MULTIPLICATION OF DIVERS DENOMINATIONS OB, COMPOUND MULTIPLICATION. WRITE the multiplier under the lowest denomination of the multiplicand. Begin at the right hand, and multiply the number of the lowest denomination by the multiplier, and divide the product by as many as make one of the next higher denomination; write the remainder, if any, and if nothing, a cipher under the denomination to which it belongs, add the quotient as so many ones, to the product arising from the multiplier, and the next higher denomination of the multiplicand, which divide by as many as make one of the next higher denomination, put down the remainder or cipher as before, and so proceed through all the denominations to the highest, the product of which, together with the quotient of the next lower denomination added thereto, put down as in whole numbers.* Compound Multiplication is proved by multiplying twice the multiplicand by half the multiplier, when the latter is an even number, and when an odd number, by multiplying twice the multiplicand by one-half of the greatest even number contained in the multiplier, and adding to the product the first multiplicand. = = * Let £3 19 74d be multiplied by 6, the product will evidently be properly expressed, if each denomination be separately multiplied by 6, that is, £3 197дd × 6: £18 114s + 42d + But 6 half-pence 3d; 42d 3-6; and 114 £5 14s Od: collecting these together by compound addition, the sum is £23 17s 9d the product, agreeably to the = = rule. When the multiplier is a composite number, and can be resolved into two or more component parts, within the limits of the multiplication table; multiply the given multiplier by one of those parts, and the product thus obtained by the others, or succeeding part or parts, and the last product is the answer. Examples. £ s. d. 4 18 12 x 16 19 12 7 4 78 10 4 Such examples as these may be proved, by multiplying in a different order. The following examples consist of three a four component parts, of which a table is subjoined, and continued as far as 1800. £. Examples. . Ꮽ d. When the multiplier is 13, 17, 19, or 23, multiply the given multiplicand by 12, and to the product add once the same for 13, five times the same for 17, seven times for 19, and eleven times for 23. The accuracy of the work may be proved by multiplying in a different order, as by 10 and 9 for 19, &c. When the multiplier is greater than 23, and not a composite number. Take the nearest composite number thereto, either greater or less, and multiply by its component parts, then add or subtract as many times the multiplicand, as the assumed number is greater or less the given multiplier. H |