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

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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 by 6407200

or

6407200

by

7304600

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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.

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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.

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When the multiplier is a series of nines, annex, or suppose to have annexed as many ciphers as there are nines, from which subtract the multiplicand.

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When the multiplier is not more than 12 less than any number, consisting of a significant figure followed by any number of ciphers, multiply by such significant figure, and annex thereto the ciphers as before; and from the product, subtract the product of the multiplicand and the number deficient.

4352 x 896
900-4

3916800
17408

3899392

Examples.

3234 × 788
800-12

2587200
38808
2548392

M

397

91. 435872 × 198
93. 396494
95. 48754
97.908753

92. 54869 X 293
94. 437523

96. 68448

496

695

98. 87359

100. 79653

99. 639084, 894

592

• 991

989
6988

To multiply by any number in one line, consisting of 2 figures under 20. Multiply by the right-hand or units figure of the multiplier, taking care to add in the past figure of multiplicand.

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When the multiplier is 112, 113, 114, 115, &c. any number may be multiplied thereby in one line, but in these cases it will be necessary, not only to add in the first, but also the second past figures of the multiplicand.*

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If the Multiplier be any digit with 1 annexed thereto, as 21, 31, 301, 3001, &c.

The multiplicand will answer for the product of the unit, and the product of the digit removed a place or more (as the case may require) towards the left, added thereto, will give the required product.

4234 x 31

12702

Examples.

5627 X 401

22508

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* This method is of use in bringing cwts. qrs, and lbs. into pounds, by thus multiplying by 112, and mentally adding in the pounds of the odd weight, if any, as.will be more particularly noticed in another partof this work.

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