XII. The RULE of THREE DIRECT. EACHETH, by having three numbers given, to find a fourth, in the as firft is to the fecond, fo is the third to the fourth, for which reafon it is called the Rule of Proportion, as it is called the Rule of three, from its having three numbers given; and because of its excellent use in arithmetic, it is often named the Golden Rule. To perform which observe the following RULE. ft. Place the three given terms in fuch order, that the first and third may be of one name; and the fecond must be of the fame name with the fourth term fought. 2. If your first and third terms confift of divers denominations, reduce them into one, and the second into the lowest name mentioned. 3. Multiply the fecond and third terms together, and divide that product by the first; the quotient will be the answer in the fame denomination you left your fecond term in. 4. If there happens to be a remainder, it will either make a fractional part, or it must be reduced to a lower denomination, and divided by the fame divifor, the quotient will be fo many of the faid next name; proceed in this manner to the least name, and all the quotients together will be the anfwer to the question. Before I fhew how to work any queftions in this rule, it will be neceffary to give the learner the following inftructions. Firft, obferve that the firft and fourth numbers are called extremes, and the fecond and third means; the product of the extremes, is equal to the product of the means▸ EXAMPLE 1. As 4 is to 12, fo is 36 to a certain number; what is that number? 4: 12 :: 36 Now it may be eafily proved, that the product of the two extremes is equal to the product of the two means, for 4X 108=12×36=432. CONTRACTION 1. When the fecond term can be divided by the firft, multiply that quotient into the third term, and the product will be the answer. Take the laft example to prove this; thus, 12 divided by 4 = 3; and 3 multiplied by 36 198, the answer, as before. K-2 E. 2. E. 5. If 48 yards of cloth cost 67. what will 64 yards cost? Yds. £. rds. £ 4868; and 6488, the Answer. CONTRACTION 4, When the first term can be divided by the third, and the fecond by that quotient; the laft quotient will be the anfwer. See the preceding exainple. E. 6. If 6 yards of cloth coft 17, 16s. what will be the value of 34 yards, at the fame rate? 4 6 Yds. £:52 52 1 20 410) 104/0 20) 216 Answer £16 Note. To prove examples in this rule, is only varying the operation, as may be seen by the preceding examples. This example plainly fhews the extenfive use of multiplication, and how much preferable, in some cases, it is to the rule of three, by folving queftions in a more concise manner, and therefore it is very neceffary for all perfons to be thoroughly acquainted with thofe moft ufeful rules, viz. compound multiplication and divifton. E. 12. If a foldier's pay be 6d. per day, how much is that per year? If you would know at what rate you must fell your goods by retail, fo as to make a propofed gain by the whole; add the money you would gain to the fum the goods coft you, and then ftate your queftion as before: Thus, if the whole be fold for the total of the coft and gain, at what rate muft any part of it be fold for? Anfwer 6d. 154 per pound. |