30. How many are 17 less 1?
17 less 7? 17 less 8? 17 less 12?
31. How many are 18 less 2?

17 less 3?

17 less 5?

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 7? 19 less 9? 19 less 16 ?

19 less 5?

33. How many are 20 less

5?

20 less 8?

20 less 9 ?

30 less 15?

20 less 12? 20 less 15? 20 less 19 ?

34. How many are 30 less 5? 30 less 10? 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.

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

OPERATION.

From 624
Take 342

282

In this question, we take the 2 units from 4 units and 2 units remain, which we write down under units, as the first figure in the answer. 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 62. This process is called borrowing and carrying. Hence the following

RULE.

Place the less number under the greater; units under units, tens under tens, &c. 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.

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

Ans. 767 dollars. 1776; how many of the last war, Ans. 39 years.

in

17. Independence was declared in years from this period to the close 1815? 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.

Section 4.

MULTIPLICATION.

TABLE OF PYTHAGORAS.

2

3

2 4 6

30

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 3 6 9 12| 15 18 21 24 27

331 36 39 42 45 48 51

66

54 57 60 63 69 72
4 8 12 16 20| 24| 28| 32| 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120
6 12 18 24 30 361 42 48| 54| 60| 66| 72 78 84 90 96|102|108|114|120|126|132|138|144|
140147
7 14 21 28 35 42 49 56 63 70| 77 84 91 98105|112|119|126|133|140|147|154|161 168
8 16 24 32 40 48 56 64 72 80 88 96|104|112|120|128|136|144 152|160 168|176|184|192|
9 18 27 36 45 51 63 72 81 90 99|108|117|126|135|144|153|162 171|180 189 198 207 216
10 20 30 40 50 60 70 80 90 100|110|120|130 140 150 160 170 180 190 200 210 220 230 240
11 22 33 44 55 66 77 88| 99|110|121|132 143 154 165 176 187 198|209 220 231 242 253 264
12 24 36 48 60 72 84 96 108 120132, 144|156| 168 | 180|192|204 216 228 240 252|264|276|288|
13 26 39 52 65 78| 91|104|117|130|143|156|169|182|195|208|221 234 247 260 273|286|299|312||
14 28 42 56 70 84 98|112|126|140|154|168 182 196|210|224|238|252|266|250 294 308 322 336
15 30 45 60 75| 90|105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360
16 32 48 64 80|96|112|128|144|160|176|192|208 224 240 256 272 288 304 320 336 352 368 384
17 34 51 68 85|102|119|136|153|170|187204|221 238 255 272, 289|06|323 340 357, 374 391 408
18 36 54 72| 90|108|126|144|162 180 198 216|234|252|270|283|306|324|342|360|378|396|414|432
19 38 57 76 95 114 133 152 171 190 209 228 247 266 285|304|323|342|361|380 399 418 437 456|
20 40 60 80|100|120|140 160 180 200 220 240 260 28000 320 340 360 380 400 420 440 460 480
21 421 63 84|105|126|147|168|189|210|231 252 273|294 315 336 357 378 399 420 441 462 483 504
22 44 66 88|110|132|154|176 198 220 242 264 286 308 330 352 374 296 418 440 462 4841506 528
23 46 69 92|115|138 161|1841207|230|253|276 299|322|345|368|391|414|437 460 483 506 529|552
24 48 72 961120|144|168|192|216 240 264 288 312 336 360 384 408 432 456 480 504, 528 552 576

MENTAL OPERATIONS.

1. What cost three bushels of wheat at three dollars per bushel?

2. What cost 5 barrels of flour at 6 dollars per barrel? 3. What cost 6 bushels of beans at 2 dollars per bushel? 4. What cost 5 quarts of cherries at 7 cents per quart? 5. What will 7 gallons of vinegar cost at 12 cents per quart?

6. What cost 9 acres of land at 10 dollars per acre? 7. If a pint of currants cost 4 cents, what cost 9 quarts? 8. If, in 1 penny, there are 4 farthings, how many in 9 pence ? In 7 pence ? In 8 pence ? In 4 pence ? In 3 pence ?

.

9. If 12 pence make a shilling, how many pence in 3 shillings In 5 shillings? In 7 shillings? In 9 shillings? 10. If 4 pecks make a bushel, how many pecks in 2 bushels? In 3 bushels? In 4 bushels? In 6 bushels ? In 7 bushels? In 9 bushels ?

11. If 12 inches make 1 foot, how many inches in 3 feet? In 4 feet? In 5 feet? In 7 feet? In 8 feet? In 9 feet? In 10 feet? In 12 feet?

12. If there be 9 feet in a square yard, how many feet in 4 yards? In 5 yards? In 6 yards? In 8 yards? In 9 yards? In 12 yards?

13. What cost 3 yards of cloth at 5 dollars per yard? 4 yards? 5 yards? 6 yards? 7 yards? 8 yards? 9 yards? 10 yards? 11 yards? 12 yards? 20 yards? 14. If I pound of iron cost 7 cents, what cost 2 pounds? 3 pounds? 5 pounds? 6 pounds? 7 pounds? 8 pounds? 9 pounds? 12 pounds?

15. If 1 pound of raisins cost 6 cents, what cost 4 pounds? 5 pounds? 6 pounds? 7 pounds? 8 pounds? 9 pounds? 10 pounds? 12 pounds?

16. In 1 acre there are 4 roods, how many roods in 2 acres? In 3 acres? In 4 acres? In 5 acres? In 6 acres? In 9 acres?

17. A good pair of boots is worth 5 dollars; what must I give for 5 pair? For 6 pair? For 7 pair? For 8 pair? 18. A cord of good walnut wood may be obtained for 8 dollars; what must I give for 4 cords? For 6 cords? For 9 cords?