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9. Add .9%, .346, .1295, .00183, .8, and .98765.

10. Find the sum of 63, 848.75, .00059, 4.8627351, 131.627, 14.5948, .867459, and 8.5497. Ans. 1072.2522841. 11. How much is .6437+ 41.75 +296.8974 + .52 ? 12. 79 +5.931+.068597 +168.6694 +9.5046?

13. .54629.8347 + 83.99999 +2.3876 + 19.65 + 8.4 +31.8327 ?

14. 2.83+55.384 +109.4627+.55555+.88+7.66+ .934+.57?

15. Add the last four answers.

Ans. 928.912227.

16. Add the numbers in Exs. 14, 15, and 16, Art. 22. 17. Add the numbers in Exs. 11, 12, and 13, Art. 22. 18. Add $46.95, $198.73, $8.875, $29.478, and $0.45. 19. Add 30 dollars; 6 dollars, 19 cents, 5 mills; 98 cents, 2 mills; 427 dollars, 50 cents; 12 dollars, 3 mills; and 97 cents.

20. Find the sum of eleven dollars; five dollars, twentyone cents; eighty-six cents, seven mills; fourteen dollars, three mills; one dollar, one cent, one mill; twenty dollars, twenty cents. Ans. $52.291. 21. Add 3 tenths; 206 thousandths; 14 hundred-thousandths; 861 millionths; 65 hundredths; 9763 ten-thousandths. Ans. 2.133301.

22. Add four, and 7 hundredths; 99 ten-millionths; ninety, and 78642 millionths; two hundred and three, and 13 thousandths; 6849 hundred-thousandths; and 7 tenths.

23. Find the whole made up of the following parts: nine billionths; seven thousandths; eight tenths; nineteen hundredths; five hundred and seven millionths; eighty-six.

24. Required, the sum of five hundred and one trillionths; fifty-six hundred-millionths; eight, and seventeen billionths; seven thousand and forty-two ten-thousandths; and eight hundredths.

25. Add the last three ans. Ans. 393.711849486501.

ADDING TWO COLUMNS AT ONCE.

50. Two columns may be footed up at once, by adding each time first the right-hand and then the lefthand term successively reached, or adding both terms at once if no carrying is necessary.

Thus, in the accompanying Example: Forty-five, sixty-eight, seventy-five, one hundred and fifty-five, one hundred and sixty-one, one hundred and seventy-one (171); write down 71, and add 1 to the next column.

One, twenty-four, thirty, sixty, seventy-nine, eighty-two, ninety-two. Ans. 9271.

1316

1987

3623

2345

9271

51. Three columns may be footed up at once on the same principle, by adding first the right-hand, then the middle, and finally the left-hand term.

EXERCISE.

52. Add the following aloud, up and down, two columns at a time, naming results only:

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ADDING LEDGER COLUMNS.

53. Book-keeping is the art of keeping accounts, or recording mercantile transactions in a systematic manner, so as to show the condition of a business.

54. The principal book is the Ledger. This shows the results of all transactions, entered under distinct heads, called Accounts.

55. Each account has two sides, the left distinguished as DR., or Debtor,—the right as CR., or Creditor.

An entry on the left is called a Debit, on the right a Credit. The difference between the sum of the Debits and the sum of the Credits is called the Balance.

56. When an account has to be continued on a new page, the debits and credits are added separately, and their sums entered on their respective sides with the words Amount carried forward. These sums are then also written as the first items under the account on the new page, with the words Amount brought forward.

57. When adding long columns in a Ledger or other book of accounts, write the footing first in pencil or on a separate paper, and prove it before entering in ink, that there may be no necessity for erasures. 58. Foot up the following Ledger account:

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CHAPTER III.

SUBTRACTION.

59. Subtraction is the process of taking one number from another of the same kind, equal to or greater than itself.

60. The Subtrahend is the number to be subtracted. The Minuend is the number from which the subtrahend is to be taken. The Remainder, or Difference, is what is left after subtracting.

61. Subtraction is the converse of Addition. Addition, when certain parts are given, enables us to find their sum. Subtraction, when the sum and one of two parts are given, enables us to find the other part. Ex. From 1725 subtract 873.

A whole is equal to the sum of all its parts; hence the whole difference will equal the sum of the differences of the units, the tens, and the hundreds. For convenience' sake, we write the less number under the greater, placing figures of the same order in the same column.

3 units from 5 units leave 2 units. 7 tens from 2 tens can not be taken. Hence from the 7 hundreds we take 1, leaving 6 hundreds. 1 hundred is equal to 10 tens, which we add to the 2 tens, making 12. 7 tens from 12 tens leave 5 tens. 8 hundreds from 6 hundreds can not be taken; but 1 thousand 6 hundreds equal 16 hundreds. from 16 hundreds leave 8 hundreds.

8 hundreds

8 hundreds +5 tens +2 units=852 Ans. 62. In stead of taking 1 from the hundreds of the minuend, as was done above, it is more convenient to add 1 to the hundreds of the subtrahend; thus, 7 from 12, 5. 1 and 8 are 9; 9 from 17, 8. Answer, as before, 852. In this case we increase both minuend and subtrahend equally, the former by 10 tens, the latter by 1 hundred; and the result is not changed.

1725 873

Or,

hun. tens un.

16 12 5 873 8 52

Or,

hun. tens un.

17 12 5

9 73

8 52

This adding of 10 to the upper figure has been called Borrowing, and the adding of 1 to the next lower figure Carrying.

63. Subtraction of Decimals and Federal Money.Decimals, and Federal Money expressed decimally, are subtracted like abstract integers. Units being placed under units, tenths under tenths, etc., the decimal points of minuend, subtrahend, and remainder, will range in line perpendicularly.

Ex. From ten dollars subtract three cents.

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Write the subtrahend decimally under the minuend, with their decimal points in line. Write ciphers in the vacant places above the figures of the subtrahend.

Subtracting as in the last Example, we get 9 units, 9 tenths, 7 hundredths. Separate the tenths and hundredths from the units with the decimal point,—which, it will be seen, falls under the decimal points in the minuend and subtrahend.

$10.00 .03

Ans. $9.97

64. RULE FOR SUBTRACTION.-1. Write the less number under the greater, placing figures of the same order in the same column.

Beginning at the right, take each term of the subtrahend from the one above it, and write the remainder under the term subtracted.

If any lower term is greater than the one above it, add 10 to the upper term, subtract, and add 1 to the next lower term.

2. Subtract decimals, and federal money expressed decimally, like integers, and place the decimal point in the remainder under the points above.

65. Proof. The minuend is a whole, of which the remainder and subtrahend are the parts; it must, therefore, equal their sum. Hence, to prove subtraction, add

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