SIMPLE ADDITION.

§ 32.-1. Addition consists in collecting several numbers into a single number, embracing the units, tens, hundreds, thousands, &c., of the several numbers.

2. The number obtained by adding several numbers together, is called the amount.

3. The addition of two or more numbers into one, is expressed by the sign +, called plus. The addition of 5, 19, and 8, is thus expressed: 5+19+8; and when added, the work is thus expressed: 5+19+8=32.. This operation is thus read: 5 plus 19 are 24, and 24 plus 8 are 32. (§ 20.)

4. Only numbers expressing things of the same kind, can be joined together, so as to form but one number. If 7 represents a number of apples, and 8 a number of oranges, when added, their sum will express neither apples nor oranges; for, while it will be composed of 15 units, (1 ten and 5 units,) 7 of these units will still be apples, and 8 oranges. When two such numbers are joined, their sum simply expresses the number of objects, without any regard to their kind.

RULE FOR ADDITION.

Write the several numbers with units standing under units, tens under tens, hundreds under hundreds, &c., and add the several columns of figures separately, commencing with the right hand. In adding the units, if they amount to more than 10, add the 10s to the column of 10s, setting down the units only; in adding the column of 10s, add the 10s of that column to the column of 100s; and in adding the column of hundreds, add the

32. In what does addition consist? What does the number obtained contain? What is the number obtained called? How is addition expressed? What is the sign called? How is an operation read? What numbers can be added? Illustrate. When such. num bers are joined, what does their sum express? How write numbers for addition? How add the several columns? If the units amount to more than 10, what is done? What, if the tens amount to more than 10 And the hundreds to more than 10? &c. How write down the amount of each column? How write down the unit figure of each column?

10s to the column of 1000s; and so on, to the left-hand column, of which write down the whole amount.

NOTE. The unit figure of the amount of each column must be written down at the foot of the column, and that one only; except at the left-hand column, where the whole amount must be written down.

§ 33. What is the amount of 2543, 4285, 6456, and 3523?

∞ &Thou.

CA&G Hund.

Cr∞ Tens.

Units.

4285

6456

3523 16807

I first write down these numbers with units under units, tens under tens, hundreds under hundreds, &c., placing units first on the right, with tens next to units, hundreds next to tens, thousands next to hundreds, &c. I first add the column of units, and find that the figures of that column amount to 17-1 ten and 7 units. The 7 units I write down, and add the 1 ten to the column of tens. I next add the column of tens, and find that with the 1 ten brought from the column of units, it amounts to 20 tens, and as this makes just 2 hundred, and no remainder, I write down a cipher at the foot of the column of tens, and add 2 to the column of hundreds. Then adding the column of hundreds, I find it amounts to 18, including the 2 brought from the column of tens. Writing down the 8, I add the 1 ten=1 thousand, to the column of thousands, and adding that column, find the amount to be 16, the whole of which I write down, this being the last left-hand column.

§ 34.-1. By carefully studying the above example and its explanation, the nature of addition will be clearly understood. Each column it will be observed, is added separately, and the right-hand figure of the amount written down, while its left-hand figure is added to the next column. This is the invariable mode of procedure with each column but the last; of this the whole amount is written down.

33. How write down the numbers? Which column add first? Which figure of the 17 write down, and which carry forward to the next column? The column of tens amounts to 20, which figure write down, and which carry forward? &c.

34. How is each column added? Which figure of the amount written down? What is done with the left-hand figure? Of which col umn is the whole amount written down?

2. The following exercise will familiarize the scholar with writing down the several amounts of the columns he adds up.

3. If a column of figures amounts to 17, which figure do you write down, and which add to the next column? Which write down, and which carry forward when the figures of a column amount to 25? to 33? to 18? to 47 ? to 59 to 27? to 35 to 46? to 54? to 63? to 71? to 89? to 54? to 96 to 84? to 66? to 28? If the whole amount of a column be only 7, what is done? if it be 3? if it be 5? if 7? if 6? if 4? if 9? if any figure of units only? Which is written down and which carried forward to the next column, if a column amounts to 50 to 60 ? to 87 to 96 to 83 ? to 90 ? to 95? to 76? to 84? to 79? The scholar will now proceed to add the following sums :

§ 35. The following sums are to be added in the usual manner, and also by couplets, triplets, &c., as indicated by the brackets. The amounts of the first addition by couplets, triplets, &c., are again to be added in the same manner, till the whole amount is expressed in a single sum. The two results may then be compared, and if the work has been rightly performed, they will be found exactly to correspond. The object of the following sums is to secure extensive exercise in adding.

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