COMPOUND DIVISION teaches how to divide a number of several denominations by any given number, or into any number of equal parts; as follows: PLACE the divisor on the left of the dividend, as in Simple Division.-Begin at the left-hand, and divide the number of the highest denomination by the divisor, setting down the quotient in its proper place. If there be any remainder after this division, reduce it to the next lower denomination, which add to the number, if any, belonging to that denomination, and divide the sum by the divisor.-Set down again this quotient, reduce its remainder to the next lower denomination again, and so on through all the denominations to the last. I. If the divisor exceed 12, find what simple numbers, multiplied together, will produce it, and divide by then separately, as in Simple Division, as below. EXAMPLES. I. What is Cheese per cwt, if 16 cwt cost 25/ 14s 8d? 4. Divide 71/ 13s 10d by 56. 5. Divide 44/ 4s by 96. per cwt?} Ans. 7 10 4 Ans. 2 14 8 Ans. O 9 2 6. At 31/ 10s per cwt, how much per lb? Ans. O 5 71⁄2 II. If the divisor cannot be produced by the multiplication of small numbers, divide by the whole divisor at once, after the manner of Long Division, as follows. Ans. 2 lb 6 oz 8 dwts 14 gr. 2. Divide 17 lb 5 oz 2 dr 1 scr 4 gr by 12. Ans. 1 lb 5 oz 3 dr 1 scr 12 gr. 3. Divide 178 cwt 3 qrs 14 lb by 53. Ans. 3 cwt 1qr 14lb. 4. Divide 144 mi 4 fur 2 po 1 yd 2 ft 0 in by 39. Ans. 3 mi 5 fur 26 po 0 yds 2 ft 8 in. 5. Divide 534 yds 2 qrs 2 na by 47. Ans. 11 yds 1 qr 2 na. 6. Divide 71 ac 1 ro 33 po by 51. 8. Divide 387 la 9 qr by 72. Ans. 1 ac 2 ro 3 po. 65. Ans. 27 gal. 7 pi. Ans. 5 la 3 qrs 7 bu. Ans. 7 mo 3 we 5 ds. THE THE RULE OF THREE teaches how to find a fourth proportional to three numbers given: for which reason it is sometimes called the Rule of Proportion. It is called the Rule of Three, because three terms or numbers are given, to find a fourth. And because of its great and extensive usefulness, it is often called the Golden Rule. This Rule is usually considered as of two kinds, namely, Direct, and Inverse. The Rule of Three Direct is that in which more requires more, or less requires less. As in this; if 3 men dig 21 yards of trench in a certain time, how much will 6 men dig in the same time? Here more requires more, that is, 6 men, which are more than 3 men, will also perform more work, in the same time. Or when it is thus: if 6 men dig 42 yards, how much will 3 men dig in the same time? Here then, less requires less, or 3 men will perform proportionably less work than 6 men, in the same time. In both these cases then, the Rule, or the Proportion, is Direct; and the stating must be thus, As 3:21::6: 42, or thus, As 6:42:: 3:21, But the Rule of Three Inverse, is when more requires less, or less requires more. As in this if 3 men dig a certain quantity of trench in 14 hours, in how many hours will 6 men dig the like quantity? Here it is evident that 6 men, being more than 3, will perform an equal quantity of work in less time, or fewer hours. Or thus: if 6 men perform a certain quantity of work in 7 hours, in how many hours will 3 men perform the same? Here less requires more, for 3 men will take more hours than 6 to perform the same work, In both these cases then the Rule, or the Proportion, is Inverse; and the stating must be thus, As 6; 14 :: 3 : 7, or thus, As 3: 7:: 6:14. And in all these statings, the fourth term is found, by multiplying the 2d and 3d terms together, and dividing the product by the 1st term. Of the three given numbers; two of them contain the supposition, and the third a demand. And for stating and working questions of these kinds, observe the following general Rule: STATE STATE the question, by setting down in a straight line the three given numbers, in the following manner, viz. so that the 2d term be that number of supposition which is of the same kind that the answer or 4th term is to be; ́making the other number of supposition the 1st. term, and the demanding number the 3d term, when the question is in direct proportion; but contrariwise, the other number of supposition the 3d term, and the demanding number the 1st term, when the question has inverse proportion. Then, in both cases, multiply the 2d and 3d terms together, and divide the product by the 1st, which will give the answer, or 4th term sought, viz. of the same denomination as the second term. Note, If the first and third terms consist of different denominations, reduce them both to the same: and if the second term be a compound number, it is mostly convenient to reduce it to the lowest denomination mentioned.-If, after division, there be any remainder, reduce it to the next lower denomination, and divide by the same divisor as before, and the quotient will be of this last denomination. Proceed in the same manner with all the remainders, till they be reduced to the lowest denomination which the second admits of, and the several quotients taken together will be the answer required. Note also, The reason for the foregoing Rules will appear, when we come to treat of the nature of Proportions.-Sometimes two or more statings are necessary, which may always be known from the nature of the question. EXAMPLES. 1. If 8 yards of Cloth cost 1/ 4s, what will 96 yards cost? yds 1 s yds 1 s As 81 4: 96: 14 8 the Answer. 20 24 96 144 216 8) 2304 2,0) 28,8$ £14 8 Answer. |