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methods at one view in the following

pler, and is generally adopted. We will exhibit the two

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How many do the English connect in a period? Which method is to be preferred? By the French method of numerating, how many figures are connected in a period?

periods of three figures, the following numbers: et him be required to numerate and read, by dividing into 7. After the pupil has carefully examined this table,

3478567321752005

1347835674116

75456278327005717

467743486921785412123456489

45654213400100205437

633456267489136545

3 Units.

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Let him also separate them into periods of six figures, According to the English method, and then numerate and read them.

It will be seen, by reference to the foregoing tables, nat the French and English methods of numeration agrce as far as nine places of figures, which is as far as we generally wish to extend numbers in the ordinary business operations of life. Numbers could be chosen which should be widely different, and still would be read precisely the same by the two methods. For instance, the French method of reading 103900000000000 is the same as the English method of reading 103000900000000000000, each reading being one hundred and three trillions, nine hundred billions.

The same is the case with infinite other numbers which might be selected. Hence the importance of knowing which system of numeration is employed. Twenty billions in the English system is a thousand times twenty billions in the French system.

ROMAN NOTATION.

8. The Romans, as well as many other nations, expressed numbers by certain letters of the alphabet. The Romans made use of only seven capital letters, viz.: I for one; V for five; X for ten; L for fifty; C for one hundred, D for five hundred; M for one thousand. The other num bers they expressed by various repetitions and combinations of these letters, as in the following

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By what means did the Romans express numbers? In this notation, how did re peating a letter affect the value which it represented? How was the value of a character affected when one of less value was placed before it? How when a char acter of less value was placed after it? How was the value affected by a bar draws ever it?

ADDITION OF SIMPLE NUMBERS.

9. SIMPLE ADDITION is putting together several numbers of the same kind or denomination.

The sum total which is obtained by adding several numbers together, is called the amount.

Before explaining the method of adding numbers, we will show the use of the two symbols, +.

The symbol, is called the sign of equality, and when placed between two quantities, it indicates that they are

equal. Thus $1=100 cents, implies that one dollar is equal to one hundred cents.

The symbol, is called the sign of addition, and when placed between two quantities, indicates that those quantities are to be added. Thus 3+4=7, denotes that the sum of 3 and 4 is equal to 7.

The symbol meaning more.

is generally read plus; a Latin word,

What is simple addition? What is the result obtained by adding several numbers together, called? Describe the symbol of equality. Describe that of addition.

By the assistance of these two symbols we may form the following

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Let the pupil be required to answer the following ques

tions:

4+3=how many?

2+5+1=how many ?

5+6+7+2=how many ?

8+9+2+1+7=how many ?

6+7+5+4+3+2=how many? 1+2+4+3+5+7+6=how many?

EXAMPLES.

1. Where the sums of the several columns are less than

ten ;

OPERATION.

Add together 2432, 3343 and 4122. Set the numbers under each other: units under units; tens under tens; hundreds under hundreds; thousands under thousands. Draw a line below the whole.

Add first, the column of units. Set the sum 7 under the column of units;

next add the tens; set the sum 9 under the column of tens-next add the hundreds; set the sum 8 under the column of hundreds. Lastly, add the thousands, and set the sum 9 under the column of thousands. The whole amount is, then, nine thousand eight hundred and ninety-seven.

Add 6264, 2532 and 1203.

Add 4132, 1001 and 1423.

Thousands.
Hundreds.

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431d

4

3

2 2

9 8

9 7

Ans. 9999.

Ans. 6556.

2. Where the sums of the several columns equal o exceed ten

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