The usual form of writing the process is as follows: N.B.-In taking the aliquot parts a little judgment should be exercised to prevent an awkward quantity from remaining at last―e.g., we might have taken the aliquot parts in the above example thus:: We should now have had d. to calculate for. But d. is 1 of 6s. 8d., so that we should have been compelled to divide "“the cost at 6s. 8d. by 160 to find the cost at d.” This would have been a comparatively awkward operation, and it will be found better to avoid such remainders when it is possible to do so. When a remainder of this kind does occur, however, it is sometimes easier to make a separate calculation for it, thus:162 pence 138. 6d. Ex. 2. 324 articles at d. each Find the cost of 8794 at 28. old. each. of 28., the of £, 4d. of that, and a = In this instance, instead of taking 28. od. 1% of a £, and a farthing last being an inconvenient divisor, we take is. 8d. of that. 169. £888 11 2 = the cost at 2s. old. each. There is another method of finding the value of a number of articles when the price of one is less than £1, thus, Since the 750 articles at 12 we obtain the cost at at IOS. Next, 6s. 8d. is see by the table that 2s. is cost at 28. the cost at £12 18 10 each. 1 each would obviously cost £750, if we multiply that sum by 12. As ros. is of £1, by dividing 750 by 2, we find the cost of £1, by dividing 750 by 3 we get the cost at 6s. 8d. Next, we of 10s.; hence, by dividing the cost at 10s. by 5 we find the 170. If the price be less than a shilling, the best way is to take parts of a shilling so as to find the price in shillings, and afterwards reduce to pounds, thus Ex. 5. Find the cost of 10374 articles at 91d. 171. The following artifice may sometimes be employed to simplify the solution of questions in practice, viz. Taking the price as if somewhat higher than that which is given, and subtracting a convenient aliquot part; thus, = £6, less is. 8d. Ex. 6. Find the price of 218 cwt. at £5 18s. 4d. per cwt. 172. When the price is an even number of shillings, multiply the number of articles by half the number of shillings, cut off the unit's figure of the result, and double it: reckon this doubled figure as the shillings, and the rest of the result as the pounds of the answer. Ex. 7. Required the cost of 313 articles at 188. each. 313 9 Answer £281 14 Here the of 188. is 98.; then 9 times 3 are 27, and doubling this we have 54; 54 shillings are 2 pounds 14 shillings; write 148. down and carry the 2 pounds: 9 times I are 9, and 2 carried are 11; set down 1 and carry 1: 9 times 3 are 27, and 1 carried are 28, set down 28; hence the answer is £281 148. 173. When it is required to find the value of a certain number of things, and a fraction, we proceed as follows: Answer £724 16 8 the cost at £2 13 8 each. The above is the most expeditious method of finding the answer, which, however, might have been obtained as follows, Since 270 cwt. will cost 270 times £2 138. 8d., cwt, will cost times of 2 138. 8d., In the last line of division the student must observe that the id. is the that £16 18. 1d. is divided by 15, instead of the line immediately above. of 18. 3d., and 174. We may sometimes take aliquot parts of the multiplied quantity instead of the original quantity, thus Here 178. 6d., which is of £1, is of £7; therefore divide 2268 by 8, the quotient is the cost at 178. 6d. each. II. COMPOUND PRACTICE. 175. In this case of Practice, the given number is not wholly (sometimes not at all) expressed in the same denomination as the unit whose value is given; as, for instance, I cwt. 2 qrs. 14 lbs. at £2 28. per cwt.; 19 ton 17 cwt. 2 qrs. at is. 2d. per cwt. The rule for Compound Practice will be easily seen by the following examples. EXAMPLES. Ex. 1. Find the value of 84 cwt. 3 qrs. 14 lbs. of sugar at £12 118. 8d. per cwt. The value of I cwt. of sugar being £12 118. 84, the value of 84 cwt. of sugar (value of 1 cwt.) = = £1057 6 5 10 3 2 II I II 5 I qr.(value of 2 qrs.) = 14 lbs. (value of 1 qr.) = therefore, by adding up the vertical columns, the value of 84 cwt. 3 qrs. 14 lbs. = 1068 o 2 Here, as 12 118. 8d. is the cost of 1 cwt., we multiply that sum successively by 12 and 7, the factors of 84, to obtain the cost of 84 cwt.; then as 2 qrs. are of 1 cwt., of the top line will be the cost of 2 qrs., and as I qr. is the of 2 qrs., we divide the cost of 2 qrs. by 2. Next, 14 lbs. being of 1 qr., we divide the value of 1 qr. by . The results being added together give the cost of 84 cwt. 3 qrs. 14 lbs. Ex. 2. Find the value of 7 cwt. 3 qrs. 11 lbs. at £2 138. 1d. per quarter. The given unit being a quarter, we reduce 7 cwt. 3 qrs. to 31 qrs., and find the value of them by multiplying by 31; then to find the value of 11 lbs., we consider that 7 lbs. are qr., and 4 lbs. are qr.; so that, dividing £2 138. Id., the value of 1 qr., by 4 and 7, and adding up, we have the value of 7 cwt. 3 qrs. 11 lbs. |