§ 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 . 17 138. 6d Sqrs, how many farthings?

OPERATION.

8. d. grs.

7 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£17 138.6d. 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. Sqrs. there are 16971 farthings..

4) 69 71

12)4 2 4 2 3qrs.
210) 3 513 6d.

£17 13s.

PROOF.

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 remain. ders will be proof of the accuracy of the operation if they agree with the sum given in the ques

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 that denomination which your question requires.

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