Observe. These two examples might have been multiplied by the shillings in a dollar, and cut off as directed; then, the figures to the left divided by 20, the shillings in a pound, would have brought the pounds and shillings; the remainder, multiplied by 12, and divided as directed, would have brought the pence, and that remainder, by 4, and divided again, the farthings. But the general rule, perhaps, will be best for the learner, as the mind is less perplexed by following one particular method; for, when the dollar is not even shillings, the general rule must be followed.

3. Change 325D. 62cts. into Connecticut currency.*

Ans. 97£. 13s. 8d. and 64 rem. Connecticut currency is 6s. or 72d. to the dollar, multiply the cents in the given sum by it, and proceed as directed in the rule.

If the remainder, (64,) had been multiplied by 4, and two figures pointed off, it would have brought 2qrs. and 56 remainder.

Had this question been given to be brought into New Hampshire, Massachusetts, Rhode Island, Virginia, Kentucky, or Tennessee currency, the operation would have been the same.

4. Change 149D. 36 cts. into New York currency.

Ans. 59. 14s. 10d. 2qr. 24 rem.

by the pence or shillings in a dollar, New York currency, and proceed according to rule. The operation would have been the same for North Carolina.

5. Change 94D. 29cts. into New Jersey currency. Ans. 35€. 7s. 2d. 10 rem. Find the pence in a dollar New Jersey currency and proceed. Pennsylvania, Delaware, and Maryland would have been the same. 6. Change 128D. 94cts. into South Carolina, and Georgia currency. Ans. 30£. 1s. 8d. 2qr. 56 rem.

rency.

7. Change 245 dolls. 61 cts. into Canada, or Nova Scotia curAns. 61£. 8s. Od. 2qr. 40 rem. pence are a dollar in the above currencies. 8. Change 300 dolls. 50cts. into English, or Sterling money.

You will find that

Ans. 67£ 12s. 3d.

9. Change 129 dollars 49 cents into Irish money.

Ans. 31£. 11s. 3d. 33 rem. See Note 2. Multiply the cents in the given sum, by the half pence in the dollar; bring the half pence into pounds.

Questions for Exercise, in Reduction of Currencies.

1. Change 38£. 7s. 9d. Massachusetts currency, into dollars. Ans. 127D. 95cts. 8m. 24 rem. Attend to the rule, tables, &c. find the pence in a dollar Massachusetts currency, and proceed.

In all the States where the dollar is an even number of shillings, the learner may proceed according to the general rule, or the observation given after the examples for illustration.

2. Change 195 dollars 40 cts. into Massachusetts currency. Ans. 58£. 12s. 4d. 3qr. 20 rem.

3. Change 249 dolls. 33 cts. into New York currency.

Ans. 99£. 14s. 7d. 2qrs. 72 rem.

4. Change 21£. 7s. 4d. Pennsylvania currency into Federal Ans. 56D. 97cts. 7 m. 70 rem.

money.

5. Change 160 dolls. 40 cts. into Georgia currency.

Ans. 37£. 8s. 6d. 1qr. 60 rem.

6. Change 430 dolls. 21 cts. into Canada currency.

Ans. 107£. 11s. Od. 2qrs. 40 rem.

7. Change 19£ 17s. 4d. English or Sterling money into dollars. Ans. 88D. 29cts. 6m. 16 rem.

8. Change 49£. 14s. 5d. Irish money into dollars.

Ans. 203D. 98cts. 2m. 106 rem.

Reduce the sum to half pence, likewise the dollar into 9. Change 16£. 18s. 4d. North Carolina currency into dolAns. 42D. 29cts. 1m. 64 rem.

lars.

སྐམ་

THE SINGLE RULE OF THREE DIRECT.

The learner has now passed through the rules necessary for an introduction to the Rule of Three. I hope he has been attentive, and thereby prepared to enter this useful rule.

THE RULE OF THREE DIRECT

Teacheth, by having three numbers given to find a fourth in such proportion to the third, as the second is to the first; for this reason, it is termed the rule of proportion, but most generally the rule of three, from its having three numbers given. It is sometimes called the golden rule, owing to its great and extensive usefulness in arithmetic.

As you proceed, endeavour to understand every part of the rule. Pay strict attention, it will save you much trouble.

Observe 1. Of the three numbers, or terms given, two of them are of the same name or kind, and one of these must be the first number, or term in stating, and the other the third; the remaining number, which is the second term in stating, is always of the same name or kind with the answer or thing sought.

