§ 7. Single Mule of Chree.

THE Single Rule of Three, fometimes called the RULE of PROPORTION, is known by having three terms given to find the fourth.

It is of Two kinds, Direct and Indirect, or Inverfe.

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 fame proportion to the third that the fecond does to the first.

It is evident that the value, weight, and measure of any commodity is proportionate to its quantity, that the amount of work, or confumption is proportionate to the time; that gain, loss, and interest when the time is fixed, is proportionate to the capital fum from which it arifes; and that the effect produced by any caufe is proportionate to the extent of that cause.

These are cafes in direct proportion, and all others may be known to be fo, when the number fought increases or diminishes along with the term from which it is derived.

Therefore,

If more require more, or lefs require lefs, 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.

Lefs requiring lefs, is when the third term is lefs than the firft and requires the fourth terin to be lefs than the second.

RULE.

"1. State the question by making that number which afks the question, "the third term, or putting it in the third place; that which is of the fame "name or quality as the demand, the first term, and that, which is of the "fame name or quality with the answer required, the fecond term."

"2. Multiply the fecond and third terms together, divide by the first, and "the quotient will be the answer to the question, which (as alfo the remain❝der) will be in the fame 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 queftion; 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 confidered, and the circumftances on which the proportion depends, obferved, 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. If 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 ftating the question.

2. If the fecond term confifts of different denominations, it must be reduc ed to the lowest denomination; the fourth term, or anfwer will then be found in the fame denomination, and must be reduced back again to the highest denomination poffible.

3. After divifion if there be any remainder, and the quotient be not in the lowest denomination, it must be reduced to the next lefs 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 fuppofition and a demand; the fuppofition is implied in the two firit terms of the stateme, the demand in the third.

5. When any of the terms are given in Federal Money, the operation is conducted in all refpects as in fimple numbers, obferving only to place the point, or feparatrix between dollars and cents, and to point off the results according to what has been taught already in Decimal Fractions, Federal Money, and further illuftrated in Compound Divifion.

6. When any number of barrels, bales, or other packages, or pieces are given, if they be of equal contents, find the contents of one barrel or piece, &c. in the lowest denomination mentioned, which multiply by the number of pieces, &c. the product will be the contents of the whole. If the pieces &c. be of unequal contents find the content of each, add these together, and the fum of them will be the whole quantity.

7. The term which asks the question, or that which implies the demand is generally known by fome of these words going before it; how much? H w many? How long? What coft? What will? &c.

EXAMPLES.

1. If 9lbs. of tobacco cost 6s. what will 25lbs. cost?

By inverting the order of the question it will stand thus, 2. If 6s. buy 9lbs. of tobacco, what will 16s8 buy?

Here the term which afks the question (1658) is of different denominations; it must, therefore, be reduced to the lowest denomi nation mentioned (pence) as muft alfo the other term of the fame name, confequently, to be the first term.

144

360

360

Again By inverting the order of the question.

3. If 168 (200 pence) buy 25lbs. of tobacco, how much will 6s. (=72 pence) buy?

4. If 1oz. of filver coft 69, what will be the price of a filver cup that weighs 9oz. 4pwts. 16grs.?

5. If 6 horfes eat 21 bufhels of oats in 3 weeks, how many bushels will 20 horfes eat in the fame time?

Ans. 70 bushels.

The fame queftion inverted.

6. If 20 horses eat 70 bushels of oats in 3 weeks, how many bufhels will 6 horfes eat in the fame time? Ans. 21 bufbels.

The statement of every queftion requires thought and confideration ;Jere are four numbers given in the

tion; to know which three are to

e employed in the statement there can be no difficulty if the Scholar proceed deliberately and as his rule directs-first, confider which of the given numbers it is, that afks the question; that determined on, put it in the third place, then feek for another number of the fame name, or kind, put that in the first place, the fecond place must now be occupied by that number which is of the fame name or kind with the number fought; when these steps are cautiously followed, the Scholar cannot fail to make his statement right.

7. If an Ingot of filver weigh 36oz. 10pwt. what is it worth at 5s. per ounce ? Ans. 9 2s. 6d.

8. A Goldfmith fold a tankard for £10 12s. at the rate of 5s. 4d. per ounce, I demand the weight of it. Ans. 39oz. 15pwt.

11. If 12 acres, 3 roods produce 78 quarters, 3 pecks, how much will 35 acres, 1 rood, 20 poles, produce?