SIMPLE ADDITION,

Is collecting two or more numbers of the same denomination in one sum. The number arising from the operation of the work, is called the sum or amount.

RULE.

I. Write the numbers to be added, so that units may stand under units, tens under tens, hundreds under hundreds, &c. and draw a line under the whole.

II. Then add the right hand column, and if the sum be less than ten, write it directly under the column added, if it exceed ten, write down the right hand figure, and add the left hand figure or figures, to the first figure of the next column. Observe the same rule in all the left hand columns, setting down the whole amount of the last column. PROOF. Add the columns downwards, as you added upwards, and if the same amount is produced, the work is presumed to be right. Two parallel lines = denote equality; thus, 6 and 2-8, that is 6 and

2 are equal to 8.

=

For the sake of brevity, addition is often denoted by the following character, thus, 2+6 signifies the amount of 2 and 6, that is 2+ 6=8.

ADDITION TABLE.

2 and 1 are 313 and 9 are 125 and 5 are 1017 and 1 are 8

43

53

11 145

7

127

63

12

1551

74

99

84

89012

39

96

124

99

106

134

8

126

9

136

5

118

7

138

148

9

158

168

"

1234∞

6

7

8

15

16

3456

NOTE. 1st. To acqure a facility in adding, the student should carefully examine this table previous to his working sums. He will thereby render his task comparatively easy.

NOTE. 2d. To test the student's knowledge of the table, the teacher should question him on the table, occasionally varying the order, and sometimes mention the last of the two numbers to be added first.

FAMILIAR QUESTIONS.

NOTE. The student should be required mentally to answer each of these sums, directly after he has read the question.

1. John had 5 apples, and James gave him two more; how many had he after receiving the two from James?

2. Peter gave 4 shillings for a grammar, and 2 shillings for an English Reader; what did both cost him?

3. William has 5 peaches and Charles 4; how many have they both? How many then do five and four make?

4. George Washington served as President 8 years, and John Adams 4 years; how long did they both serve?

8

5. James Monroe served as President of the United States years, James Madison 8 years, and J. Q. Adams 4 years; how long did the three serve? How many then do 8 and 8 and 4 make?

6. Joseph paid 3 shillings for a slate, 5 shillings for an arithmetick, and 2 shillings for paper; how much did he pay out?

7. Henry was two days in learning addition, he learned subtraction in one, multiplication in two, and division in three; how long was he going over the four rules? How many are two, one, two and three?

8. Charles has 3 notes, one of 6 dollars, one of 8 dollars and 1 of 4 dollars; what is the amount of the three?

9. A man bought 8 bushels of wheat for 12 dollars, and cight bushels of corn for 6 dollars; how much did he pay for both? How many are 12 and 6?

10. A farmer paid 10 dollars for a plough, and five for a harrow; what did he pay for both?

Exercises to be performed on the slate.

1. Find the amount of 6 and 8.

6 units 8 units

Here we find the amount oy saying 8 anci 6 are 14. By adding 6 directly to eight we mount several steps at once, thereby saving the 14 Amount. trouble of adding unity to 8 six times, or of add ing unity to 6 eight times; for in both cases the amount is 14.

8

PROOF. In proving the work we commenc adding at the top, by saying 6 and 8 are 14 Here we find the last amount to equal the first: consequently the work is right according to our method of proof; and it is evident that it can make no difference whether we say 8 and 6 are 14, or 6 and 8 are 14.

14 Amount.

Addition is sometimes proved by crossing off the top line and adding the remaining lines; and if this last amount add ed to the top line, equal the first amount, the work is right; for this simple reason, that the sum of the parts must equal the whole, in whatever order they are put together.

2. Lent a friend at one time 14 dollars, at another 45, at another 50, and at another 66; how much is he in my debt?

4 5

50 66

1 7 5 D. Amount.

