METHOD OF READING THE TABLE.

8. Commencing at the unit's place on the right hand we say, first place units; then looking towards the left we proceed thus: second place tens; third place hundreds; fourth place thousands; fifth place tens of thousands; sixth place hundreds of thousands ; seventh place millions; eighth place tens of millions; ninth place hundreds of millions, &c.

The Table should also be read from left to right, and from any place towards the right and left, until the pupil can readily name the value attached to each place.

The figures in the Table are grouped into periods by means of loops or brackets, each period containing three figures. The periods are named units, thousands, millions, &c., from the value of the first place in each group. They are read from right to left: first period units; second period thousands; third period millions.

Let us substitute other figures for those in the Table, and not insert the names of the periods; thus :

How many units are expressed in the above line? How many hundreds? Tens? Tens of thousands? Thousands? Millions? Hundreds of thousands?

Hundreds.

Tens.

Units.

What figure expresses thousands? Millions? Tens of thousands? Tens of millions? Hundreds of thousands?

In what period does the 8 stand? The 7? The 9? The 3? What is the value of the 8? The 7? The 9? The 3? The 2?

How much greater in value is the 7 than the 5? The 3 than the 6?

Again, let us substitute other figures, and not insert the names of the places or the brackets, but mark off the periods with commas; thus:

422,876,547.

What is the value of a figure in the Fourth place? In the Third? Seventh? Fifth? Ninth? Sixth? Eighth?

In the above line what figure stands in the thousand's place? In the hundred's? The hundreds of thousand's?

What does 5 express in the above line? What does 8? 2? 6? 4?

In what place should the figure 1 be put to represent a thousand? A hundred? A hundred thousand? A million? Ten thousand? Ten million?

How many ciphers must be put on the right of the figure 1 to represent a hundred? Ten thousand? One thousand? One hundred thousand? Ten millions? One million ?

How many ciphers must be placed by the side of the figure 6 to make it six thousand? 10, to make it ten thousand? 10, to make it one hundred thousand? 21, to make it two hundred and ten thousand? 100, to make it a million? Make 8 with 9 represent eight hundred and nine. 5 with 8, to express five thousand and eighty. 3 with 7, to express three thousand seven hundred.

A number has four figures in it, and another has three; which number is the greater?

A number has five nines in it, and another has six ones; which number is the greater?

A number has six nines in it, and another has the figure 1 with six ciphers to the right of it; which number is the greater?

What is the value of the 28 in the upper line? Of 84? 57? 45?

What is the value of the 4th and 5th figures in the second line? Of the 5th and 6th? The 7th and 8th?

We may now proceed to Exercises in Notation and Numeration.

A

11

ELEMENTARY PRINCIPLES OF

ARITHMETIC.

ADDITION.

9. Suppose you had 3 oranges, and 2 more were given to you; you would then have 5.

If these figures were written upon a slate or black board, they would read thus:

3 and 2 are 5,

which means that 3 has been increased by 2, and the result is 5.

Now the method of putting numbers together, or adding them, is called ADDITION, and the number which is as large as all the numbers together is called their sum: thus, in the above line, where 3 and 2 are taken together, 5 is called their sum.

SUBTRACTION.

10. If you had 7 apples, and you gave away 5, you would then have 2. These figures being written down, they would read thus:

From 7 take 5, and 2 remains ;

which means, that if from 7 you take 5 away, 2 will be left.

The method of taking one number from another is called SUBTRACTION; and when a less number is taken from a greater, that number which is left is called the remainder or difference; thus, in the line where 7 has been made less by 5, 2 which is left, is called the remainder, or difference.

MULTIPLICATION.

11. Suppose you received 4 oranges, then 4 more, and then 4 more; you would then have 12. Writing down these figures, they would read thus:

4 and 4 and 4, are 12;

which means, that 3 fours added together make 12. If we know how many times the same number is to be added, we can proceed by a shorter way than by writing it down several times as above. For instance, in the above line, since 4 is to be taken 3 times, we can at once say, 3 fours make 12, or 3 times 4 are 12.

Now, the method of finding that number which results from repeating the same number several times is called MULTIPLICATION, which is only a short way of doing Addition.

The numbers multiplied are called factors, and the result is called the product. Thus, if 3 be taken 4 times, or 4 taken 3 times, the result is 12.

Here 3 and 4 are the factors, and 12 is their product.

DIVISION.

12. If you had 12 apples, and you wished to know how many times you could take 4 apples away from the 12. If you took away 4 apples, there would be