2 Addition and Subtraction of Decimals of different denominations may easily be performed, after the Decimals are reduced to their proper quantities. EXAMPLES. I What is the sum of .487 and 16s reduced to their proper quantities? Ans. 9s 9.12d. 2 What is the sum of .17 lb. Troy and .84 oz? Answ. 2 oz 17 dwt 144 gr. 3 What is the sum of .17 ton .19 C .17 qr. and .7 lb. ? Ans. 3 C 2 qrs 15.54 lb. 4 What is the difference between .177 and 7s? Answ. 2s 8d 1.6 qrs. 5 What is the difference between .41 days and .16 hrs? Ans. 9 hrs 40 min 48 sec. OF THE SINGLE RULE OF THREE DIRECT IN DECIMALS. Q How do you prove the following questions ? EXAMPLES. 1 If 1.4 lb of mace cost 14.5s what cost 75.31 lb ? Ans. 381 198 11d 3.52qrs. 2 If 1.6 C. of Sugar cost 31 12.76s what cost 3 hhds. each 11 C 3 qrs 10.12 lb Ans. 801 15s 3d 3.36 qrs. 3 If 1.5 oz. of Silver be worth 7.8s what is the value of 9.7 lb? Ans. 30l 58 3d 1.44 qr. 4 If 1.47 C. of Sugar be worth 4.57 what is 1.7lb wor at that rate ? Ans 11.1d. 5 If 1 pint of wine cost 1.2s what cost 12.5 hhds? Ans. 3781. 6 If 8.4 lb of Tobacco cost 16s 4.6d what cost 3 bhds. each 4 C. 2 qrs 7.4 lb ? Ans. 1497 12s 3d 2qrs. 7 If a yard of cloth cost 12.38 what cost 3 pieces, each 21.5 yards? Ans. 391 13s 4.2d. 8 A man bought a piece of cloth for 6/ 13.12s. I demand how many Yards there were in the same, when he gave after the Rate of 4s 2.9d per yard? Answer 31.569. Yards. 9 A man bought 5.8 tuns of oil for 60.4 but by misfortune it chanced to leak out 50.9 gallons? I demand how he must sell the rest per gallon to be no loser? Answer 10.27d per gallon. 10 Two men bartered, A had 40.7 yards of linen, for which B gave him 25.6 ells of Holland, at 4.5s per ell; I demand the price of the linen per yard? Ans. 2s 9d 3.8qr. 11 A Grocer bought 7.6 C of sugar, at 40. Is per C. and sold the same out at 4.5 per lb I demand whether he gained or lost, and how much? Ans. 14s 5d 1.12 qr gain. 12 A Brewer made a quantity of Beer, which cost him 90.41 and afterwards sold it out at 26.7s per barrel, by which he gained 10. I demand the quantity that was brewed? Ans. 75 barrels 7.4+gals. 13 A Grocer bought 3 C 1.5 qr of cloves, at the rate of 2.75s per lb and sold them for 60 11s 6d what did he gain or lose by the bargain? Aus. he gained 81 12s 14 A Merchant bought 436 yards of Cloth for 8.5s per yd and sold it again at 10.75s per yard, what did he gain by the sale thereof? Ans. 491.1s gain. 15 A owes B 296.851.but he compounds for 7.5s in the pound, what must B receive for his debt? Ans. 1117 6s 4d 2 qrs. 16 Bought 3 hhds of Tobacco, each weighing 4 C 1.9 qr at 5.61 per C. which I sold out at 77 16s per C. what did I gain by the whole? Ans. 291 10s 8d 1.0 qr. 17. A Jeweller bought a Diamond for 60 guineas, and after it was neatly cut, weighed 1.5oz which he sold again for 3.25s per grain: I demand how much he gained by the said Diamond; and also at what rate per cent he made his gain? Ans. Whole gain 541 Os Od Oqr. Gain per cent. 85 14 3 1.7+ Q. OF THE SQUARE ROOT. WHAT is a Square? A. Any number multiplied by itself produces a square Q. What is the Extraction of the Square Root? A. If a square be given to find one side, it is called the extraction of the Square Root. Q. How is the given Square to be prepared for extraction? A. By pointing off at every two figures, from the units place, both ways for a resolvend. Q. What is a Surd? A. It is an imperfect Square, or such a number whose Square Root can never be exactly found. EXAMPLES. 1 What is the Square of 17.1? 2 What is the Square of .09 ? 3 What is the Square of .0094? 4 What is the Square Root of 4712.81261? 5 What is the Square Root of 9712.718851? 6 What is the Square Root of 3.1721812 ? 7 What is the Square Root of 1.3976121? 8 What is the Square Root of 761.801216? 9 What is the Square Root of 0007612816? 10 What is the Square Root of 4.000067121 ? Answ. 292.41 Answ. .0081 Answ. 68.649 + Answ. 98.553+ Answ. 1.78106+ Answ. 1.1822+ Answ. 27.6007+ Answ. .02759+ Answ. 2.000016+ 11 There is an army consisting of a certain number of men, who are placed rank and file, that is, in the form of a Square, each side having 472 men; I demand how many men the whole square contains? Ans. 222784 men. 12 The floor of a certain great room is made exactly square, each side of which contains 75 feet? I demand how many Square feet are contained therein? Ans. 5625 feet. 13 Suppose 12544 Soldiers are to be put into rank and file in the form of an equal square; I demand how many soldiers will be in the front,and how many deep? Ans. 112. 14 A certain square pavement contains .97 36 square stones all of the same size; I demand how many are contained in one of its sides? Ans. 414. 15 The wall of a town is 17 feet high, which is surrounded by a moat, of 20 feet in breadth; I demand the length of a ladder which shall reach from the Butside of the moat to the top of the wall ? Answer 26.2+feet. OF THE SQUARE ROOT OF A VULGAR FRAČTION. Q. How is the Square Root of a Vulgar Fraction extracted? A. Reduce the Fraction to its lowest terms. 2 Extract the Square Root of the Numerator for a new Numerator, and the Square Root of the Denominator for a new Denominator 3 If the fraction be a Surd, reduce it to a Decimal, and then extract the Square Root from it. 4 The Decimal Fractions must consist of an even pumber of places, as two, four, &e. 8192 772 Answer. ? Answer.71528+ 5 What is the Square-Root of 293? 6 What is the Square-Root of 37? Answer.72414+ OF THE SQUARE-ROQT OF A MIXT NUMBER. Q. How is the Square-Root of a mixt number extraeted? A. Reduce the Fractional part of the mixt number to its lowest term. 2 Reduce the mixt number to an improper fraction. 3 Extract the Roots of the Numerator and Denominator, for a new Numerator and Denominator. 4 If the mixt number given be a Surd, reduce the fractional part to a Decimal, and annex it to the whole number, and extract the Square-Root from the whole. EXAMPLES. 1 What is the Square-Root of 3734? 2 What is the Square-Root, of 171? 3 What is the Square-Root of 528? SURDS. Answer 63 4 What is the Square-Root of 7644? Answer 8.7649+ 5 What is the Square-Root of 77? Answer 2.7961++ |