PKOPOHTION. 109 



Note i. It is sometimes most convenient to multiply 

 and divide as in compound multiplication and division j 

 and sometimes it is expedient to multiply and divide ac- 

 cording to the rules of vulgar or decimal fractions. But 



■when 



the rule, as applied to ordinary inquiries, may be made very evi- 

 dent by attending only to the principles of compound multiplica- 

 tion and division. It is shewn in multiplication of money, that 

 the price of one, multiplied by the quantity, is the price of the 

 .whole ; and in division, tliat the price of the whole, divided by 

 the quantity, is the price of one. Now, in all cases of valuing 

 goods, &c. where one is the first term of the proportion, it is plain, 

 that the answer, found by this rule, will be the same as that found 

 by multiplication of money ; and, where one is the last term of the 

 proportion, it will be the same as that found by division of money. 

 In like manner, if the first term be any number whatever, it is 

 plain, that the product of the second and third terms will be great- 

 er than the true ansv/er required by ns much as the price in the 

 second term exceeds the price of one, or as the-first term exceeds 

 an unit. Consequently this product divided by the first term will 

 give the true answer required, and is the rule. 



There will sometimes be difficulty in separating the parts of 

 complicated questions, where two or more statings are required, 

 and in preparing the question for stating, or after a proportion is 

 wrought J but as there can be no general directions given for the 

 management of these cases, it must be left to the judgment and 

 experience of the learner. 



The Rule of Three inverse teacheth, by having three num- 

 bers given, to find a fourth, that shall have the same proportion to 

 the second, as the first has to the third. 



If more require morcy or less require less, the question belongs 

 to the rule of three direct. 



But if more require less, or less require ff^crc; it belongs to the 

 rule of three inverse. * ' 



Note. 



