16. From 1728 dollars, I paid 961 remain ?

dollars; how many Ans. 767 dollars.

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

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.

3

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

22

23 24

42 44

46 48

3

6

9 12 15

18 21 24 27 30 33 36 39 42 45 48 51

51

571 60 63 66 69 72

4

8 12 16 20

241 28 32 36 40 44 48 52 56

60

64

68

72

76 80 84 88 92 96

Section 4.

MULTIPLICATION.

TABLE OF PYTHAGORAS.

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 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126|132|138|144
7 14 21 29 351 42 49 56 63 70 77 84 91| 98|105|112|119|126|133|140|147|154|161|168|
8 16 24 32 40 48 56 721 80 881 96 104 112 120 128 136 144 152|160|168|176|184|192|
91 18 27 36 45 51 63 81 90 99 108 117 126 135 144 153 162 171|180|189|198 207|216||
10 20 30 40 50 60 70 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|108 120 132|144|156|168|180|192|204|216|228|240|252|261|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|210 224 238 252 266 280 294 308 322 336
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|170 187|204 221 238 255 272 289 306|323|340 357 374 391|408|
18 36 54 72 90 108|126|144|162 180 198|216 234 252 270 288 306 324 342 360 378 396|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 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480
21 42 63 84105|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|220 242 264 286 308 330 352 374 396 418 440 462 484 506 528
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 96 120|144|168|192|216|240 264 288|312|336 360 384 408 432 456 480 504 528 5521576

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?

per acre

6. What cost 9 acres of land at 10 dollars ? 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 1 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?

19. A gallon of molasses is worth 25 cents, what is the value of 2 gallons? Of 3 gallons? Of 4 gallons? Of 5 gallons? Of 6 gallons?

20. What cost 4 quarts of milk at 5 cents a quart? and 8 gallons of vinegar at 10 cents a gallon?

21. If a man earn 7 dollars a week, how much will he earn in 3 weeks? In 4 weeks? In 5 weeks? In 6 weeks? In 7 weeks? In 9 weeks?

22. If one thousand feet of boards cost 12 dollars, what cost 4 thousand? 5 thousand? 6 thousand? 7 thousand? 12 thousand ?

23. In 1 pound there are 20 shillings, how many shillings in 3 pounds? In 4 pounds? In 6 pounds? In 9 pounds?

24. If 3 pair of shoes buy 1 pair of boots, how many pair of shoes will it take to buy 7 pair of boots ?

25. If 5 bushels of apples buy 1 barrel of flour, how many bushels of apples are equal in value to 12 barrels of flour?

The foregoing questions having been performed, it will be perceived, that

MULTIPLICATION is a compendious way of performing Addition, and that it consists of three parts; the multiplicand, or number to be multiplied; the multiplier, or number to multiply by; and the result, which is called the product.

The pupil, having thoroughly committed the multiplication Table, will notice the following

RULE.

Place the larger number uppermost, and then set the multiplier under it, so that units may be under units, &c., and multiply by the multiplier, beginning at the unit's place and carry for tens as in addition.

When the multiplier consists of more places than one, multiply each figure in the multiplicand by every figure in the multiplier, beginning with the units, and placing the first figure of each product directly under its multiplier, then add all their several products together in the same order, as they stand, and their sum will be the true product required.

When there are ciphers between the significant figures of the multipliers, omit them, and multiply by the significant figures only.

If there be ciphers at the right hand of the multiplier or multiplicand, they may be neglected in the operation, but their number must be affixed to the product.

PROOF.

Multiplication may be proved by division, or by multiplying the multiplier by the multiplicand, as in 12th and 13th questions, or by casting out the 9's, thus; cast the 9's from the multiplicand and place the remainder at the right hand of a cross, then cast the 9's from the multiplier and set the remainder at the left hand of the cross, then cast the 9's from the product, and set the remainder at the top of the cross. Multiply the numbers together on each side of the cross, and cast the 9's from their product, and if the remainder be like the number at the top of the cross, it may be presumed the work is right. See question 14.