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three farthings, shows that a penny is divided into four parts, the 3 determines the number of the parts, and we call it three-fourths of a

penny.

Inches are usually divided in eighths, or eight parts in each inch; and the fractional parts are thus expressed:

means three-eighths.

means seven-eighths.

means five-eighths.

means four-eighths, equal to one half.

Sixteenths are likewise in common use, and we say,

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* The word thousand is often expressed by a line drawn over the top of a number: thus X signifies ten thousand, and M a thousand thousands.

The annexing to the number 1, increases its value ten times: thus Ɔ is 5000, and ɔɔɔ is fifty thousand.

The prefixing C, and at the same time annexing a ɔ to the number CIC, makes its value ten times greater; CCɔɔ is 10,000, and CCCI၁၅) is 100,000.

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50000

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50 CCC, XI, or M,DCCC,XI

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1811

ADDITION.

ADDITION teaches the method of finding the sum or total of several numbers.

RULE. (1.) Place the numbers under one another, so that units may stand under units, tens under-tens, &c.

(2.) Add up the figures in the row of units: set down what remains above the even tens, or if nothing remains, a cypher, and for the tens carry as many ones to the next column.*

(3.) Add up the other rows in the same manner, and in the last column put down the whole sum contained in it. † Ex. 1. What is the sum of 3684, 4863, 365, 29, 56874, and 609?

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PROOF. Add the numbers together in a contrary order, beginning at the top instead of the bottom.

NOTES.

*Ten on the right-hand line is equal only to one, or unit, in the next line on the left of it, as we have seen in Numeration: when therefore the sum of any column amounts to, or exceeds ten, or any number of tens, we carry unit for every ten to the next column; for g being the highest digit, any number above it requires more thon one place to express it, which is done by removing the tens as so many units to the next place.

The following Table is thought by some persons to be proper to be committed to memory. The use of it may be easily explained to children of five years old, and when once learnt completely, no difficulty will be found in Addition; for if the pupil knows, at first thought, the sum of any two of the digits, the rest is easy: for instance, if he knows that 6 and 7 are thirteen, he will know that 36 and 7 are 43, because 5

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and 7 being 13, he knows there must be a three in the answer to the question of how many are 36 and 7, or 46 and 7, and so on,

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To use this table :-Take the greater of the two digits, whose sum is sought, in the upper line, and the lesser on the left-hand column; in the same line with this, and underneath the other, stands the sum sought. If I want to know the sum of 8 and 5, I look for 8 on the head line, and on the same row of figures with 5 on the left hand side stands 13, the sum.

This table may be converted into a SUBTRACTION TABLE, (see p. 12): and the use of it, in this way, is "To find the difference of any two numbers." Look for the largest number in the same line in which the least stands on the left hand column, and the difference will be found in. the head line over the largest number. Thus if I want the difference between 7 and 16, I look for 16 in the same line in which 7 stands, in the left hand column, and in the head line above the 16.I find 9, the difference sought.

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*This and the seven following sums may be rendered very useful
in shewing the pupil the foundation of the Multiplication Table; thus
he may be desired to take two or three rows of each of the eight sums
on his slate, and add them up, he will then see how three twos, or a
times 2 make 6; how three fours, or three times 4 make 12, and so of
the rest. When he has done the eight sums consisting of two figures,
he may be required to commi the results to memory, which will be
rendered a very easy business, when he sees the results before him on
the slate. Let him then proceed to the eight sums consisting of three
figures each; then with four figures, and so on till the whole nine figures
are finished, and the table learnt.

Ex. 20.9 Ex. 21. 24 Ex. 22. 56 Ex. 23. 87 Ex. 24. 25

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*The teacher may, from the three examples in p. 10, form for his

pupil an indefinite number, by desiring him to copy on his slate the

first three, or four, or five, or any other number of lines: or he may

desire him to take only a single column, or half a column, or the half

of two or of three columns, according to the progress 'he has already

made..

To make young persons ready and accurate in Addition, which is of

vast importance in almost every situation of life, the master may call a
class round him, who have the same sum on their slates, and desire them
to add each a figure till the sum is done; a place in the class to be lost
whenever there is a mistake or a pause. The sum neatest set down to
take precedence in the first instance.

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