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In the first of the foregoing exain ples say, 5 times 5 are 25 ; then write ; and carry 2 to the next, saying 5 times 6 are 30, and 2 are 32; write 2 and carry 3, saying 5 tiines 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 e in like manner, only observing to put the product of the first figure under the multiplying figure, as set down, and multiply on as before; when both are performed, the rule of additiou 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 19, because twice 19 are 24, thus;
To show, in the third example, the amount of 6 times £24 35.6;d. multiply thus: 6 times are 12; 12 farthings being 3 pence, carry S to the pence: theu 6 times 6 are s6 and 3 are 39; 39 pence beịog 3 shillings and 3 pence, set down 3 and carry's; then 6 times s are 18 and's are 21; Q1 shillings being ! pound 1 shilling, set down ļ and carry 1: ihen times 4 are 24 and I are 25; 5 and carry 2: then 6 limes 2 are 12 and 2 are 14. Hence 6 pounds weight, or 6 barrels, or 6 pieces of any article, at £24 $s. 6 d. would amount to £ 145 ls. 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 res mainder, thus: 2405
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 dowu in this manner;
Divide by 6)478634
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 3 6's in 34, 5 times and 4 over; therefore 79775 and 4 over, is the answer. In order to prove it multiply it thus:
Multiply 79775—4 the Quotient,
6 the Divisor.
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:
Finding that 10 twenty fives make 25) 265(10 250; place 10 on the right and mul
950 tiply the 25 by 10, as here stated,
15 then by subtracting 250 froin 265, there remains 15 ; so that the aoswer 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. iuto 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 twu preceding ones, namely, Multiplication and Division,
Of money descending. d. In 32
14 0f how many farthings. 20
Proved thus : 654 shillings
4)31419 farthings 12
12)78544 7854 pence
32-14s. 31419 answer:
2.32 14 64 answer.
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 down in its proper place; then multiply by the 2, saying twice 2 are 4 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 froin the pence to the first figure múltiplied, 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 divison, which is the way to ascertain any similar som, 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 S4, 8 times, and 2 over; 4's in 21, 5 times, and i 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 put 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 a's in 6, 3 times; 2's in 5, twice and i 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 mes thod 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.
REDUCTION. 28 Pieces of Irish Linen cost £6 17s, 4d. 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?
Plaiu Directions for keeping u regular Account of Expenses, necessary to be observed by Ilouse-keepers 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 pluinmet, and in the margins on the right