SECTION II.

ADDITION.

ART. 16. Ex. 1. Henry paid 4 shillings for a pair of gloves, 7 shillings for a cap, and 2 shillings for a knife: how many shillings did he pay for all?

Solution.-4 shillings and 7 shillings are 11 shillings, and 2 shillings are 13 shillings. He therefore paid 13 shillings for all.

OBS. The preceding operation consists in finding a single number which is equal to the several given numbers united together, and is called Addition. Hence,

17. ADDITION is the process of uniting two or more numbers in one sum.

The answer, or number obtained by addition, is called the sum or amount.

OBS. When the numbers to be added are all of the same kind, or denomination, the operation is called Simple Addition.

18. Sign of Addition (+). The sign of addition is a perpendicular cross (+), called plus, and shows that the numbers between which it is placed, are to be added together. Thus, the expression 6+8, signifies that 6 is to be added to 8. It is read, " 6 plus 8," or "6 added to 8."

Note.-The term plus, is a Latin word, orignally signifying "more." In Arithmetic, it means "added to."

QUEST.-17. What is addition? What is the answer called? Obs. When the numbers to be added are all of the same denomination, what is the operation called? 18. What is the sign of addition? What does it show? Note. What is the meaning of the word plus?

19. Sign of Equality (=). The sign of equality is two horizontal lines (=), and shows that the numbers between which it is placed, are equal to each other. Thus, the expression 4+3=7, denotes that 4 added to 3 are equal to 7. It is read, "4 plus 3 equal 7," or of 4 plus 3 is equal to 7." 18+5=7+16.

ADDITION TABLE.

66

the sum

Note. It is an interesting and profitable exercise for young pupils to recite tables in concert. But it will not do to depend upon this method alone. It is indispensable for every scholar who desires to De accurate either in arithmetic or business, to have the common

QUEST.-19. What is the sign of equality? What does it show?

2

arithmetica tab es distinctly and indelibly fixed in his mind. Hence, after a taule has been repeated by the class in concert, or individ◄ ually, the teacher should ask many promiscuous questions, to prevent its being recited mechanically, from a knowledge of the regular increase of numbers.

EXAMPLES.

20. When the sum of a column does not exceed 9. Ex. 1. George gave 37 cents for his Arithmetic, and 42 cents for his Reader: how many cents did he give for both?

Operation.

units.

co tens.

3 7 price of Arith. 4 2 66 of Read.

Directions.-Write the numbers under each other, so that units may stand under units, tens under tens, and draw a line beneath them. Then, beginning at the right hand or units, add each column separately in the following manner:2 units and 7 units are 9 units. place under the column added. 4 tens and 3 tens are Write the 7 in tens' place. The amount is 79

7 tens.

cents.

7 9 Ans.

Write the 9 in units

Write the following examples upon the slate or blackboard, and find the sum of each in a similar manner:

10. What is the sum of 4321 and 2475 ?

11. What is the sum of 32562 and 56214? 12. What is the sum of 521063 and 465725?

21. When the sum of a column exceeds 9.

13. A merchant sold a quantity of flour for 458 dollars, a quantity of tea for 887 dollars, and sugar for 689 dollars how much did he receive for all?

Operation. 458 price of flour.

887

of tea.

66 of sugar.

689

2034 dollars. Ans.

Having written the numbers as before, we proceed thus: 9 units and 7 units are 16 units, and 8 are 24 units, or we may simply say 9`and 7 are 16, and 8 are 24. Now 24 is equal to 2 tens and 4 units. We therefore set the 4 units or right hand figure in units' place, because they are units; and reserving the 2 tens or left hand figure in the mind, add it to the column of tens because it is tens. Thus, 2 (which was reserved) and 8 are 10, and 8 are 18, and 5 are 23. Set the 3 or right hand figure under the column added, and reserving the 2 or left hand figure in the mind, add it to the column of hundreds, because it is hundreds. Thus, 2 (which was reserved) and 6 are 8, and 8 are 16, and 4 are 20. Set the O or right hand figure under the column added; and since there is no other column to be added, write the 2 in thousands' place, because it is thousands.

N. B. The pupil must remember, in all cases, to set down the whole sum of the last or left hand column.

22. The process of reserving the tens or left hand figure, when the sum of a column exceeds 9, and adding it mentally to the next column, is called carrying tens.

Find the sum of each of the following examples in a similar manner:

23. From the preceding illustrations and principles we derive the following

GENERAL RULE FOR ADDITION.

I. Write the numbers to be added under each other, so that units may stand under units, tens under tens, &c.

II. Beginning at the right hand, add each column separately, and if the sum of a column does not exceed 9, write it under the column added. But if the sum of a column exceeds 9, write the units' figure under the column and carry the tens to the next column.

III. Proceed in this manner through all the orders, and finally set down the whole sum of the last or left hand column.

24. PROOF.-Beginning at the top, add each column downward, and if the second result is the same as the first, the work is supposed to be right.

9. What is the sum of 46 inches and 38 inches?

QUEST.-23. How do you write numbers for addition? When the sum of a column does not exceed 9, how proceed? When it exceeds 9, how proceed? 22. What is meant by carrying the tens? What do you do with the sum of the last column? 24. How is addition proved?