2. The first and second terms are a supposition, the last a dem

1. Place the number which you want to find the value of, for the third term.

2. Place the one which is of the same name or kind of the third, for the first term.

3. Place the remaining one, which is of the same name or kind with the answer, for the second term.

If there be a difficulty in determining which the first and third terms are, it may be removed by reading the question, and finding which term is the demand, or the one you want to find the value of; for this must be the third term, and the other of the same name or kind, the first;* consequently, the other, or remaining one, which is of the same kind with the answer, must be the second.†

Note. When the first or third term, or both, consist of different names or denominations, (which is often the case,) they must be reduced to the lowest denomination mentioned in either. That is, if the first term is pence, the third term must be pence likewise. If the third term be ounces, the first term must be ounces. If the second term be of different names or denominations it must be reduced to the lowest mentioned. After the statement is thus prepared, proceed by the following

Rule for Working the Question.

1. Multiply the second and third terms together, and divide the product by the first term. The quotient will be the answer to the question in the same name or denomination the second term was left in. This you must remember; for, by it, you can determine what name the answer has; and this answer may be brought into any denomination required.

2. If there be a remainder, after dividing by the first term. reduce it to the next denomination below the last quotient, and divide by the same divisor again; the quotient of this will be so many of the name you reduced it into. In this manner proceed, till you get the lowest, or least name required; and the different quotients will be the answer. Or, if the answer comes in a small name, as farthings, mills, ounces, &c. they can be

When the third term is money, the first must be money; when it is weight, the first must be weight; when it is measure, the first must be

measure.

When the answer is money, the second term must be money; when it is weight or measure, the second term must be weight or measure.

brought into the denomination required, by dividing, as taught in Reduction.

PROOF.

Change the order of the question, making the third term the first, and the answer the second, &c.

Note. The Rule of Three consists of two kinds: the Rule of Three Direct, and the Rule of Three Inverse.

THE RULE OF THREE DIRECT

More re

Is, when more requires more, or less requires less. quires more, is when the third term is greater than the first, and requires the fourth term, or answer, to be greater than the second; and less requires less, is when the third term is less than the first, and requires the fourth term, or answer, to be less than the second.

THE RULE OF THREE ÎNVERSE

More re

Is, when more requires less, or less requires more. quires less, is when the third term is greater than the first, and requires the fourth term or answer to be less than the second; and less requires more, is when the third term is less than the first, and requires the fourth term, or answer, to be less than the second.

Observe.--There are some methods of operation in direct proportion, when they can be used, perform the work in a shorter manner than the general rule, which are as follows:

1. Divide the second term by the first, multiply the quotient by the third term, and the product will be the answer.

2. Divide the third term by the first, multiply the quotient into the second, and the product will be the answer.

3. Divide the first term by the second, and the third term by that quotient, and the last quotient will be the answer.

4. Divide the first term by the third, and the second by that quotient, and the last quotient will be the answer.

The following is another method of stating The Single Rule of Three. It will apply to both Direct and Inverse proportion. Read from the commencement of the Single Rule of Three, to Obs. 1. as what is there given will apply to this method.

RULE FOR STATING THE QUESTION.

1. Place that number or term in the third place, which is of the same name or kind with the answer, or thing sought. 2. Then examine, and see whether, from the nature of the Bon, the answer is to be more than the third term. If place the greater of the two remaining terms in the

cond place, and the less one in the first place; if the answer be less than the third term, then place the less one for the second term, and the greater for the first.

When the first, or second term, or both, consist of differen denominations, (which is often the case,) they must be reduced to the lowest name or denomination mentioned in either; that is, if the first term be pence, the second term must be pence likewise; If the second term be ounces, the first term must be ounces; the third term, if of different names or denominations, must be reduced to the lowest name mentioned. After the question is thus prepared, proceed by the following

RULE FOR WORKING THE QUESTION.

1. As in the former method, multiply the second and third terms together, and divide that product by the first; the quotient will be the answer to the question in the same name or denomination you left the third term in; remember this; for, by it, you can determine what name your answer has, and this answer may be brought into any denomination required.

2. If there be a remainder after dividing by the first term, reduce it to the next denomination below the last quotient, and divide by the same divisor again; the quotient of this will be so many of the name you reduced it into; in this manner proceed till you get the lowest or least name required, and the different quotients will be the answer; or, if the answer comes in a small name, as farthings, mills, ounces, &c. you can bring them into the denomination required by dividing as taught in Reduction.