $ 114,44,5, what was it per lb. ? Ans. 52 cents. 10. If 15 hogsheads of sugar, cach weighing net 12 C. I qr. 16 lb. cost $ 1041, how much was it per lb? Ans. 5 cents. 11. If 35 tons of hay cost $ 525, how much was it Ans. 75 cents. 12. If 57 yards of stuff cost $ 21,09, what was it a Ans. 37 cents. 13. If 9 lb. of coffee cost $ 2,97, how much was it per lb.? Ans. 33 cents. 14. If 5 barrels of sugar, containing each 2 C. I qr. 15 lb. net, cost 893,45, how much a pound ? Ans. 7 cts. 15. If 25 bushels of wheat cost $ 28,12}, what is it a bushel ? Ans. 8 1,124 Any articles bought or sold by the thousand, as boards, plank, bricks, &c. the value of several thousands, hundreds, &c. given, to find the value, or price of one thousand. RULE. To the whole value given, annex three ciphers, then divide it by the given quantity, the quotient will be the price of one thousand, in the lowest denomination of the given value, which may be reduced as above. EXAMPLES. 1. If 25374 feet of boards cost $ 190,29,5, how much is it per thousand ? H yard? 25374)$190,29,5000(87,50,0 Ans. 177 60 8 12 68 70 00 2. If 46487 feet of boards cost $ 314,02, how much per thousand ? Ans. 86,75,5+ 3. If 22736 bricks cost $126,18,5 how much per thousand ? Ans. $ 5,55+ 4. If 237385 bricks cost $ 1483,65,6, how much per thousand ? Ans. % 6,25. When the given quantity is a fraction, and the price of one required. Rule. Multiply the given value by the denominator of the fraction, and divide the product by the numerator, the quotient will be the price of one. EXAMPLES. 1. If of a yard of cloth cost $ 3,18,71 how much is it per yard ? NOTE. These questions 3,18,7,5 may be proved by multiplication of Federal Money, by fractions. 3)12 75 00 dols. 4,25 Ans. 2. If ** of a ton of timber cost 43 cents, 7{ mills, how much per ton ? Ans. $3,50.* 3. If of a ton of hay cost $ 16,24, what is it per ton ? Ans. $18,56. 4. If į of an acre of land cost $ 1,96,2, what is it per acre ? Ans. $17,65,8. When the given quantity is a mixed number, and the value of one required. . * When the numeratoris 1, division is unnecessary, therefore, only multiply by the denominator, the product will be the answer. Rule. Multiply the integer of the given quantity, by the denominator of the fraction ; to the product add its numerator, for a divisor. Multiply the given value by the same denominator, for a dividend. Divide this new dividend, by the new divisor, the quotient will be the answer. EXAMPLES 1. If 264 bushels of wheat cost dolls. 33,43,7, how much per bushel ? 33,43,7,5 26 4 107)133,75,00($1,25 Ans. 107 NOTE. These questions may be proved by multiplica. 267 tion of Federal Money, by 214 mixed numbers. 535 2. If 375į bushels of salt cost dolls. 281,62,5, how much per bushel ? Ans. 75 cents. 3. If 97 yards of cloth cost dolls. 44,43,71, how much Ans. dolls. 4,50. per yard ? Questions for exercise in Division of Federal Money. per dozen ? 1. If 4 dozen of buttons cost dolls. 2,21,2, how much Ans. 55 cents, 3 mills. 2. If 90 gallons of brandy cost dolls. 96,75, how much per gallon? Ans. dolls. 1,07,5. 3. If 536 quintals of fish cost dolls. 1913,52, how much per quintal ? Ans. dolls. 3,57. 4. If 46 hogsheads of lime cost dolls. 167,90, how much per hogshead ? Ans. dolls. 3,65. 5. If 84 lb. of tea cost dolls. 114,24, how much per lb. ? Ans. dolls. 1,36. |