1 The different variations of this rule are so numerous, that it would be tedious and perhaps impossible to enumerate all of them, and some would not be entitled to the epithet of conciseness; the annexed are, I hope, as unexceptionable in this way, as any that have been yet adopted. CASE 1st.-When the given price is a part or parts of a penny, consider the given quantity as pence, and divide by the denominator or denominators of the aliquot part or parts of a penny, which will give the answer in pence. *One farthing being , divide by 12 and 80. One halfpenny being is d. divide by 12 and 40. being of a £ sterling, therefore, when the price is of a £ sterling, therefore, when the price of a £ sterling, therefore, divide by 8 and 40. CASE 2d. When the price is an aliquot part of a shilling, and also of a pound. If the given quantity be small, consider it as shillings, and divide by the denominator of the given aliquot part of a shilling, which will be the answer in shillings. If the given number is large, consider it as pounds, and divide by that aliquot part of a pound, of which the given price is a part; this will give the pounds of the answer, and the remainder divided by the denominator of the given aliquot part of a shilling, will give the shillings; the remainder, if any, will be so many ones of the given price. CASE 3d. When the price is the complement of a shilling. Divide the quantity considered as shillings, by the denominator of such aliquot part as the remainder may be after subtracting the given price from a shilling, which subtract from the given quantity, the remainder will be the answer in shillings Examples. Practice can always be proved by the Rule of Proportion, and in general, a case can be found by which an other can be proved by a different operation. CASE 4th.-When the price is an aliquot part of a shilling. Consider the quantity as pounds or shillings, which ever will most readily answer the question, and divide it by the denominators of the several aliquot parts of which the given ali quot part is composed. 6d=1473 at 74 Examples. 6d1821 at 94 1041735at102 111 16 6 3 20 10 672 5 10 272 L14 3 8 10 5 3 5851 2 11 34 L77 14, 3 59. 6417 at10 60. 1523 at 7 CASE 5th. When the price is 2s. or an aliquot part thereof double the units place for shillings, the other figures will give the pounds of the answer when the price is 2s. When an aliquot find the price at 2s. which divide by the denominator of the given aliquot part. 25. When the price is 10d. annex a cipher to the given number, and divide by 12 and 20, or without annexing the cipher divide 2 and 12. 26. When the price is 11d, multiply by 11 as taught in Multiplication and divide by 12 and 20. 31. 1 is an aliquot part of a pound therefore divide by 16 and 12. 34, 24 is an aliquot part of a pound therefore divide by 12 and 8. 37. & 38. For 34 or 34 take an 80th of a and an aliquot part thereof. 42. For 5 divide 12 and 4. 51. For 7 divide by 8 and 4. 32. From 2d. an 120th part of a £ subtract d. of 2d. = 38. 3 is also an aliquot part of a therefore divide by 8 and 3, CASE 6th.-When the complement of 2s. Find the price at 2s. as before from which subtract the amount at the difference between the given price and 2s. Examples. 78. 1733 at 1 8 shillings. CASE 7th.-When the prices are even Multiply by half the number of shillings, doubling the first figure of the product for the shillings of the answer, the remainder of the product will be pounds.. And instead of placing half the given number of shillings under the given quantity, a line will be saved by placing this number in the margin as a fraction with 10 for a denominator, and by multiplying by this numerator and doubling the units figure the operation will be exactly the same. Cramples. 79. 1493 at 4s. 82. 1733 at 12s. 83. 4391 at 14s. 85. 1347 at 18s. 88. 4735 at 22s. 89. 1342 at 24s. 90. 3174 at 12s. CASE 8th-When the prices are odd shillings. Find the amount at the highest number of even shillings therein as before directed, and for the odd shilling add th part of the given quantity considered as pounds, the sum will be the answer. |