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103. When the multiplier is a composite number. RULE. Multiply the given compound number by one of the component parts, and that product by the other. To prove the operation, change the order of the multipliers, that is, multiply by that part first which you multiplied by last in the preceding work, and by that last which you multiplied by first g.
s This rule is evident from what has been said in the note on the corresponding rule in simple Multiplication, Art, 35.
89. Multiply I lb. 3oz. 5dwt. 7 gr. by 15. Prod. 191b. 19dwt. 99r. 90. Multiply 3!ea. 2m. Ifur. 10p. by 28, Prod. 104lea. 3fur. 91. Multiply 7 yds. 3gr. 2n. by 36. Prod. 2839 ds. 24r. 92. Multiply 4tuns, 3hhd. 2gal. 1gt. by 54. Prod. 256tuns, 3hhd. 58gal. 24t. 104. When the multiplier is not a composite number. Rule. Find the greatest composite number contained in the ltiplier; multiply by its component parts as in the last rule; D multiply the top line by as many as the composite number Jund, wants of the given multiplier; set this product under the former, and add them both together".
4 3 24 × 3 The greatest composite number contained
6 in 39 is 36, or 6 × 6, and this wants 3 of 39. 2.TT9 TI. I therefore multiply by 6 and 6, the re
* sult is the product of the top line multiplied
6 by 36. Next I multiply the top line by 3,
149 14 9. and place the product 12l. 9s. 6d.; under the
12 9, 6: former product. Lastly, I add both products
—f together for the answer. Prod, 162 4 3+
* Thus in Ex. 93, 1491. 14s. 9d. is the Product by 36, (Art. 103.), and 12. 8s. 6d. } is the product by 3; wherefore both sums added together will be the product by 36+ 3, or 39; whence the rule is manifest.
Rule I. Multiply successively by as many tens as (when multiplied together) make 1 of the highest place in the multiplier, and you will have the several products of 10, 100, 1000, &c. up to the said highest place. II. Multiply each of these products severally by the figure which is of the same name with the product to be multiplied, (proceeding from the highest to the lowest in order,) place the products under one another, and add them all together; the result will be the answer required.