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ARITHMETIC.

THAT every young woman should have a knowledge of the art of computing by numbers, is indispensable, if she would fit herself for some of the most useful employments of life. Indeed, without an acquaintance with the first principles of this science, she must forego many of the advantages and pleasures which others enjoy, and be exposed to the mistakes of the ignorant, or submit to the imposiLions of the designing. Its utility is id fact so general, that there is no situation in which females can be placed where the benefits to be derived from it will not be evident.

The following narrative is given as a striking instance, illustrative of the necessity of being acquainted with the art of computation.

A poor farmer had sold a certain number of cattle, at so much per head, and being unacquainted with arithmetic, relied on the calculation of the buyer, and was about to receive the amount; when the farmer's daughter, a little girl; the mother of whoin he had often reproved for giving her so much“ larning," as he called it, happened to pick up the paper containing the price and number, which her father had

accidentally dropped ; and, either in the hope of amusement, or to see if the sum was right, unknown to her

parents she made ihe calculation herself, and found a deficiency in the amount of upwards of twenty pounds ; which, without this timely inspection of the child, the father must certainly have lost.

In the following system the professed object is simplicity. The rules will appear so plain and easy that it is unnecessary to perplex the learner with prolix directions ; and as females are seldom called upon to practise as deep skilled accountants, it will not be advisable to go beyond the rudiments, of this most useful science.

NUMERATION.

NUMERATION is the art of expressing properly and methodically any proposed number by figures. Thus the whole series are described : 1, 2, 3, 4,

5, 6, 7, 8, 9. One, two, three, four, five, six, seven, eight, nine.

Another character formed by the letter 0, is called a cipher, signifying, when alone, nothing, but when joined to another figure it adds tenfold to its original value, thus : 10, 20, SO, 40,

40, 50, 60, 70, 80, 90. Ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety. Other ciphers added, still increase it tenfold, thus : 100, - 1,000,

200,000, 1,000,000. One hundred, one thousand, 2 hundred thousand, one million.

1

The value of any number may be known by 'learning the following Table, which must be read from right to left, beginning with No. 1, calling it units.

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tens of thousands only of millions.

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thousands.
thousands.
hundreds.

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The figures together in one sum, thus, 10,987,654,321, would read or be called as follows, ten thousand, nine hundred eighty seven millions, six hundred fifty-four thousand, three hundred and twenty one.

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The Roman figures, called numerals, are I. II. III. IV. V. VI. VII. VIII. IX. X. L. C. D. M. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 50, 100, 500,1000,

ADDITION. Addition is the next step, which is the art of collecting many given numbers into one, and of expressing the amount correctly. It is either simple or compound; simple when it relates only to figures, and compound when those figures have a reference to value, measure, &c. Thus in simple ad. dilion the following examples will serve as specimens.

EXAMPLES No. 1. No. 2.

No. 3.

No. 4. No. 5. 13 247 4379 5674301

10 47 958 5643

4210: 100 59 421

7524

* 34765 1000 90 650 6000

4000 47 700

4760

761

20 196 2376 28306

5714078 5190 In casting up these sums begin with the column of units on the right. Thus, in No. 1, say 7 and 9 are 16, and 7 are 23, and 3 are 26;-then as there are 6 units and two tens over, place the 6 under the column of units, and carry 2 to that of the tens, and proceed thus; 2 and 4 are 6, and 3 are 9, and 5 are 14, and 4 are 18, and I are 19; which being the whole, place the 9 under the column of tens, it being 9 tens'; and the i being 100 place next to it on the left. Thus the whole will be, one hundred and ninety six. This general rule will serve for all the others, carrying all the lens in one column to the other throughout the whole.

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COMPOUND ADDITION.

Before the learner proceeds in this part of Arithmetic, as it will be to money accounts chiefly to which she will wish to direct her atiention, it is absolutely necessary to learn perfectly, the following Tables.-Note, a farthing, being one fourth of a penny, is written thus, i ; a haltpenny thus, t; ebree farthings thus, t

4 Farthings make One Penny. 12 Pence

One Shilling.
20 Shillings

One Pound
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PENCE. 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

5 6 7 8 9 10 10 ji 12 13 14 15 15 16

2

0 - 10

8 6 4 2

0 . 10

8

S.

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S.

EXAMPLES. Note, the Column with an £. signifies Pounds, s. Shil. lings, and d. Pence. No. 1. No. 2.

No. 3.

No. 4.
d.
S. d.

d. £. d. 0 41 0 3 1

32 4 7 0 31 2 ay

0 3 6 653 2 64 0 73 S 4 6 7 9

475 7 2 0 5 2 7 1 4 2

45 6 7 0 64 15 9

5 3 4

2 3 2

3} 2

24 £ Pi 4 6 £14 1 1 #1208 4 1

S.

Thus, in the first example, begin with the farthings, and say :- 1 and 3 are 4, and 2 are 6, and į are 7; which being 1 penny and 3 farthings write $ underneath, and carry 1 to the pence: then 1 and 6 are 7, and 5 are 12, and 7 are 19, and 3 are 22, and 4 are 26; then 26 pence being 2 shillings and twopence over, place 2 under the column of pence and 2 under that of shillings; the whole şum making, iwo shillings and twopence three farthings, In order to prove any sum in addition, cast it up again the reverse way, namely, from the top to the bottom.

The other examples must be performed in the same manDer, taking care to carry one pound for every 20 shillings, and one for every 10 in the pounds, as in simple addition.

Compound Addition also includes Weights and Measures, but it is thought proper not to perplex the learner with them in this early stage of her progress, though a correct table will be given of them in the course of the work, which may be referred to as occasion may require. It is necessary however to observe here, that all sums in weights and measures are cast up in the same way as pounds, shillings and pence; with this difference only; the proper number must be carried to each line, for example, as

60 Minutes make 1 Hour
24 Hours

1 Day
7 Days

1 Week We may compose a suin thus :

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From the minutes every 60 is carried as 1 to the hours, and the remainder set down; from the next every 24; and from the last every 7; so that the above sum is 2 weeks, 1 day, 19 hours, and 23 miņutes,

SUBTRACTION. This rule teaches the art of taking one number from another in order to find what remains.

EXAMPLES

COMPOUND NUMBERS.
SIMPLE NUMBERS.

No. 3.

No. 4.
No. 1. No. 2.

d.

. From 9876 45321 23 6 4 423

£. S.

6 7 take 367 34510

12 3 24

25 12 9 Rem. 9509 10811 11 3

It £397 13 10

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