WRITTEN ARITHMETIC.

A.

NUMERATION.

LESSON I.

NUMERATION is the art of expressing the value

of numbers by words or characters.

B. For convenience, the value of numbers is usually expressed by characters called Figures, of which there are ten, thus: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

The first nine of these figures are called significant figures, because they signify, or express, some number, when standing alone.

C.-The cipher (0) is called insignificant, because it signifies nothing when standing alone. But, when the cipher stands at the right hand of a significant figure, it increases the value of that figure ten times. Thus, 4, when standing alone, means simply four units; but, if we place a cipher at the right of it, thus, 40,- we have forty units, or the number 40.

NOTE TO THE TEACHER. This should be fully illustrated on the black-board; the simple and local values of figures should also be explained.

D.-The following table will show the manner of numerating:

1. How many figures express Units? How many express Tens? Hundreds ? Thousands? Tens of

Thousands? Hundreds of Thousands?

Millions?

LESSON II.

A.-NUMERATE the following numbers and read

them; or write them in words on the slate.

B.-Express the following words in figures on the

slate:

1. Forty-five. One hundred and twenty-five. Four hundred and one. Five hundred and fifty-five. One thousand. One thousand and one. Four thousand two hundred and twenty-four. Seven thousand eight hundred and ninety-six. T'en thousand. Ten thousand and one. Twelve thousand and one hundred. Forty thousand. Forty thou and and seventy. Seventy-five thousand. Eighty thousand and fifty.

2. One hundred thousand. One hundred thousand and six. Four hundred thousand and seventy-two. Six hundred and forty-two thousand eight hundred and

sixty-one. One million.

One million. One million and seven.

Two

million four hundred and forty-six thousand five hundred

and sixty-eight.

ADDITION.

LESSON III.

A.-To add numbers mechanically, or to perform addition by means of the slate:

I. Write the given numbers under each other, so that units may be under units, tens under tens, &c., and draw a line beneath them.

II. Then add together the figures in the column of units; and if their sum be less than ten, write it under the units' column, but if the sum be ten or more, write down the unit figure under the column of units, and add, or carry, the tens to the column of tens.

III. Then add together the figures in the column of tens, and proceed as in the column of units; and so continue until all the columns are added, writing down the total amount of the last column.

B.-The following example will illustrate the method of performing Addition:

EXAMPLE.

948

123

476

Amount, 1547

EXPLANATION.

In performing this operation, we first add together the column of units, by saying, 6 and 3 are 9, and 8 are 17. In 17 there are 7 units, which we write under the column of units, and

1 ten, which we carry to the column of tens, saying, 1

and 7 are 8, and 2 are 10, and 4 are 14 (tens). The 4 (tens) we write under the column of tens, and the 1 (hundred) is carried to the column of hundreds; thus, 1 and 4 are 5, and 1 are 6, and 9 are 15 (hundreds), which we write down, and the work is finished.

PROOF. Commence at the top of each column, and add the numbers downward in the same manner as they were added upward, and if the two sums are alike, the work is supposed to be correct.

LESSON IV.

A.-WRITE on the slate, and add together, the fol

lowing numbers: