30 To mangly by any number of figures at once. RE Ft Ty warmly walls; then each figure of the malarla qui in order by the wals of the multiplier, carrying as Barleting to coci, pr due fie pruduct, or products, ob"44","iplying, successively, fie preceding figures of the 1 by the suceeding figures of the multiplier, up to the 104, are multiplied, till all have been multiplied by the alier; then drop the unit-figures, and proceed es in the same manner. Finally, multiply together ures of the multiplicand and multiplier, add the arried, if any, and write the result. NOTE. This process is not so difficult as is generally imagined, and if once clearly comprehended, it can readily be applied in practice, especially in multiplying numbers of two and three places. 31. The elucidations which follow will give a better idea of the process than the rule, which may appear complicated to a novice. 10, the last result, and the figures to the right of the perpendicular line, form the product. The figures on the left of the line represent the numbers carried. NOTE. It will be seen that there is a perfect system in the operation, which can be followed with facility and accuracy by any skillful person, with sufficient practice. 2. Multiply 4738 by 6523. 4738 Elucidation. 3 x 3 + 3 × 7 + 2 + 2 × 30905974, Ans. 3 × 4 + 6 + 2 × 7 + 5 × 2 × 4+ 9 + 5 × NOTE.-To become familiar with the operation, impress upon the mind the order of procedure. Thus, observe that we multiply units by units; tens by units, units by tens; hundreds by units, tens by tens, units by hundreds; thousands by units, hundreds by tens, tens by hundreds, units by thousands; and so on. The figures of the multiplicand are taken in order from left to right, and those of the multiplier from right to left. The above diagram illustrates the operation of multiplying three figures by three. The different steps are indicated by the arrows, numbered in order, 1, 2, 3, 4, and 5. This, with the previous elucidations, will, it is believed, give a clear idea of the process, and enable any one of ordinary comprehension to understand it. CASE XV. 32. To multiply by aliquot parts of 10, 100, 1000, etc. RULE.-Multiply the multiplicand by the number of which the multiplier is an aliquot part, by annexing ciphers; then take such part of the product as the multiplier is of that number. 33. This rule, with a slight variation, may also be used when a part of the multiplier is an aliquot part of 10, 100, etc. EXAMPLES. 1. Multiply 456 by 2125. 21252 × 1000; hence, 456 × 2125 = 456000 × 2, 34. When the multiplier is,,, etc., it is easier to subtract †,†,§, etc., of the product from itself than to multiply by the fraction. RULE.—Annex a cipher to the multiplicand, and divide by 2. Or, If the multiplicand be an even number, annex a cipher to onehalf of it; if odd, annex 5 to one-half of the next lower number. |