26. Sir Isaac Newton was born in the year 1642, and he died in 1727; how old was he at the time of his decease?

Ans. 85 years.

27. Gunpowder was invented in the year 1330; how long was this before the invention of printing, which was in 1441 ? Ans. 111 years.

28. The mariners' compass was invented in Europe in the year 1302; how long was this before the discovery of America by Columbus, which happened in 1492 ?- Ans. 190 years.

29. What number is that, to which if 6956 be added, the sum will be one million? Ans. 993044.

30. A man bought an estate for seventeen thousand five hundred and sixty-five dollars, and sold it for twenty-nine thousand three hundred and seventy-five dollars. Did he gain or lose, and how much? Ans. $11810.

31. Bought a pair of oxen for 85 dollars, a horse for 126 dollars, three cows at 25 dollars apiece; and sold the whole for three hundred dollars; how much did I gain? Ans. $14. 32. Bonaparte was declared emperor in 1804; how many years is it since ? Ans. 32 years.

33. The union of the government of England and Scotland was in the year 1603; how long was it from this period to the time of the declaration of the independence of the United States ? Ans. 173 years. Titus in the year time of the first Ans. 1026 years.

34. Jerusalem was taken and destroyed by 70; how long was it from this period to the Crusade, which was in the year 1096.

SECTION IV.

MENTAL OPERATIONS IN MULTIPLICATION.

1. What will 2 oranges cost at 3 cents a piece? 2. What will 3 apples cost at 2 cents a piece?

3. What will 7 bushels of wheat cost at 2 dollars a bushel? 4. At 6 cents a quart, what will 5 quarts of cherries cost? 5. At 4 cents a pound, what will 3 pounds of raisins cost? 6. At 9 dollars per acre, what will 8 acres of land cost? 7. At 3 shillings a bushel, what will 9 bushels of oats cost? 8. At 5 shillings a bushel, what will 9 bushels of corn cost? 9. At 8 cents per yard, what will 5 yards of cloth cost? 10. What will 10 loads of hay cost at 9 dollars a load? 11. At 8 dollars per ton, what will 12 tons of lead cost? 12. At 7 dollars per box, what will 9 boxes of lemons cost? 13. What will 12 pounds of rice cost at 7 cents per pound? 14. What will 11 pounds of sugar cost at 9 cents a pound? 15. What will 6 pounds of pepper cost at 12 cents a pound? 16. What will 9 pounds of coffee cost at 11 cents a pound? 17. What will 10 pounds of mace cost at 11 cents a pound? 18. What will 8 yards of ribbon cost at 8 cents per yard? 19. What will 8 ounces of peppermint cost at 6 cents per oz.? 20. What will 7 pair of hose cost at 3 shillings a pair? 21. What will 6 papers of pins cost at 12 cents a paper ? 22. What will 11 cwt. of sugar cost at 9 dollars per hundred weight?

23. What will 7 yards of buckram cost at 12 cents per yard? 24. What will 10 oranges cost at 9 cents a piece?

25. What will 9 pair of boots cost at 4 dollars a pair?

26. What will 6 dozen of hoes cost at 11 dollars a dozen ?

27. What will 15 doz. of penknives cost at 8 dollars a dozen ?

28. What will 7 sheep cost at 5 dollars a piece?

29. What will 6 cwt. of copperas cost at 6 dollars a cwt.? 39. What will 25 oxen cost at 50 dollars each ?

31. What will 15 calves cost at 3 dollars each? 32. What cost 13 shad at 13 cents each?

33. At 20 dollars each, what cost 20 cows?

34. At 15 dollars each, what cost 14 bales of cloth?
35. At 25 dollars each, what cost 10 bureaus ?
36. At 15 cents per pound, what cost 9 lbs. of starch?
37. At 11 cents per oz., what cost 11 oz. of cloves?
38. What cost 6 lbs. of logwood at 9 cents per lb. ?
39. What cost 7 cwt. of iron at 8 dollars per cwt. ?

