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RITHMETIC is the art of computing by numbers. It has five principal rules for its operations, viz. numeration, addition, subtraction, multiplication, and division. NUMERATION.

N

UMERATION teaches to express numbers by figures, set down or named, and consists of two parts, viz. First, The right placing of them.

Second, The true valuing of each figure, in its proper place; both are exhibited in the following

which

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Nine figures are sufficient to express any number in common practice: Nevertheless, the following table may be thought necessary.

Nonillions

857342,

OЯillion's Septillions Sextillions Quintillions

4

1.62486, 345986, 437916, 423147, Trillions Billions 248016, 235421, 261734, 368149,

Quadrillions

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Millions Units

628137.

EXAMPLES.

In figures express the following numbers

One hundred and six

Five hundred and thirty-eight

Six thousand and seventy-four

Twelve thousand, five hundred and ten

Forty-five thousand, six hundred and one.

Two hundred fifty-one thousand, six hundred.

Eight million, one hundred forty-two thousand and six. -Sixty-five million, one hundred four thousand and ninety. Five hundred and two million, three hundred and four thousand

Nine hundred forty-eight million, six hundred thirty-two thousand, seven hundred and fifty-one

Numbers are also expressed by letters, and are called Numeral Letters, or Roman Numbers, thus:

1 2 3 4 5 6 7 8 9 10 I, II, III, IV, V, VI, VII, VIII, IX, X,

70

20 30

XX, XXX,

500 1000

40 50 60 80 90 100 XL, L, LX, LXX, LXXX, XC, ̊C, D, M,

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A letter of less value, standing before one of greater, diminishes, but when placed after, increases the value of the greater. Hence, by combining the above letters, other numbers are formed.

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SIMPLE ADDITION.

DDITION of integers is the collecting of several numbers, of like signification, into one sum; as 6 and 8 make 14.

RULE.

RULE.

Place units under units, tens under tens, &c. then begin at the right hand column and, add upwards, set down the total, if less than 10; if 10 or more, the right hand figure, and add the left to the next row of figures, which is carrying 1 for every 10; and so proceed to the last column, and there set down the whole of said column.

PROOF.

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Perform the addition downwards :-Or, Add the line to the sum of all the rest; and if right, the total will be equal to the first.

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Note.

In this, and fome fucceeding collections, the pupil may be directed to write the question on his flate, with vacancies, in which the tutor may infert other numbers.

Application.

1. Add 5856, 3840, 395, 265, 25, and three thousand seven hundred and eighty-four together.

facit 14e

2 A man was born in the year 1718, in what year

be 99 years of age?

answer in 1817 3 If a person have owing to him on bond 807/. in book accounts 10477. in bills and notes 861. and have in cash 478/. how much is the amount?

answer 24187. 4 Admit a bond to be 4687 dols. interest due thereon 178 dols. what is the amount?

answer 4865 dols. 5 Suppose 5784 dollars in one purse, 588 in another, 84 in a third, and seven hundred and seventy-nine in a fourth, what number is there in them all?

answer 7235 6 Admit a boy had 357 nuts given him at one time, 127 at another, 78 at another, 378 at another, 57 at another; how many had he in all?

answer 997

7 Suppose a person dying left his widow 3840d. to his eldest son 6850d, to two other sons each 2584d. to each of his three daughters 1685d. and in other legacies 950d. what is the sum of these bequests? answer 21863d.

8 A draper bought 10 bales of cloth, viz. No. 1, 2, each 367 yards; No. 3, 4, 5, each 407 yards; No. 6, 7, 8, each 228 yards; No. 9, 10, esch 300 yards; how many yards in the whole purchase? answer 3239 yards

9 A grocer bought 8 casks of indigo, viz. No. 1, 210. No. 2, 1966. No. 3, 4, 5, each 205lb. No. 6, 184lb. No. 7, 125/b. No. 8, 127416. how many lbs. in all? answer 2604/b.

10 A merchant bought 7 bales of cloth, in four of which were 52 pieces, which contained 1352 yards, the other 3 had 40 pieces, and contained 1098 yards; how many pieces and yards were there? answer 92 pieces, 2450 yards

11 If from the creation to the flood be 1650 years, from that to the calling of Abraham 427, from that to the building of the temple 909, thence to the founding of Rome 266, from that to the birth of Christ 752, and since to the present year 1820; how many years since the creation?

answer 5824 12 How many strokes does a regular clock strike in a week?

ansiver 1092

13 There are two numbers, the less is 9876, and their difference twice as many; what is the greater?

answer 29628 14 Borrowed a sum of money: paid at sundry times 89d. 196d. 226d. 327d. and the remainder to pay is 162d. what Was the sum borrowed?

answer 1000d.

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