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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:

ans three-eighths. means five-eighths. means seven-eighths. means four-eighths, equal to one half. Sixteenths are likewise in common use, and we say,

is five sixteenths. 1 eleven sixteenths.
Is three sixteenths. fifteen sixteenths.

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1 2 3 4

5

12, or D

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TABLE. 1 LX

60 11 LXX

70 III LXXX

80 IV, or IIII XC

90 у с

190 VI 6 CI.

101 VII 7 CCC

300 VIII 8

500 IX 91°C, or DC

600 X. 10 13CCC, ni DCCC

800 XI 111CCCC, or DCCCC, or CM

900 XII 12 Cly, or M

1000 XIII 13 CIOC, or MC

1100 XIV MM, or II*

2000 15 XVI

5000 ..16 | 15 t, or V XVII 17 1ɔɔM, or VI

6000 XVIII

18

1ɔɔMMM, or VIII XIX

8000 19 XX. 20 CClɔɔ I, or X

10000 XXI

21
CCIɔɔM, or XI

11000 XXX.

30
I၁၁၁

50000 XL 40 1500MM .

52000 XLI 41 CCC13ɔɔM

101000 50 C15,17CCC, XI, or MDCCC,XI 1911 # 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 15, increases its value ten times:. thus [ɔɔ is 5000, and 1ɔɔɔ is fifty thousand.

I The prefixing C, and at the same time annexing a ) to the number CIC, makes its value ten times greater ; CCIp is 10,000, and CCClo5 is 100,000.

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ADDITION.

ADDITION teaches the method of finding the sum ortotal of several numbers.

RULE. (1.) Place the numbers under one another, som 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 lens, or if nothing remains, a cypher, and for the tens curry 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 contuired in it. †

Ex. 1. What is the sum of 368 4, 4863, 305, 29, 56874, and 609?

3684
4803
365

29
56874

609

Answer

664 24 is the sum total. PROF. Add the numbers togtther 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 exceed- ten, or any number of tens, we carry unit for every ten to the next column; for 9 being the highest digit, any number above it requires more thon one place to express ir, 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 know's 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, tha, 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 2
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 consisuing of three
figures each ; then wi i four figures, and so on till the whole nine figuras
are finished, and the table Icarnta

Ex. 19. 8

8

8

8

8

Ex. 20.9 Ex. 21. 24 Ex. 22. 56 Ex. 23. 84 Ex. 24. 25
9
35
65
33

56
9
64
74

29
28
48
86

88
9
74
82
39

64 9 19 98 45

77 45 33 20

25 35 66 31

66 64 59 99

33

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NOTE. * 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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