Why 1 must be subtracted from the right-hand figure of the remainder (Rule). By subtracting the repetend as a finite decimal, instead of adding the common denomi nator of the repetends, 9, 99, &c. to the upper repetend (when it is less) I add 10, 100, &c. which is always 1 more than the real common denominator whereby the remainder results 1 too much; wherefore I deduct that 1 from the remainder. MULTIPLICATION of Circulating DECIMALS. R EDUCE the Circulate to its equivalent Vulgar Frac-tion, and multiply the finite Decimal thereby. 410.350 1 1 10)4103.519 410.3519' Answ. 6.5599'03'. Answ. 302.326's'. To multiply a circulate by a circulate. Reduce them both to their equivalent vulgar fractions, then multiply their numerators into each other, and divide that product first by the denominator of one, and then by the denominator of the other. CHAP. XI. DIVISION OF CIRCULATING DECIMALS. I. To Divide a Circulate by a Finite Decimal, &c. IVIDE as if they were both Finite Decimals carrying on the operation by bringing down the figures of the Repetend (nstead of cyphers) so oft till either the Quote Circulate; or till a sufficient number of places result. 1. Divide 195.02' by 4. 4)195.022, &c. II. If the divisor be a circulate, make the repetends of the divisor and dividend similar. Then instead of them using the numerators of their equivalent vulgar fractions, and bringing them to one common denominator, divide the numerator of the dividend by the numerator of the divisor as finite decimals. Explanation and Reason. 5. Divide 2.16595' by 4'. .04)2.16595′ · The mixt number 2.16595' having the 21659 figure 5' a repetend is given similar to the 4)19.4936 divisor. Then by subtracting the finite part I reduce it to its equivalent vulgar 0 4.8734 fraction 194936 Then by making the decimal places equal in number to the cyphers of the denominator 90000, 1 reduce it to a mixtfraction whose denominator is 9, the same with that of the numera or: Sɔ I divide 19.4936 by . ་ Note. The decimal places in the divisor and dividend will still be equal to the cyphers in their denominators. BOOK III. MERCANTILE ARITHMETIC. PRAC CHAP. I. PRACTICE. RACTICE is a compendious way of finding the price of any Quantity of goods, having the price of 1 given. If any aliquot Part be subtracted from its Whole, I call the remainder its complement, as 5s. subtracted from 20s. of which it is an aliquot Part, the remainder is 158. which I call the complement of 5s. and the correspondent parts the complement of 4. Case I. Of Multiples of 11. 1s. or 2s. I. When the price is pounds only, or a multiple of 11. multiply the quantity by the price, and the product is the answer in pounds. The application and reason are evident. 1. What come 110C. of hops to, at 41. C.? Answ. 4401. 2. What come 227 yards of brocade to, at 31. ' yard? Answ. 6811. 1 3. What's the amount of 56 pieces of chintz, at 57. D piece? Answ. 2801. 4. What's the amount of 27 ton of tallow, at 261. ton? Answ, 7021. II. When II. When the price is shillings only. 1. If the price of 1 be 2s. then the price of any quantity is discoverable at sight, viz. by accounting the double of the units figure shillings; and the other figures of the given quantity pounds: So 278 yards at 2. yard, will cost 271. 16s. for the double of 8 is 16, which write down apart as shillings, then 27 the other figures of the quantity are to be esteemed pounds: so the -answer is 271, 163, 2. If the shillings be any even number. 278 £.27: 16 Multiply the quantity by half the number of the given shillings, and double the units of the product for shillings, the other figures of the product are pounds. 736 Application. Let it be required to find the price of 736 yards, at 4s. yard. Imultiply 736 by 2, (the half of 4.) saying twice 6 is 12; the double of 2 (viz. the units in the product) is 4. to be set apart for shillings, Answ. £.147 4 keeping 1 in mind for one ten. Again, twice 3 is 6 and 1 I carry is 7 ; and so proceeding as in Multiplication, I find the answer 1477. 4s, Examples. 6. What cost 256 gallons of shrub, at 6s. d' gallon? 7. What cost 984. of green tea, at 8s. .? Answ. 3931. 12s. 8. What cost 120 C. of beef, at 10s. C.? Answ, 601, 9. What |