THE

SCHOLAR'S ARITHMETIC.

OBSERVATIONS.

THE Scholar has now surveyed the ground work of Arithmetic. It has before been intimated that the only way in which numbers can be affected, is by the operations of Addition, Subtraction, Multiplication and Division. These rules have now been taught him, and the exercises in a supplement to each, suggest their use and application to the purposes and concerns of life. Further, the thing needful, and that which distinguishes the Arithmetician, is to know how to proceed by application of these four rules to the solution of any arithmetical question. To afford the scholar this knowledge is the object of all succeeding rules.

SECTION II.

RULES ESSENTIALLY NECESSARY FOR EVERY PERSON TO FIT AND QUALIFY THEM FOR THE TRANSACTION OF BUSINESS.

These are ten: Reduction, Fractions,* Federal Money, Exchange, Interest, Compound Multiplication, Compound Division, Single Rule of Three, Double Rule of Three, and Practice.

A thorough knowledge of these rules is sufficient for every ordinary occurrence in life. Short of this a person in any kind of business will be liable to repeated embarrassments. It is the extreme usefulness of these

rules which commends them to the attention of every Scholar.

* FRACTIONS are taken up here no further than is necessary to shew their signification, and to illustrate the principles of FEDERAL MONEY.

i

1. REDUCTION.

"REDUCTION teaches to bring or exchange numbers of one denom"ination to others of different denominations, retaining the same value.”

IT IS OF TWO KINDS.

1. When high denominations are to be brought into lower, as pounds into shillings, pence and farthings; it is then called Reduction descenDING, and is performed by Multiplication.

2. When lower denominations are to be brought into higher, as farthings into pence, or into pence, shillings and pounds; it is then called REDUCTION ASCENDING, and is performed by Division.

REDUCTION DESCENDING.

RULE.

MULTIPLY the highest denomination by that number which it takes of the next less to make one of that greater; so continue to do till you have brought it as low as your question requires.

PROOF" Change the order of the question, and divide your last product by the last multiplier, and so on."

EXAMPLES.

1 In £17 13s. 6d. 3qrs. how many farthings?

OPERATION.

3

£. S. d. grs.
17 13 6
20 Shillings in a pound.

3 5 3 Shillings in £17 13s.
1 2 Pence in a Shilling.

In this example, the highest denom ination is pounds, the next less, is shillings, and because 20 shillings make one pound, therefore, I multiply £17 by 20, increasing the product by the addition of the given shillings (13) which it must be remembered, must always be done in like cases; 4 Farthings in a penny. then because 12 pence make one shilling, I multiply the shillings (353) by A. 1 6 9 7 1 Farthings. 12, adding in the given pence (6d.) lastly, because 4 farthings make one penny, I multiply the pence (4242) by 4, and add in the given farthings (3qrs.) I then find that in £17 13s. 6d. Sqrs. there are 16971 farthings.

4 2 4 2 Pence in £17 13s. 6d.

PROOF.

4) 1 6 9 7 1 3qrs.

12) 4 2 4 2 6d.

210) 3 53 13s.
£17

To prove the above question, change the order of it, and it will stand thus: in 16971 farthings, how many pounds?

Divide the last product by the last multiplier the remainder will be farthings. Proceed in

this way till all the steps of the operation have been retraced back; the last quotient with the remainders will be proof of the accuracy of the operation if they agree with the sum given in the question.

་

REDUCTION ASCENDING.

RULE.

Divide the lowest denomination given by that number which it takes of the same to make one of the next higher, and so continue to do till you have brought it into the denomination which your, question requires.