222. 221 yards of linen, at 221 cents a yard.
223. 27 bushels of apples, at 271⁄2 cents a bushel.
224. 321 bushels of oats, at 32 cents a bushel.
225. 371 acres of land at $37 an acre.
226. 421 pounds of tea, at 42 cents a pound.
227. 471 gallons of molasses, at 47 cents a gallon.
228. 521 days' work, at 52 cents a day.

229. 57 bushels of potatoes, at 572 cents bushel.
230. 621 yards of cloth, at 62 cents a yard.
231. 67 bushels of corn, at 671⁄2 cents a bushel.
232. 72 gallons of oil, at 72 cents a gallon.
233. 77 bushels of peaches, at 771 cents a bushel.
234. 82 pounds of indigo, at 82 cents a pound.
235. 873 bushels of wheat, at 871 cents a bushel.
236. 92 yards of satinet, at 92 cents a yard.
237. 972 acres of land at $971 an acre.

To square any number of nines, as 999, or 99999, &c.— Write from left to right as many nines, less one, as the given number contains, one 8, then as many ciphers, less one, as the given number contains nines, and lastly 1.

Thus, the square of

999=998001

9999-99980001

99999 9999800001

CONTRACTIONS IN MULTIPLICATION.

To multiply by any number of nines.-Annex as many ciphers to the right of the multiplicand as there are nines in the multiplier, and from this number subtract the multiplicand, the remainder will be the product required.

EXAMPLES.

1. Multiply 37645 by 9999.

376450000

37645

376412355

Here, by annexing four ciphers, the multiplicand is made ten thousand times larger, which is once the multiplicand too many, hence, by subtracting the multiplicand, we get the true product.

2. Multiply 47036 by 999. 3. Multiply 26475 by 9999.

4. Multiply 364364 by 99999.

Ans. 264723525.

To multiply by 25.-4 times 25 make 100; therefore annex two ciphers to the right of the multiplicand, and divide by 4, and you have the product.

To multiply by 125.-8 times 125 make 1000, therefore annex three ciphers to the right of the multiplicand and divide by 8.

EXAMPLES.

10. Multiply 3762 by 125.

8)3762000
470250

Ans. 4704625.

11. Multiply 6329 by 125. 12. Multiply 37637 by 125. 13. Multiply 57539 by 125. 14. Multiply 976351 by 125. 15. Multiply 713659 by 125.

To multiply by 11.-Add the figures of the multiplicand, after the first, from right to left.

EXAMPLES.

16. Multiply 37643 by 11. 414073.

Here we write down the 3, and then say, 3 and 4 are 7, then 4 and 6 are 10, put down the 0 and carry 1, then 6

and 7 and 1 to carry are 14, set down 4 and carry 1, then 7 and 3 are 10 and 1 to carry make 11, set down 1, and carry 1 to the 3 makes 4.

17. Multiply 79632 by 11. 18. Multiply 47896 by 11. 19. Multiply 316943 by 11. 20. Multiply 137823 by 11. 21. Multiply 789645 by 11.

Ans. 8686095.

To multiply by any number, from 12 to 20.-Multiply in regular succession, the figures of the multiplicand, by the unit figure of the multiplier, and add to the product of each multiplication that figure which stands next on the right-hand of the one which you multiply, and to the last figure add what you carry.

EXAMPLES.

22. Multiply 36435 by 13.

36435x13 473655

Here we say, 3 times 5 are 15, set down 5 and carry 1, then 3 times 3 are 9, and 1 to carry are 10, and 5 which stands on the right of the 3 make 15, set down 5 and carry 1, then 3 times 4 are 12, and 1 to carry, together with the 3 on the right of the 4 make 16, then 3 times 6 are 18, and 1 to carry, together with the 4 make 23, set down 3, and carry 2, then 3 times 3 are 9, and 2 to carry, together with the 6 on the right of the 3, make 17, set down 7, and carry 1 to 3, making 4.

23. Multiply 3792 by 14. 24. Multiply 37523 by 15. 25. Multiply 6579×16. 26. Multiply 7845×17.

27. Multiply 8732×18. 28. Multiply 2341×19. 29. Multiply 76374×13. 30. Multiply 56732×16.

To multiply by 21, 31, 41, 51, 61, 71, 81, and 91.— Write down the unit figure of the multiplicand, as the first figure of the product, then multiply in regular succession every figure of the multiplicand, by the left-hand figure of the multiplier, and to each product add the figure which stands

next on the left, and of that which you multiply, and you have the required product.

EXAMPLES.

31. Multiply 3725 by 21.

3725×21 78225

Here we set down the 5 and then multiply by the 2, thus, twice 5 are 10, and the 2 on the left of the 5 make 12, then twice 2 are 4 and 1 to carry, together with the 7 next on the left of the 2 make 12, then twice 7 are 14 and 1 to carry, together with the 3 on the left of the 7 make 18, then twice 3 are 6 and 1 to carry make 7.

Here we simply multiply by 7 and place the first product in the hundreds place, and then add the product to the multiplicand.

43. Multiply 3792 by 1007.

3792×1007

26544 3818544

Here observe that the multiplicand is made to

occupy the

SHIRTS of every Description MADE to MEASURE and FIT GUARANTEED

CONTRACTIONS IN MULTIPLICATION.

143

place of 1000, and the 7 being units its product must be placed 3 figures to the right.

44. Multiply 73496 by 9001.

73496×9001

661464

661537496

Here the only figure which it is necessary to multiply by is
the 9, which being thousands, the first product must be made
to occupy the place of thousands.
45. Multiply 5737 by 108.

46. Multiply 3796 by 801.
47. Multiply 49765 by 9001.
48. Multiply 63754 by 1009.
49. Multiply 38462 by 60001.

50. Multiply 39876 by 10006.
51. Multiply 74863 by 12001.
52. Multiply 97842 by 10012.
53. Multiply 54687 by 30001.
54. Multiply 45679 by 10003.
55. Multiply 79847 by 4001.
56. Multiply 49723 by 1004.
57. Multiply 64732 by 102.
58. Multiply 37475 by 201.
59. Multiply 4687 by 301.
60. Multiply 8643 by 103.

61. Multiply 3746 by 7, the product by 11, and the product of 11 again by 13.

3746

7

26222×11

288442 × 13

3749746

A better method, 3746×1001=(7×11×13)

3746 3749746

2. Multiply 26375 by 7, 11, and 13, as in the last ex

ample.