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Exercises to be performed on the slate.

1. Find the amount of 6 and 8.

6 units S units

14 Amount.

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

PROOF. In proving the work we commence adding at the top, by saying 6 and 8 are 14. Here we find the last amount to equal the 14 Amount. 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.

Addition is sometimes proved by crossing off the top line and adding the remaining lines; and if this last amount added 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.

tens

cr A units

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? 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.

50

6 6

17 5 D. Amount.

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 numhers; 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.

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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. Whole Estate, 7,500.

Ans.

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14. Four lads counting their Oranges, found that Joseph

had SO, 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 ?

Ans. 2431.

ADDITION OF DECIMALS.

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.

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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 frour the right hand of the amount, as many figures for decimals as are cqual 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 dollar, or $1, 16 cts. 3 mills.

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Ten in an inferiour denomination being equal to one in the next superiour, it is plain that we may add the same as in whole numbers.

4. Add 1 dollar, 65 cents and 3 mills, 5 dollars, 65 cents and 8 mills, 20 dollars, 8 cents and 4 mills, 14 dollars and 1 mill.

$cts. m.

1, 6 5 3
5, 658

20, 084
1 4, 0 0 1

$4 1, 3 9,

6

Care should be taken to supply ciphers in the place of vacant denominations, thus, 14 dollars and 1 mill must be written $14,00 cts. 1 mill.

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Ans.

Expressed in words, forty one dollars, thirty nine cents, six mills.

NOTE. Ciphers at the right hand of decimals, or in the place of decimals do not alter the value, therefore they may be omitted; thus, $5,00, is the same as $5.

5. Find the sum of 39 cents, 4 dimes, 5 dimes, 38 cents, 40 cents, 3 mills, 80 cents and 2 dimes.

cts. m.

,3 9 ,4 0

,5 0

,3 8

,4 0

,0 0 3

,8 0
,20

$3, 0 7 3

The student will perceive that every dime is ten cents, consequently 2 dimes make 20 cents; 3 dimes, 30 cents: 4 dimes 40 cents; &c. So for 2 dimes we write 20 cents, for 3 dimes, 30 cents, and for 4 dimes, 40 cents, &c.

6. What is the sum of 180 dols. 1 ct., 136. dols. 40 cts., 300 dols. 10 cts., 100 dols. 1 ct. 1 mill. 4 dols, and 2 mills?

Ans. $720,52,3

7. A man has 5 notes, viz: one of $36,75 cts., one of

$84,25 cts., one of $40,80 cts., one of $101,90 cts., and one of $40,11 cts. ; what is the amount of the notes ? Ans. $303,81 cts. 8. I received of A, B and C, the following sums; A paid me $140,50 cents, B $500,58 cents, C $1000; can you tell me how much I received from the three?

Ans. $1641,08 cts. 9. A paid me $300, B paid me $400, and C paid me as much as A and B both, what did they all pay me, and what did I receive from C?

$1400.

They all paid me I received of C $700. 10. A man has four farms, one is worth $2000, one $2560, one $1206 and one $5600; what is the worth of the four? Ans $11366.

NOTE. Where half (4) cents occur, it is evident that every two halves make a whole; you will then add one to the cents for every two halves; thus in the eleventh sum, we have 3 halves, that is, one cent and a half, so you will write down the half and add one to the cents.And it is also evident, where a half is given to find the whole, that the half twice repeated or added will equal the whole; one third, (3) three times repeated will equal the whole, and one fourth, (4) four times repeated will equal the whole.

11. Bought 5 gallons of molasses for $2,50 cts., 2 pounds of coffee.for 37 cts., 2 skeins of silk for 121 cts., 1 pound of tea for 371cts. ; how much did the whole cost me ?

Ans. $3,37 cts. 12. One half of a vesssl is worth fifteen hundred dollars; what is the whole worth? Ans. $3000. 13. One third of a man's estate is in land which is worth $2000; what is his whole estate? Ans. $6000. 14. If a man receive one thousand dollars for one quarter (1) of his property; what should he receive for the whole? Ans. $4000.

QUESTIONS ON SIMPLE ADDITION.

What is simple addition? A. Collecting several numbers in one.--What is the number called that arises from the operation of the work? A. Sum or amount. How do you place your numbers for adding A. Units under units, tens under tens, &c. Where do you commence adding? A. At the right hand. How do you proceed in the work? A. Add the right hand column, and write down the right hand figure of the amount under the column added, and add the left to the first figure of the next column; and so proceed through all the columns, remembering to set down the whole amount of the left hand column.

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