10. IF 670 gallons of wine cost 3. IF 670 gallons of wine cost £.147 $490,32; what is that per gallon? 18. 11d. what is that per gallon? Ans. $0,73. And 4f4 SUPPLEMENT to Compound Division. QUESTIONS. 1 WHAT IS Compound Division? 2. WHEN the price of any quantity, not exceeding 12, of yards, pounds, &c. is given in pounds, shillings, pence & farthings, how is the price of one yard found? 3. WHEN the quantity is such a number as cannot be produced by the multipli cation of small numbers, what is the method of procedure? 4. HAVING the price of an hundred weight given, in what way is found the price of 1lb. ? 5. If there be several hundred weight what are the steps of operating ? Pounds, Shill. Pence, Farthings- Dolls. Cents, Mills. Let the Scholar reduce the price of the sheep and of the cows to Federal Money, and perform the operations in Dolls. Cents, Mills, 2. IF 84 cows cost £253 13s. what is the price of each ? Ans. £30 4d. ри Price of 1 sheep, $1,426, Price of 1 cow, $10,065. 3. IF 121 pieces of cloth measure 4. IF 66 tea-spoons weigh 2/6. 10oz. 2896 yards, 1qr. 3na. what does each | 14pwt. what is the weight of each? piece measure? Ans. 10pwt. 1213grs. Ans, 23 yards, 3qr. 3na, 5. Ir 2 cut. of rice cost £2 11s 63d what is that per lb. ? Ans. 23d. 6. AT £2 11s. 6d. for 2 cwt. of rice, what is that in Federal Money, and what is that per lb. ? Price of 1 lb. 3cents, 8 mills. 7. IF 47 bags of Indigo weigh 12 cwt. 8. IF 8 horses cat 900 bushels, Iqr. 26lbs. 4oz. what does each weigh? | and 1 peck of oats in 1 year, how Imuch will each horse eat per day? Ans. 1gr. 1lbs. 12oz. Ans. 1 peck, 1qt. 1pt. 2 gills. 9. Divide £297 2s. 3d. among 4 men, 6 boys, and give each man 3 times so much as one boy; what will each man share, and each boy? 10. DIVIDE £.39 12s 5d. among 4 men, 6 women, and 9 boys; give each man double to a woman, each woman double to a boy. £. s. d. § 7. Single Hule of Three. THE Single Rule of Three, sometimes called the RULE of PROPORTION, is known by having three terms given to find a fourth. It is of Two kinds, Direct and Indirect, or Inverse. SINGLE RULE OF THREE DIRECT: THE Single Rule of Three Direct teaches, by having three numbers given to find a fourth, which shall bear the same proportion to the third that the second does to the first. Ir is evident that the value, weight, and measure of any commodity is proportionate to its quantity, that the amount of work, or consumption is proportionate to the time; that gain, loss, and interest, when the time is fixed, is proportionate to the capital sum from which it arises; and that the effect duced by any cause is proportionate to the extent of that cause. pro THESE are cases in direct proportion, and all others may be known to be so, when the number sought increases or diminishes along with the term from which it is derived. Therefore, IF more require more, or less require less, the question is always known to belong to the Rule of Three Direct. MORE requiring more, is when the third term is greater than the first and requires the fourth term to be greater than the second. LESS requiring less, is when the third term is less than the first, and requires the fourth term to be less than the second. RULE. "1. STATE the question by making that number which asks the question "the third term, or putting it in the third place; that, which is of the same "name or quality as the demand, the first term, and that, which is of the same "name or quality with the answer required, the second term." "2. MULTIPLY the second and third terms together, divide by the first, and "the quotient will be the answer to the question, which (as also the remainder) will be in the same denomination in which you left the second term, and may be brought into any other denomination required." THE chief difficulty that occurs in the Rule of Three, is the right placing of the numbers, or stating of the question; this being accomplished there is nothing to do, but to multiply and divide, and the work is done. To this end the nature of every question must be considered, and the circumstances on which the proportion depends, observed, and common sense will direct this if the terms of the question be understood. THE method of proof is by inverting the order of the question. Note. 1. Ir the first and third terms, both or either, be of different denominations, both terms must be reduced to the lowest denomination mentioned in either, before stating the question. 2. If the second term consist of different denominations, it must be reduced to the lowest denomination, the fourth term, or answer will then be found in the same denomination, and must be reduced back again to the highest denomination possible. 3. AFTER division if there be any remainder, and the quotient be not in the lowest denomination, it must be reduced to the next less denomination, dividing as before. So continue to do, till it is brought to the lowest denomination, or till nothing remains. 4. In every question there is a supposition and a demand; the supposition is implied in the two first terms of the statement, the demand in the third. |