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691,392 ; in Alabama 590,756 ; in Mississippi 375,651 ; in Louisiana 352,411.

Ans. 4,597,824. 34. How many inhabitants in the Western States, there being in Tennessee 829,210 ; in Kentucky 779,828 ; in Ohio 1,519,467 ; in Indiana 685,866 ; in Illinois 476,183 ; in Missouri 383,702 ; in Arkansas 97,574 ; in Michigan 212,267 ?

Ans. 4,984,097. 35. How many inhabitants in the following Territories and the District of Columbia, there being in Florida 54,477 ; in Wisconsin 30,945 ; in Iowa 43,112 ; and in the District of Columbia 43,712 ? Ans. 172,246. 36. How many are the inhabitants of the United States, there being in New England 2,234,822 ; in the Middle States 5,073,577 ; in the Southern States 4,597,824 ; in the Western States 4,984,097 ; in the Territories 172,246 ?

Ans. 17,062,566.

Section 3.

SUBTRACTION.

MENTAL OPERATIONS.

1. James has three dollars, and John has two dollars ;

how many has James more than John ? 2. Thomas had five oranges, he gives two to John ; how many

has he left ? 3. Peter had six marbles, he gives two to Samuel ; how many has he left ? 4. Lydia had four cakes, having lost one ; how many

has she left ? 5. Daniel having eight cents, he gives three to Mary ;

how many has he left ? 6. Benjamin had ten nuts, he gives four to Jane, and

three to Emily ; how many has he left ? 7. Moses gives eleven oranges to John, and eight to

Enoch ; how many more has John than Enoch? 8. Agreed to labor for a man twelve days ? how many remain, after I have been with him five days ?

B*

9. I owed Thomas nine dollars, and having paid him seven ; how many remain due ? 10. From ten dollars, I paid four dollars and three dol

lars ; how much have I left ? 11. Timothy had eleven marbles, he lost seven; how many had he left ? 12. John is thirteen years old, and his brother Thomas

is seven ; how much older is John than Thomas ? 13. From 15 dollars, I paid five ; how many have I

left ? 14. Sold a barrel of flour for eight dollars, and a bushel of wheat for two dollars ; what was the difference in the prices ? 15. Paid seven dollars for a pair of boots, and two doltars for shoes ; how much did the boots cost more than the shoes ? 16. How many are 4 less 2 ? 4 less 1 ? 4 less 4 ? 17. How many are 4 less 3 ? 5 less 1 ? 5 less 5 ? 18. How many are 5 less 2 ? 5 less 3 ? 19. How many are 6 less 1 ? 6 less 2 ? 6 less 4 ? 6

less 5? 20. How many are 7 less 2 ? 7 less 3 ? 7 less 4 ? 7

less 6 ? 21. How many are 8 less 6 ? 8 less 5 ? 8 less 2 ?, 8

less 4 ? 8 less 1 ? 22. How many are 9 less 2 ? 9 less 4 ? 9 less 5 ? 9

less 7 ? 9 less 3 ? 23. How many are 10 less 8 ? 10 less 7 ? 10 less 5 ?

10 less 3 ? 10 less 1 ? 24. How many are 11 less 9 ? 11 less 7 ? 11 less 5 ?

11 less 3 ? 11 less 4 ? 25. How many are 12 less 10 ? 12 less 8 ? 12 less 6 ?

12 less 4 ? 12 less 7 ? 26. How many are 13 less 11 ? 13 less 10 ? 13 less 7 ?

13 less 9 ? 13 less 5 ? 27. How many are 14 less 11 ? 14 less 9 ? 14 less 8 ?

14 less 6 ? 14 less 7 ? 14 less 3 ? 28. How many are 15 less 2 ? 15 less 4 ? 15 less 5 ?

15 less 7 ? 15 less 9 ? 15 less 13 ? 29. How many are 16 less 3 ? 16 less 4 ? 16 less 7 16 less 9 ? 16 less 11 ? 16 less 15 ?

30. How many are 17 less 1 ? 17 less 3 ? 17 less 5 ?

17 less 7 ? 17 less 8 ? 17 less 12 ? 31. How many are 18 less 2 ? 18 less 4 ? 18 less 7 ?

18 less 8? 18 less 10 ? 18 less 12 ? 32. How many are 19 less 1 ? 19 less 3 ? 19 less 5 ?

19 less 7 ? 19 less 9? 19 less 16 ? 33. How many are 20 less 5 ? 20 less 8? 20 less 9 ?