We first say 6 and 5 are 11, and 4 are 15, which is the amount of the first column; we then set down 5, the right hand figure of the amount, directly under the column added; and add 1, the left hand figure, to the first figure of the next column; by saying 1 and 6 are 7, and, 5 are 12, and 4 are 16, and 1 are 17, setting down the whole amount, it being the left hand column.

DEMONSTRATION.-Setting down the right hand figure, and adding the left to the next column, is what is called carrying the tens and setting down the units, for in adding the first column, we find the amount to be 15, which is 1 ten and 5 units; therefore we write down the 5 and add the 1 (which is 1 ten) to the column of tens.-The reason of this is plain, when we recollect, that in all simple numbers; ten at the right is equal to one next at the left.

NOTE.--We do not mention the cipher in adding; because it has no value in itself, and it would be useless to say 6 and 0 (a cipher) are 6.

7. A lady being asked how old she was, answered, she was 19 years old on the day of her wedding, and had been married 7 years; how old was she? Ans. 26 years.

8. The lesser of two numbers is 1600, their difference is 179; what is the greater number?

Ans. 1779.

9. George Washington was born A. D. 1732, and lived 67 years; in what year did he die ?

Ans. 1799.

10. America was discovered by Columbus 1492 years after the birth of our Saviour, and the deluge happened 2348 before his birth; how many years intervened?

Ans. 3840 years.

11. According to the census taken in 1820, the number of inhabitants in the several New England states was as follows: Maine 298,335; New Hampshire 244,161; Vermont 235,764; Massachusetts 523,287; Rhode Island 83,059 Connecticut 275,248; how many inhabitants did New England at that time number? Ans. 1,659,854.

12. A butcher bought four fat oxen; the first ox slaughtered weighed 1045 pounds, the second 20 pounds more than the first, the third 40 pounds more than the second, and the fourth 55 pounds more than the first; what was the weight of the four oxen? Ans. 4315 pounds.

13. A father having only two children, in making his will gave his daughter Maria three thousand dollars, and his son William fifteen hundred dollars more than Maria; what was William's portion, and what was the amount of the whole estate? ( William's portion $4,500.

Ans. Whole estate, 7,500.

14. Four lads counting their oranges, found that Joseph

had 80, Jacob 50 more than Joseph, George had 99, and Henry 2 more than George: how many had they all.

Ans. 410.

15. A gentleman paid four hundred dollars for a span of fine horses, three hundred for a carriage, and eighty for a set of harness; what did they all cost him? Ans, $780.

16. A merchant settling his accounts finds that he owes A, 80 dollars, B, $120, C, $150, and D, $480; how much does he owe in all? Ans. $830. 17. Maps and Globes were invented by Anaximander, 600 years before the birth of our Saviour; how long have they been in use up to the year 1831 ?

ADDITION OF DECIMALS.

Ans. 2431.

Decimal or Federal money, (which is the coin of the United States,) increases in a ten-fold proportion, and in simplicity is next to whole numbers. The rules, which you observed in adding whole numbers, are applicable here.

Place dollars under dollars, cents under cents, and mills under mills, (remembering to place a comma or separatrix directly after dollars,) and add the same as in whole numbers; then point off from the right hand of the amount, as many figures for decimals as are equal to the greatest number of decimal parts in any of the given numbers. Or place the separatrix directly below the decimal point in the numbers added. We usually express eagles and dollars, in dollars; and dimes, cents, and mills, in cents and mills; thus, 4 eagles, 6 dollars, 5 dimes, 6 cents and 2 mills, may be expressed 46 dollars 56 cents and 2 mills; or thus, $46, 56cts. 2m.

When you write dollars and cents only, if the cents be less than ten, place a cipher between the cents and dollars, thus, $4 and 6 cents must be written $4,06 cts.

A dollar is unity; dimes, cents and mills are, as the table of decimals expresses, tenths, hundredths, and thousandths; thus, $1, 1 dime, 6 cents and 3 mills, may be expressed $1 and 163 thousandths of a dol lar, or $1, 16 cts. 3 mills.