QUESTIONS.

First. If 1 fathom cost 34£. 19s. 7d, what cost 245fm. 4ft. 10in? Ans. 8598 £. 1s. 53‡d.

Second. If for 1 pound, I get 4fm. 0 ft. 8in. how many for 178£. 13s. 5d? Ans. 734fm, 3ft. 21zin.

Third. How much will cost 316 C. 3qrs, 11h. if 1 C. cost 7£. 9s. 8d.? Ans. 2371£; Is. 71⁄21⁄2d.

Fourth. If for 1£. I get 2lb. 9oz. 13dwt, how many will I have for 645£. 17s. 6d? Ans. 181176. 30%. 137dwt.

Fifth. At 19£., Os. 144., the tun, what will 186 T. 11 C. 2qrs. come to? Ans. 3546£, 55. 81d.

CONTRACTIONS.

We have said, (page 40) that the multiplication of complex numbers contains a great number of particular cases, which can be solved by abridged methods; we shall here lay down these cases.

FIRST CASE.

When the multiplier does not surpass 12.

Begin the operation by multiplying the units of the lowest denomination.

EXAMPLES.

147 £. 17s. 81. multiplicands, 309£. 19s. 5d. 7 multipliers,

12

1035£. 3s. 8d. Products, 3719£. 13s. Od.

SECOND CASE,

When the multiplier is greater than 12, but the exact product of two factors, both not exceeding 12.

Multiply first by one of the factors, and then the product so found, by the other factor; this last product will be the answer.

EXAMPLES.

Let 547 £. 7s. 9d. be multiplied by 27 = 3 × 9 multiply first 547 £. 78, 9d.

by

3

3

9

14779£. 9. 3d. product of

£. s. d.

When the multiplier is composed of the product of two factors, more a number which does not exceed 12.*

* It may be easily conceived that the following method is applicable to any multiplier, how great foever it be. Suppofe, for inftance, that we have 728 for multiplier, this number refults from 10 X 10 X 7+10X2+8; Then we fhould first multiply the multiplicand by 10; this first product being

First, find the product (per last Rule) of the multiplicand by the two factors, then multiply the same multiplicand by the last part of the multiplier, and add the two products together; the sum is evidently the product required.

EXAMPLES.

Let 1. 17s. 44d. be multiplied by 2321+2= 3 x 7 + 2.

£. s. d.

multiplied again by 10, and this fecond by 7, we would obtain a third product, to which fhould be added twice the product of the first multiplicand by 10, then the product of the fame multiplicand by 8; and the fum of these three products would be the final refult of the operation. This method is fome times ufed in practice, to avoid the calculation by the aliquot parts, which in some cafes may be more complicated, but which cannot be avoided when the multiplier is a complex number.

PRACTICE.

This is the natural place of this article, since by the name of practice, are meant rules for the more expeditious solution of questions, depending entirely on Multiplication.

There are none of these questions, but can be solved by the general method given for complex multiplication; It will then suffice to point out the particular cases, in which this method admits of being abridged.

1st. When the rate of the unit is Is. to have the price of the whole quantity in pounds and shillings.

You must take at once the twentieth part of the number expressing the total quantity; which is done by witing the figure of units of that number in the column of shillings, and taking the half of the other figures, which you write in the column of pounds; but, if this half is not a whole number, write 1 on the left of the figure representing the shillings.

QUESTIONS.

First. What cost 447 yards of ribbon, at 1s. per yard? Ans. 22£. 78.

Second. What cost 27 dozen of knives, at 1s. per piece? Ans. 16£. 4.

Third. What cost 257 forks at 1s. per piece. ? Ans. 12. 17s.

N. B. We have seen that, when the rate of a unit is of two shillings, we must take the tenth part of the hole number.

Secondly, When the rate of a unit is an even number of shillings greater than 2.

The shortest method is to multiply the figure of units of the total number by the number of shillings, to count this product as shillings, then to multiply all the other figures by the half of the same number of shillings, and write this product as pounds.

QUESTIONS.

1st. What cost 256 gallons of shrub, at 6s. per gallon? Ans. 76£. 16s.

2nd. What cost 453 yds, at 2s. per yd? Ans.

£. S.

6

Thirdly, When the rate of the unit is an odd number of shillings greater than 1.

The solution of this case is obtained by the two preceding rules, taking first the product by one shil