Q. How OF DIVISION OF DECIMALS. LOW are Decimals divided? 4. As whole Numbers are. Note 1. The Decimal places of the Divisor and Quotient must always be equal to those in the Dividend. 2. If there be more Decimals in the Divisor than in the Dividend, annex as many Cyphers as you please to the Dividend, so us to be equal at least to the Divisor. 3 If Decimal Places are wanting in the Quotient, they must be supplied with Cyphers to the Decimal Point. 4. Observe the same Note here, which is given in Division of Fulgar Fractions. Q. How are the following examples to be proved? How do you reduce a Vulgar Fraction to a De 4. Divide the upper Term by the lower. Note 1. Both Terms are to be esteemed whole Numbers. By this Case, Tables containing the Decima! Parts of an Inger ure constructed. 4 Reduce 7s 6d to the Decimal of a pound. Facit 3751. 5 Reduce 10s 9d to the Decimal of a pound. .585416+.. Facit Reduce 24 Grains to the Decimal of a lb. Troy. Facit 60416664lb. 7. Reduce 14 drams to the Decimal of a lb. Avoirdupois. Facit .0546875 lb. 8. Reduce 4 C. 2 qts. to the Decimal of a ton. Facit .225 T. Facit 9. Reduce 14 C. to the Decimal of a ton. Facit .7 ton. 10. Reduce 174 drams to the decimal of an C. .0060686+ C. 11 Reduce 4 inches to the Decimal of a yard. .1111111+yard. 12 Reduce 76 yards to the Decimal of a mile. .043181+mile. Facit Facit 13. Reduce a mile to the Decimal of a league. Facit 33333333+league. 14 Reduce 3 qrs. 2na. to the Decimal of a yard. Facit .875 yd. 15 Reduce 4 perches to the Decimal of an acre. Facit ,025 acre. 16 Reduce 1 pint to the Decimal of a gallon Facit .125 gal. 17 Reduce 1 gallon of wine to the Decimal of a hhd. Facit .015873+bhd. 18 Reduce 7 minutes to the Decimal of a day. Facit .0048611+day. 19 Reduce 2 days to the Decimal of a week. Facit 2857142+ week. 20 Reduce 72 days to the Decimal of a year. Facit .1972602+ year. CASE 2. Q. How do you find the proper quantity of a Decimal Fraction in the known parts of an Integer? A. Multiply it by the common parts of the Integer. A. By Case 1. EXAMPLES. 1. What is the proper quantity of .76 of a Pound? Ans. 158 2d 1.6qr. 2. What is the proper quantity of 86 of a C. weight? Ans. 3 qrs. 12lb. 6oz. 14.592dr. 3. What is the proper quantity of .461 of a shilling? Ans 5d. 2.128 qrs. 4. What is the proper quantity of .761. of a hhd. of wine? Ans. 47 gals. 3 qts. 1.544 pt. 5 What is the proper quantity of .17 of a tun of wine? Ans. 42 gals. 3.36 qts. 6 What is the proper quantity of .761 of a day? Ans. 18 hrs. 15 min. 50.4 sec. 7. What is the proper quantity of .7 of a pound of silver? Ans. 8 oz. 8 dwts. 8. What is the proper quantity of .71 of 4 oz. of gold? Ans. 2 oz. 16 dwts. 19.2 gr. 9 What is the proper quantity of .67 of a league? Ans. 2 miles. O fur. 3 poles, 1 yd. O feet, 3 in. 1.8 b. c. 10. What is the proper quantity of .712 of a furlong? Ans. 28 poles, 2 yards, 1 foot, L1.04 in. 11 What is the proper quantity of .07 of a barrel of ale? Ans. 2 gals. 1.92 pt. 12 What is the proper quantity of .4712 of an ell English ? Ans. 2 qrs. 1.424 na. 13 What is the proper quantity of .72 of a hhd. of Beer? Ans. 38 gals. 3.52 qts. 14 What is the proper quantity of .61 of a tun of wine ? Ans. 2 hhds. 27 gals. 2 qrts. 1.76 pt. 15 What is the proper quantity of .092 of 3 acres, 2 roods ? Ans. 1 rood, 11.52 poles. 16 What is the proper quantity of .461 of a chaldron of coals? Ans. 16 bush. 2.384 pecks. 17 What is the proper quantity of .712 of 3 qrs. of corn? Ans. 17 bush. 2.816 qrs. 18 What is the proper quantity of .3 of a year? Ans. 109 days, 12 hrs. 19 What is the proper quantity of .5 of an hour? Ans. 30 min. 20 A certain Tenant hired an House for 9 years, at 12.47. per annum; how much was due at the end of the term ? Ans. 111/ 12s. Note 1. To this Case is referred Case 4 in Practice, p. 55. 2 Addition and Subtraction of Decimals of different denominations may easily be performed, after the Decimals are reduced to their proper quantities. EXAMPLES. 1 What is the sum of .481 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. 38 198 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. 80l 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. 301 5s 3d 1.44 qr. 4 If 1.47 C. of Sugar be worth 4.5l what is 1.7lb wor at that rate ? Ans 1.1d. 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 hhds. each 4 C. 2 qrs 7.4 lb ? Ans. 149/ 12s 3d 2qrš. 7 If a yard of cloth cost 12.3s what cost 3 pieces, each 21.5 yards? Ans. 397 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 48 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 40.1s 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 10l. 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 2.758 per lb. and sold them for 60 11s 6d what did he gain or lose by the bargain? Ans. he gained 8/ 12s 14 A Merchant bought 436 yards of Cloth for 8.5s per yd. and sold it again at 10.758 per yard, what did he gain by the sale thereof ? Ans. 491. Is gain. 15 A owes B 296.85/ 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 qrat 5.61 per C. which I sold out at 71 169 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 1.50z which he sold again for 3.258 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 54 Os Od Oqr. |