6. COMPOUND MULTIPLICATION. COMPOUND MULTIPLICATION is when the Multiplicand consists of several denominations. It is particularly useful in finding the value of Goods. The different denominations in what was formerly called Lawful Money, render this rule with some others in Arithmetic, as Compound Division and Practice, rules of great usefulness, quite tedious, and the variety of cases { necessarily introduced, extremely burthensome to the memory.-This lumber of the mind might be almost wholly dispensed with, were the habit of reckoning in Federal Money generally adopted throughout the United States. For important reasons, pounds, shillings, pence and farthings, ought to fall wholly into disuse: Federal Money is our national currency; the scholar might encompass the most useful rules in Arithmetic in half the time; the value of commodities bought and sold, might be cast with half the trouble, and with much less liability to errors, were all the calculations in money universally made in Dollars, Cents, and Mills. But this, to be practised, must be taught; it must be taught in our schools, and so long as the prices of goods, and almost every man's accounts are in Pounds, Shillings, Pence and Farthings, this mode of reckoning must not be left untaught. To comprise the greater usefulness, and also to shew the great advantage which is gained by reckoning in Federal Money, I have contrasted the two modes of account, and in separate columns on the same page, have put the same questions in Old Lawful and in Federal Money. When the multiplier, that is, the quantity, exceeds 144, multiply first by 10, and this product again by 10, which will give the price of 100 yards, &c. and if the quantity be even hundreds, multiply the price of 100 by the number of hundreds in the question, and the product will be the answer; if there be odd numbers, multiply the price of 10 by the number of tens, and the price of unity, or 1, by the number of units, then these several products added together will be the answer. POUNDS, SHILLINGS, PENCE, PARTH. DOLLARS, CENTS, MILLS. EXAMPLES. 8. What will 563 yards of cloth 1. What will 563 yards of cloth cost at $4,43 per yard? cost at £1 6s. 7d. per yard? OPERATION. $4, 4 3 1 6 8 9 25 2 2 2 5 2 $2 4 9 4, 09 Ans. 6 times 10 yds. 8 times lyd. 3 SUPPLEMENT TO COMPOUND MULTIPLI CATION. QUESTIONS. 1. What is Compound Multiplication? 2. What is its use? 3. Are operations more easy in OLD LAWFUL or FEDERAL MONEY? 4. What is the Rule of Compound Multiplication? 5. When the quantity, that is the Multiplier, exceeds 12, and is within the Multiplication Table, what are the steps to be taken? 6. When no two numbers multiplied together will produce the given quantity, what then is to be done? 7. When the multiplier exceeds 144, what is the method of procedure? 8. When the price of goods are given in Federal Money, what is the general and universal rule for finding their value by Multiplication? EXERCISES. 1. A man has 38 silver cups, each weighing 1oz. 3pwts. 16grs. how much silver do they all contain? Ans. 3 lb. 8 oz. 19 pwts. 8 grs. 2. If a man travel 34 miles, 3 furlongs, and 17 rods in one day, how far will he travel in 62 days? Ans. 2134 miles, 4 fur. 14 rods. 3. What will 235 yards of cloth come to at £1 28. 54d. per yard? Ans. £263 17s. 81d. 4. If a horse run a mile in 12 minutes, 16 seconds, in what time would he go 176 mlies? Ans. 1D. 11h. 58m. 56sec |