Let the following numbers be written in figures: *—

1. Twenty-nine.

2. Four hundred and seven.

3. Twenty-three thousand and seven.

4. Five millions and twenty-seven.

5. Seven millions, two hundred five thousand and five. 6. Two billions, two hundred seven millions, six hundred four thousand and nine.

7. One hundred five billions, nine hundred nine millions, three hundred eight thousand two hundred and one.

8. Nine quintillions, eight billions and forty-six.

9. Fifteen quintillions, thirty-one millions and seventeen. 10. Five hundred seven septillions, two hundred three trillions, fifty-seven millions and eighteen.

11. Nine nonillions, forty-seven trillions, seven billions, two millions, three hundred ninety-two.

12. Fifteen duodecillions, ten trillions, one hundred twentyseven billions, twenty-six millions, three hundred twenty thou sand four hundred twenty-six.

To express numbers by figures, begin at the left hand with the highest order mentioned, and, proceeding to units, write in each successive order the figure which denotes the given number in that order. If any of the intervening orders are not mentioned in the given number, supply their places with ciphers.

SECTION II.

ADDITION.

ADDITION is the collecting of numbers to find their sum.

1. A man has three farms; the first contains 378 acres, the second 586 acres, and the third 168 acres. How many acres are there in the three farms?

OPERATION
Acres,

378

586

168

In this question, the units are first added, and their sum is found to be 22; in 22 units there are two tens and two units. The two units are written under the column of units, and the 2 (tens) are carried to be added with the tens, which are found to amount to 23 tens= 2 hundreds and 3 tens. The 3 is written under the column of tens, and the 2 (hundreds) is carried to the column of the hundreds, which amount to 11=1 thousand 1 hundred. The whole of which is set down. Hence the propriety of the following

1132

RULE.

Write units under units, tens under tens, &c. Then begin at the bottom and add the units upwards, and, if the amount be less than ten set it down under the column of units; but if the amount be ten or more write down the unit figure, and add the figure denoting the number of tens to the column of tens. Thus proceed, till every column of figures is added, writing down on the left the sum total of the left.. hand column, and the result will be the sum of the whole as required.

PROOF.

Begin at the top and add all the columns downwards, in the same manner as they were before added upwards; then, if the two sums agree, the work may be presumed to be correct.

789037

901234 965887 567890 445566 891133 987654 788743 477666 321178 667679 321032 399378 557788 123456 998889 765437 456789 888878 789561 671236

456789

888888

987654

444444

45. Add the following numbers, 763, 4663, 37, 49763, 6178, and 671.

Ans. 62075. 46. A butcher sold to A 369 lbs. of beef, to B 169 lbs., to C 861 lbs., to D 901 lbs., to E 71 lbs., and to F 8716 lbs. ; what did they all receive? Ans. 11087 lbs.

47. A owes to one creditor 596 dollars, to another 3961, to another 581, to another 6116, to another 469, to another 506, to another 69381, and to another 1261. What does he owe them all? Ans. $82871. 48. If a boy earn 17 cents a day, how much will he earn in 7 days? Ans. 119 cts. 49. If a man's wages be 19 dollars per month, what are they per year? Ans. $228. 50. If a boy receive a present every New Year's day of 1783 dollars, how much money will he possess, when he is 21 years old? Ans. $37443.

51. How many inhabitants were there in Essex county, Mass., In 1840, Haverhill having 4336, Amesbury 2471, Andover 5207, Beverly 4689, Bradford 2222, Boxford 942, Danvers 5020, Essex 1450, Georgetown 1540, Gloucester 6350, Hamilton 818,

Ipswich 3000, Lynn 9369, Lynnfield 707, Manchester 1355, Marblehead 5575, Methuen 2251, Middleton 657, Newbury 3789, Newburyport 7161, Rockport 2650, Rowley 1203, Salem 15082, Salisbury 2739, Saugus 1098, Topsfield 1059, Wenham 689, West Newbury 1560? Ans. 94,989.

52. How many were the members of Congress in 1846, there being 2 Senators from each State, and Maine sending 7 Representatives, New Hampshire 4, Massachusetts 10, Rhode Island 2, Connecticut 4, Vermont 4, New York 34, New Jersey 5, Pennsylvania 24, Delaware 1, Maryland 6, Virginia 15, North Carolina 9, South Carolina 7, Georgia 8, Alabama 7, Mississippi 4, Louisiana 4, Tennessee 11, Kentucky 10, Ohio 21, Indiana 10, Illinois 7, Missouri 5, Arkansas 1, Michigan 3, Florida 1, Texas 2 ?

Ans. 282.

53. According to the census of 1840, Maine had 501,793 in habitants, New Hampshire 284,574, Massachusetts 737,699, Rhode Island 108,830, Connecticut 309,978, Vermont 291,948. New York 2.428,921, New Jersey 373,306, Pennsylvania 1,724,033, Delaware 78,085, Maryland 469,232, District of Columbia 43,712, Virginia 1,239,797, North Carolina 753,419, South Carolina 594,398, Georgia 691,392, Kentucky 779,828, Tennessee 829,210, Ohio 1,519,467, Indiana 685,866, Mississippi 375,651, Missouri 383,702, Illinois 476,183, Louisiana 352,411, Alabama 590,756, Michigan 212,267, Arkansas 97,574, Florida 54,477, Wisconsin 30,945, Iowa 43,112, and on board U. S. vessels 6,100. What was the whole number of inhabitants? Ans. 17,068,666.

SECTION III.

SUBTRACTION.

SUBTRACTION teaches to find the difference between two numbers by taking the less from the greater.

OPERATION. In this question, we take 3 units from 5 units From 935 and 2 units remain, which we write down under Take 673 units, as the first figure in the answer. In at262 tempting to take the 7 tens from 3 tens we find a difficulty, as 7 cannot be taken from 3. We therefore borrow 1 (hundred) from the 9 (hundred), which being equal to 10 tens, we add it to the 3 tens in the upper line, making 13 tens; from which we take 7 tens, and 6 tens re