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ARITHMETIC.

Characters used in this Book.

1s. signifies that 12 penco are equal

ARITHMETIC is the art of computing and has five principal rules for its operation, tion, Addition, Subtraction, Multiplication, an

dition; as, 5+7=12, signifies that er, are equal to 12.

n of Şubtraction; as, 6–2=4, sigo d from 6, leaves 4.

the sign of Multiplication; as, at 4 multiplied by 3, is equal to 1.2

NUMERATION. Numeration is the art of numbering. It press the value of any proposed number hy characters, or figures :

1, 2, 3, 4, 5, 6, 7, 8, 9, 0-or ci Besides the simple value of figures, eac value, which depends upon the place it stan ngure in the place of units, represents only it: ar so many ones; but in the second place, or cecomes so many tens, or ten times its simple the third place, or place of hundreds, it becom times its simple value, and so on, as in the fol

*; as, 8=2=4, signifies that 8 die

4; or thus, £=4, each of which

e middle of four numbers, dengte

al to one another, by the rule of 16; that is, as 2 to 4, so is 8 to 16.

er, supposes that the square root of

Note.-Although a cipher standing alone signifies no Is placed on the right hand of figures, it increases their proportion, by throwing them into higher places. Thus, nexed to it, becomes 20, twenty, and with two ciphers, thus

2. When numbers consisting of many figures, are e will be found convenient to divide them into as many pe six figures each, reckoning from the right hand towards first the period of units, the second that of millions, the fourth trillions, &c. as in the following number :

8 07 3 6 2 5 4 6 2 7 8 9 0 1 2 5 4. Period of 3. Period of 2. . Period of Trillions. Billions.

Millions.

er, supposes the cube root of that

root, or fourth power,

&c.

8073
625462

789012 The foregoing number is read thus-Eight thousand trillions ; six hundred and twenty-five thousand, four two billions ; seven hundred and eighty-nine thousand a five hundred and six thousand seven hundred and ninet

N. B. Billions is substituted for millions of millior 'Trillions for millions of millions of millions. Quatrillions for millions of millions of millions of m

TABLE.

Millions,
Tens,
C. of Millions,
X. of Millions,
Units,
C. of Thousands,
Hundreds,
X. of Thousands,
Thousands,

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1 -One • 2 1 -Twenty-one. • 3 2 1 -Three hundred twenty-one. 1 4 3 2 1 -Four thousand 321. • 5 4 3 2 1 -Fifty-four thousand 321. 1 6 5 4 3 2 1 -654 thousand 321. • 7 6 5 4 3 2 1 -7 million 654 thousand 321. • 8 7 6 5 4 3 2 1 -87 million 654 thousand 321. 9.8 7 6 5 4 3 2 1 -987 million 654 thousand 321. 1 2 3 4 5 6 7 8 9 -123 million 456 thousand 789. 9 8 7 6 5 4 3 4 8 -987 million 654 thousand 348.

To know the value of any number of figures : RuLk.-1. Numerate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundreds, &c. as in the Numa ration Table.

2. To the simple value of each figure, join the name of its place, beginning at the left hand, and reading to the right.

EXAMPLES.
Read the following numbers.
365, Three hundred and sixty-five.
5461, Five thousand four hundred and sixty-one.

1234, One thousand two hundred and thirty-four.
54026, Fifty-four thousand and twenty-six.
123461, One hundred and twenty-three thousand four

hundred and sixty-one. 4666240, Four millions, six hundred and sixty-six thou

sand two hundred and forty. NOTE. For convenience in veading large numbers, they may be divided into periods of three figures each, as follows:

987, Nine hundred and eighty-seven.
987 000, Nine hundred and eighty-seven thousand.
987 000 000, Nine hundred and eighty-seven million.
387 654 321, Nine hundred and eighty-seven million, six

hundred and fifty-four thousand, three hun.
dred and twenty-one.

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BLE.

To write numbers. RULE.-Begin on the right hand, write units in the Jens in the tens place, hundreds in the hundreds plac luwards the left hand, writing each figure according to it in numeration ; taking care to supply those places a order with ciphers which are omitted in the question,

EXAMPLES.

Write down in proper figures the following
Thirty-six.
Two hundred and seventy-nine.
Thirty-seven thousand, five hundred and for
Nine millions, seventy-two thousand and two
Eight hundred millions, forty-four thousand a

ty-one.

hundred twenty-004 housand 321. four thousand 321. cousand 321.

on 654 thousand 321. ion 654 thousand 391. llion 654 thousand 321. llion 456 thousand 789. Ilion 654 thousand 348 ny number of figures : hi to the left hand, each figura s, hundreds, &c. as in the form igure, join the name of its plach ng to the right ES.

SIMPLE ADDITION. IS putting together several smaller numbers denomination, into one larger, equal to the v total; as 4 dollars and 6 dollars in one sum is

RULE.—Having placed units under units, tens under a line underneath, and begin with the units ; after a figure in that column, consider how many tens are co sum ; set down the remainder under the units, and ca you have tens, to the next column of tens; proceed in ner through every column or row, and set down the of the last row.

EXAMPLES, (1.) (2.)

(3.)

ng numbers.

sixty-five.
mindred and sixty-one

. ndred and thirty-four

. nd twenty-six

enty-three thausand four

e.

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dred and sixty-six thor forty.

20 Units.

o CG A Co er C. of Thous. 100 hoek or X. of Thous.

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4
2 9 1
8 5 1
1 5 2
6 98

1
0 4 3 2
9 4 7 8
1 6 6 6
7 4 2 2

Eighty-seven.

ding large numbers

, they figures each, as follows: ighty-seven thousand. ghty-seven million. ghty-seven million, siz I thousand, three hua

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To prove Addition, begin at the top of the sum, and

reckon the hgures downwards in the same manner as they were added up

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wards, and if it be right, this sum total will be equal to ti cut off the upper line of figures, and find the amount of th if the amount and upper line, when added, be equal to tl work is supposed to be right.

2. There is another method of proof, as follov

Reject or cast out the nines in each row or sum of figures, and set down the re 3 may mainders, each directly even with the figures 57 in its row ; find the sum of these remain- 87 ders; then if the excess of nines in the sum found as before, is equal to the excess 18 3 of nines in the suin total, the work is supposed to be right.

15. Add 8635, 2194, 7421, 5063, 2196, and gether.

Ans 16. Find the sum of 3482, 783645, 318, 9678045.

Ans. I 17. Find the sum total of 604, 4680, 98, 64,

Ans. Fifty-five 18. What is the sum total of 24674, 16742, 34 and 13439?

Ans. One hundred t 19. Add 1021, 3489, 28763, 289, and 6438,

Ans. Forty t 20. What is the sum total of the following n 2340, 1066, 3700, and 4005 ?

An
21. What is the sum total of the following ni
Nine hundred and forty-seven,
Seven thousand six hundred and five,
Forty-five thousand six hundred,
Three hundred and eleven thousand,
Nine millions, and twenty-five,
Fifty-two millions, and nine thousand ?

(12.) 3 7 1 8 4 5 6 87 51 1704 2 29 1 9 4 6 6 3 7 % 834073 270155 3 6 0 23

1 950

(14.)

2 5 900 340 0 4 5 5 40 4 4 3 3 370 5 5 3 2 6

4052174 4 0 64 762 6 9

2 0 68591

Answer,

22. Required the sum of the following numbe

Five hundred and sixty-eight,
Eight thousand eight hundred and five,
Seventy-nine thousand six hundred,

op of the sum, and reckor per as they were added up

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