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4. A CERTAIN man sold a lot of land for .735 11 6; he received at one time .61 5: at another time, £195 13 11: how much is there yet due ? Ans. 478 12 7.

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THE

SCHOLAR'S ARITHMETIC.

OBSERVATIONS.

THE

HE 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 nine: REDUCTION, FRACTIONS*, FEDERAL MONEY, 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 everf Scholar.

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

H

§ 1. Reduction,

"REDUCTION teaches to bring or exchange numbers of one denomination "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.

II. 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 Sqrs, how many farthings?

OPERATION.

S. d. grs.

17 1 3 6 3

20 Shillings in a pound.

In this example, the highest, denomination 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 4 2 4 2 Pence in£17 13s.6d. done in like cases; then, because 12 4 Farthings in a penny.pence make one shilling, I multiply the

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

Ans. 1 6 9 7 1

Farthings.

shillings, (353) by 12, adding in the giv en 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. 3grs. there are 16971 farthings..

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