In the first of the foregoing examples say, 5 times 5 are 25; then write 5 and carry 2 to the next, saying 5 times 6 are 30, and 2 are 32; write 2 and carry 3, saying 5 times 3 are 15 and 3 are 18; therefore 365 multiplied by 5 makes

1825.

In the second example the multiplier being two figures, namely 24, begin with the 4 and go through the whole of the sum to be multiplied, as in No. 1. Then with the 2 in like manner, only observing to put the product of the first figure under the multiplying figure, as in the example, and multiply on as before; when both are performed. the rule of addition must be applied to ascertain the whole product, as both are to be added, and the amount will be the sum required.

Another way of working this, and which will also prove whether the sum here stated is right, is, by multiplying by 2 and 12, because twice 12 are 24, thus:

To show, in the third example, the amount of 6 times £24 3s. 6d. multiply thus: 6 times 2 are 12; 12 farthings being 3 pence, carry 3 to the pence: then 6 times 6 are 36 and 3 are 39; 39 pence being 3 shillings and 3 pence, set down 3 and carry 3: then 6 times 3 are 18 and 3 are 21; 21 shillings being 1 pound 1 shilling, set down 1 and carry 1: then 6 times 4 are 24 and 1 are 25; 5 and carry 2: then 6 times 2 are 12 and 2 are 14. Hence 6 pounds weight, or 6 barrels, or 6 pieces of any article, at £24 3s. 6d. would amount to £145 1s. 3d.

When either the multiplier or the multiplicand (that is the sum multiplied) or both, contains ciphers on the right hand, set down so many ciphers as there are in both, on the right of the product; and multiply only by the remainder, thus ;

DIVISION.

As Multiplication teaches the art of finding any number when repeated so many times, so Division instructs us how often one given number is contained in another. Thus to know how many times 6 are contained in 478654, set them down in this manner :

This is performed by saying 6's in 47, 7 times, and 5 over, because 7 times 6 are 42; then placing the 5 before the next figure 8, it makes 58; 6's in 58, 9 times, and 4 over; which placed before the next figure 6 makes 46; then 6's in 46, 7 times, and 4 over; 6's in 45, 7 times, and 3 over; 6's in 34, 5 times, and 4 over; therefore 79775 and is the answer. In order to prove it multiply it thus: Multiply 79775-4 the Quotient.

by

6 the Divisor.

over,

Here 6 times 5 are 30, and 4 the remainder are 34; 4 and carry 3, and so on.

When the divisor exceeds 12, it is necessary to proceed as in the following example:

25)265(10

250

15

Finding that 10 twenty fives make 250; place 10 on the right and multiply the 25 by 10, as here stated, then by subtracting 250 from 265, there remains 15; so that the answer is 10 times, and 15 over; and in order to prove it, multiply it as before.

REDUCTION.

THE next step is to reduce sums of money, &c. into an amount of different denominations; as, for instance, pounds into shillings, pence, or farthings; years into days, hours, or minutes, &c. It is not, properly speaking, a distinct rule in arithmetic, but rather the application of the two preceding ones, namely, Multiplication and Division.

In the first of these examples, begin to multiply by 20, because 20 shillings make one pound; but as it contains a cipher on the right hand, take the 4 from the 14 shillings, and set it down in its proper place; then multiply by the 2, saying twice 2 are four and 1 from the 14 which was left are 5, and twice 3 are 6: then multiply the 654 shillings by 12, because 12 pence make one shilling, adding the 6 from the pence to the first figure multiplied; and lastly multiply the 7854 pence by 4, because 4 farthings make one penny, adding the 3 farthings to the first figure multiplied.

In the second example, the sum is proved by division, which is the way to ascertain any similar sum: here you begin by dividing the 31419 farthings by 4, in order to bring them into pence, thus 4's in 31, 7 times, and 3 over; 4's in 34, 8 times, and 2 over; 4's in 21, 5 times, and 1 over; 4's in 19, 4 times, and 3 over, which are 3-4ths of a penny, and therefore you find that in 31419 farthings, are contained 7854 pence and 3 farthings; thus you proceed through the whole, dividing the pence by 12, because 12 pence make one shilling, and the shillings by 20, taking care to carry out as here stated the overplus that remains, which must be brought down when the answer is given.

In dividing by 20, cut off the cipher, and the last figure in the quotient, which you carry out; and divide by 2, it being more easily done; thus 2's in 6, 3 times; 2's in 5, twice and 1 over, which by carrying out to the 4, makes 14 shillings over.

These two plain examples will give the learner a sufficient idea of the general principle of reduction, as the same method is adopted in the reducing of weights, measures, &c.

The whole therefore of this plain and concise system of arithmetic, which has been formed on an entirely new scale, shall be concluded with a few lessons to be performed unaided by any additional instruction.

28 Pieces of Irish Linen cost £6 17s. 44d. each; how many farthings do they amount to?

125 Yards of Thread. Lace cost 6027 farthings; how many pounds, shillings, pence, and farthings, do they

amount to?

Plain Directions for keeping a regular Account of Expenses, necessary to be observed by Housekeepers, and others.

Get a book of blank paper, with ruled lines, from the stationer's, or you may make it yourself with some writingpaper; rule the lines regularly, on which you are to write, with a pencil or plummet, and in the margins on the right