40. If one peck of meal weigh 15 lbs., what will 12 pecks weigh?

41. If a man travel 7 miles in one hour, how far will he travel in 5 hours? In 6? In 7? In 8? In 9? In 10? In 11?

42. If one pound of sugar cost 9 cents, what will be the cost of 4 lbs.? 5 lbs.? 6 lbs.? 7 lbs.? 8 lbs.? 9 lbs.? 10 lbs.? 11 lbs.? 43. If in 1 shilling there be 12 pence, how many pence in 5 shillings? In 6? In 7? In 8? In 9? In 10? In 11? In 12? 44. If in 1 mile there are 8 furlongs, how many furlongs in 3 miles? In 4? In 5? In 6? In 7? In 8? In 9? In 10? 45. If 12 oz. make a pound troy, how many ounces in 10 lbs. ? 46. If 5 quarters make one ell English, how many quarters in 7 ells English? In 8? In 9? In 10? In 12? In 14 ?

47. If there be 9 square feet in one square yard, how many square feet in 7 yards? In 8? In 9? In 10? In 11? In 12?

48. If there be 16 ounces in one pound avoirdupois, how many ounces in 5 lbs.? In 7? In 8? In 9 ? In 10? In 12?

Let the pupil perform the last 12 questions on the slate, and notice, that

MULTIPLICATION is a compendious way of performing Ad

dition.

It consists of three parts, the number to be multiplied or the multiplicand, the number to multiply by or multiplier, and the result or product, which is the answer to the question.

RULE.

Place the larger number uppermost, and then set the multiplier under it, so that units may be under units, &c., and multiply each figure in the multiplicand by the multiplier, beginning at the unit's place and carry for ten, 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 these several products together in the same order as they stand, and their sum will be the true product required.

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.

The regular way to prove questions in Multiplication is by Division ; but a more expeditious way is by casting out the 9's, thus; cast the 9's from the multiplicand and place the remainder at the right of a cross, then cast the 9's from the multiplier and place the remainder at the left of the cross; then cast the 9's from the product and set the remainder at the top of the cross. Multiply together the numbers on each side of the cross, and cast the '9s 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 Ex. 11.

TABLE OF PYTHAGORAS.

2

41

6 8

10

12

14

16

3 6

9

12

15 18 21

24

16 20 24 28

4 8 12
32 36 40
5 10 15 20 25 30 35 40 45 50
6 12 18 24 30

10 20 30 40 50 60 70 11 22 33 44 55 66

18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 44 48 52 56 60 64 68 72 76 80 84 88 92 96 55 60 65 70 75 80 85 90 95 100 105 110 115 120 36 42 48 54 60 66 72 78 84 90 96 102|108|114|120|126|132 138|144 7 14 21 28 35 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 64 72 80 88 96 104 112 120|128|136|144|152|160 168|176 184 192 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153|162 171|180 189|198|207|216| 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 77 88 99|110|121|132|143|154 165 176 187 198|209|220 231|242 253 264 84 96|108 120|132|144|156|168|180|192|204|216|228|240|252|264|276|288 78| 91 104 117 130 143 156| 169 182 195 208|221|234|247|260|273|286|299|312 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

12 24 36 48 60

13 26 39 52 65

14 28 42 56 70

72

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 21 421 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|308 330 352 374 296 418 440 462 484 506 528 231 46 69 921115 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|312 336 360 384 408 432 456 480 504 528 552 576|

123456789

740740784

16. Multiply 75432 by 47.
17. Multiply 76785316 by 7615.
18. Multiply 67853000 by 8765.
19. Multiply 38123450 by 31243.
20. Multiply 40670007 by 10002.
21. Multiply 31235678 by 10203.
22. Multiply 76786321 by 30070.
23. Multiply 317160070 by 700500.
24. Multiply 467325812 by 167000.
25. Multiply 6176777 by 22222.
26. Multiply 123456789 by 987654321.

Ans. 121932631112635269.

27. What will 27 oxen cost at 35 dollars each?

Ans. $945.

28. What will 365 acres of land cost at 73 dollars per acre?

Ans. $26645.

29. What will 97 tons of iron cost at 57 dollars a ton ?

Ans. $5529.

30. What will 397 yards of cloth cost at 7 dollars per yard? Ans. $2779.

31. What will 569 hogsheads of molasses cost at 37 dollars per hogshead? Ans. $21053. 32. If a man travel 37 miles in one day, how far will he travel in 365 days? Ans. 13505 miles. 33. If one quire of paper have 24 sheets, how many sheets are in a ream, which consists of 20 quires ? Ans. 480 sheets.