COMPOUND MULTIPLICATION is the multiplying of sums of different denominations; it is useful in finding the value of Goods, &c. And, as in compound Addition, we carry from the lowest denomination to the next higher, so we begin and carry in Compound Multiplication; one general rule being to multiply the price by the quantity.

NOTE. The product of a number, consisting of several parts or denominations, by any simple number whatever, will be expressed by taking the product of that simple number, and each part by itself, as so many distinct questions: Thus, 331. 15s. 9d. multiplied by 5, will be 1651. 75s. 45d.=(by taking the shillings from the pence, and the pounds from the shillings, and placing them in the shillings and pounds respectively,) 1681. 18s. 9d. and this will be true when the multiplicand is any compound number whatever.

CASE I.

When the multiplier or quantity does not exceed 12.

Multiply the price of one yard, pound, &c. by the whole quantity or number of yards, pounds, &c.-the product will be the

answer.

186. What is Compound Multiplication ?—187. What is the rule when the mul tiplier does not exceed 12 ?

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EXAMPLES.

1. What will 5 yards of broadcloth amount to, at £1 12s. 44d. a yard ?

£.

1

S. d.

124

5

£8 1 101

In this example, we write down £1. 12s. 4 d. the price of one yard, and then write 5, the number of yards, under the least denomination. We multiply 2 farthings by 5, and the product is 10 farthings, which we bring into pence by dividing them by 4; we write down the remaining 2 farthings, and reserve the quotient, 2 pence, We then multiply 4 pence

to be added to the product of the pence. by 5, and the product is 20 pence, and 2 pence which we reserved are 22 pence, which we bring into shillings by dividing them by 12; we write down the remainder 10 pence, and reserve the quotient, 1 shilling, to be added to the product of the shillings. We then multiply 12 shillings by 5, and the product is 60 shillings, and 1 shilling that we reserved are 61 shillings, which we bring into pounds by dividing them by 20; we write down the remainder 1 shilling, and reserve the quotient, 3 pounds, to be added to the product of the pounds. We then multiply 1 pound by 5, and the product is 5 pounds, and 3 pounds which we reserved are 8 pounds; this being the highest denomination, we write down the whole amount 8 pounds, and find the product or answer to be £8 1s. 10дd.

2. Multiply £4 13s. 4ąd. by 10.

3. Multiply £8 15s. 113d. by 11.

4. Multiply £13 12s. 11d. by 7.

5. Multiply £14 17s. 8d. by 9.

Ans. £133. 19s. 2 d.

REMARK.-The facility of reckoning in Federal Money, compared with pounds, shillings, &c. may be seen from the examples given in this and the following cases.

The general rule is

Multiply as in simple mutiplication, and from the product point off so many places for cents and mills, as there are places of cents and mills in the price.

2. Six yards at 9s. 10d. per 2. Six yards at $1.22c. 9m. per

yard?

Ans. £2 19s.

yard?

Ans. $7.37c. 4m.

CASE II.

Where the multiplier, that is, the quantity, is above 12.

Multiply by two such numbers, as, when multiplied together, will produce the given quantity, or multiplier.

CASE III.

When the quantity is such a number, that no two numbers in the Table will produce it exactly.

Multiply by two such numbers as come the nearest to it; and for the number wanting, multiply the given price of 1 yard by the said number of yards wanting, and add the products together for the answer; but if the product of the two numbers exceeds the given quantity, then find the value of the overplus, which subtract from the last product, and the remainder will be the

NOTE. This may be performed by first finding the value of 48 yards, from which if you subtract the price of 1, the remainder will be the answer as above.

189. How do you proceed when the multiplier or quantity is such a number as no two numbers in the Multiplication Table will produce exactly?

CASE IV.

When the quantity is any number above the Multiplication Table. Multiply the price of 1 yard by 10, which will produce the price of 10 yards: This product, multiplied by 10, will give the price of 100 yards; then you must multiply the price of 100 by the number of hundreds in your question; the price of ten by the number of tens; and the price of unity, or 1, by the number of units lastly, add these several products together, and the sum will be the answer.

EXAMPLES.

1. What will 359 yards of cloth, at 4s. 74d. per yard, amount to?

To find the value of a hundred weight or 112 pounds, having the price of one pound given.

Multiply the price of 1 pound by 7, the product will be the price of pounds; multiply the price of 7 pounds by 4, the pro

190. When the quantity is a number above the Multiplication Table, ho do you proceed? -191. What is the method of finding the value of a cret. or 112 lbs. the price of 1 pound being given?