20 less 12 ? 20 less 15 ? 20 less 19 ? 34. How many are 30 less 5 ? 30 less 10 ? 30 less 15 ?

30 less 20 ? 30 less 25 ? 35. Bought a horse for 63 dollars, and sold him for 70 ;

what did I gain? 36. Sold a barrel of flour for 8 dollars, which cost me

10 dollars ; what did I lose ? 37. John travels 25 miles a day, and Samuel 32 miles ?

what is the difference ? 38. I have 100 dollars, and after I shall have given 17 to Benjamin, and paid a debt of 30 dollars to J. Smith ; how many dollars have I left ?

The pupil, having performed the above, will perceive, that

SUBTRACTION teaches to take a less number from a greater, and to find the difference.

FOR THE SLATE,

OPERATION.

1. If I have 624 dollars and lose 342 of them, how many remain ?

In this question, we take the 2 From 6 24 units from 4 units and 2 units remain, Take 342 which we write down under units,

as the first figure in the answer. 282 In attempting to take the 4 tens, we

find a difficulty, as 4 cannot be taken from 2. We therefore borrow 1 (hundred) from the 6 (hundred), which being equal to 10 tens, we add it to the 2 tens in the upper line, making 12 tens, and 8 (tens) remain, which we set down. We then proceed to the hundreds. As we have borrowed 1 from the 6 hundreds, the 6 is too large by 1. We must, therefore, take the 3 from 5, and we find 2 (hundreds) remain, which we set down. Or because the 6 is too large by 1, we may add 1 to the 3 and say 4 from 6=2. This process is called borrowing and carrying. Hence the following

RULE.

Place the less number under the greater ; units under units, tens under tens, fc. Begin with the units; and, if the lower figure be smaller than the upper, take it therefrom, and write the difference below ; but, if the upper figure be less than the lower figure, add ten to the upper one, and place the difference between them under the units as before, and carry one to the next number at the bottom, and proceed thus, till all the numbers are subtracted.

Note. The upper line is called the Minuend, and the lower one the Subtrahend. The result of the question is called the Remainder.

PROOF.

Add the Remainder to the Subtrahend, and, if their sum be like the Minuend, the work is right.

[blocks in formation]

779

5 2819

From
Take

10.

Miles. 67895 19999

11.

Dollars.
4 5 6 7 98
190899

12.
Minutes.
765 3 2 1
177777

13. Seconds. 5 5 5 5 5 5 177777

14.

Rods.
From 100 200 300 400 500
Take 908 07 06 05 04 03 0

15.

Acres. 1000000000000 999999999999

in

16. From 1728 dollars, I paid 961 dollars ; how many remain ?

Ans. 767 dollars. 17. Independence was declared in 1776 ; how many years from this period to the close of the last war, 1815 ?

Ans. 39 years. 18. The last transit of Venus was 1769, and the next will be 1874, how many years will intervene ?

Ans. 105 years. 19. In 1830, the number of inhabitants in Bradford was 1856 ; and in 1840 it was 2222 ; what was the increase ?

Ans. 366. 20. How many more inhabitants are there in New York city than in Boston, there being, by the last census, 312,710 inhabitants in the former, and 93,383 in the latter city ?

Ans. 219,327 inhabitants. 21. In 1821 there were imported into the United States 21,273,659 pounds of coffee, and in 1839, 106,696,992 pounds ; what was the increase ?

Ans. 85,423,333 pounds. 22. By the last census, 11,853,507 bushels of wheat are raised in New York, and 13,029,756 bushels in Pennsylvania ; how many bushels in the latter State more than the former ?

Ans. 1,176,249 bushels. 23. The real estate of James Dow is valued at 3,769 dollars, and his personal estate at 2,648 dollars; he owes John Smith 1,728 dollars, and Job Tyler 1,161 dollars ; how much is J. Dow worth ? Ans. 3528 dollars. 24. If a man receive 5 dollars per day for labor, and it cost him 2 dollars per day to support his family ; what will he have accumulated at the close of one week ?

Ans. 18 dollars. 25. The city of New York owes 9,663,269 dollars, and Boston owes 1,698,232 dollars ; how much more does New York owe than Boston ?

Ans. 7,965,037 dollars. 26. From five hundred eighty-one thousand take three thousand and ninety-six.

Ans. 577,904. 27. E. Webster owns 6,765 acres of land, and he gave to his oldest brother 2,196 acres, and his uncle Rollins 1,981 acres ; how much has he left ?

Ans. 2,588 acres.

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