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MULTIPLICATION.

McLTIPL1cation is a compendious kind of Addition, consisting of three terms, called Multiplicand, Multiplier, and Product. The first is the number given to be multiplied, the second that by which the work is performed, and the third the result of the operation or answer. × This sign, or a period, interposed between two numbers, shows that one is to be multiplied by the other; that is, the number contained in one, shall be expressed as often as there are units in the other. Thus, 5X4=20, or 5-4-20, shows that 5 is to be multiplied by 4; the product of which is 20. Here 5 is the multiplicand, 4 the multiplier, and 20 the product arising from the multiplication of those numbers. The multiplier and multiplicand are also called factors. Before the learner proceeds farther, it will be necessary that he shall commit to memory the following

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To multiply one number by another, both of which shall be of the same name or denomination, take the following

RULE.

Place the multiplicand, and multiplier, if they consist of significant figures, or have ciphers intermixed under each other, units under units, tens under tens, &c.; but if they have ciphers annexed to one or both, proceed in this manner with the other figures only; after which, annex the ciphers in their proper places, without regard to the former limitation.

Then commencing at the first right-hand significant figure of the multiplier, multiply every digit or figure of the multiplicand successively thereby, and set down the right-hand or unit's figure of each product, directly under the figure then multiplying, carrying the other figure as so many ones to the mext product in succession, and set down the entire of the last product, as is done with the sum of the last column in Addition.

Multiply, in like manner, by the next significant figure of the multiplier, taking care to put the first and each succeeding first figure of every product directly under the figure then multiplying, as before directed, placing each product in a line under the former; thus proceed, until all the figures in the multiplier are gone through, when there will or ought to be, as many rows of figures as there are significant figures in the multiplier; add up the several products, and annex to the sum as many ciphers (if there were any) as were at the right of the multiplier or multiplicand, or both, as the case may be, for the total product required.*

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Multiplication is proved by making the former multiplieand the multiplier, and multiplier multiplicand, and again performing the operation.

Crampleg. Multiply 416 504 896 by 6 7 8 2496 3528 71.68 6 7 8 416 504 896 36 28 48 6 35 72 24 - 64 Products as before 2496 3528 * 7168 Multiply 516 839 5408 by 54 69 1042 - 2064 7551 10816 - 2580 5034 21632 - - 5408 27864 57891 5635.136 54 69 1042 516 839 5408 324 621 8336 54 - - 207 41.68 270 552 5210 Products as before 27864 57891 5635.136 Or which is the same thing. 32142 624 32142 x 4 = 128568 128568 32142 x 20 = 642840 64284. 32142 x 600 = 19285200. 192852. . 32142 x 624 = 20056608

And it is evident whatever numbers or multipliers are employed, the same reasoning will apply. - ... for some time, the learner should annex the ciphers usually omitted,

which will render this matter perfectly plain.

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Multiply 7304600 or 6407.200
by 6407.200 by 7304600
146092 - 384432
511322 256288
292184 - 192216
'438276 448504 .
46802033120000 46802033120000
57. 7586080 x 6040 58. 604900 x 7090
59. 8190730 x 7050 60, 1819000 x 92070

61. 63509600 x 81050 62. 830600, x 380600 63. 58006700 × 578000 64. 960800 x 402700

To multiply by a unit, with ciphers annexed, as 10, 100, 1000, &c. Put down the multiplier, and annex thereto the ciphers, and it is done.

erumples.
Multiply 8478 by 10 - 7487 by 100
84780 - 748700

65. 47058 x 10 . 66. 431409 x 10
67. 84916 - 100 68. 93.65080 - 100
69. 496.100 - 100 70. 540870 - 1000
71. 69740 - 1000 72. 590740 - 10000
73. 57407 - 10000 74.6793800 - 100000

==

to Multiply by 11, 111, 101, &c.

Repeat the multiplicand as often as there are figures of 1 in the multiplier, taking care to put each row of figures according to the directions in the general rule.

*. Cramples. * 473 x 11 568 x 101 - 73 × 1010 473 568 734 5103 57368 74.1340 75, 187604 x 11 - 76. 431409 × 11 77. 697560 - 11 78. 758463 ... 111 79. 216759 - 101 80. 859387 - 1011"

81. 749583 • 1001 82.764850 - 10011

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