DUODECIMALS. Duodecimals are parts of a foot, the denominations of which increase continually by 12. Ruie. Add as in Compound Addition, and carry one for 12 to the next denomination. Question. How is addition of duodecimals performed? every 3. Three boards measure as follows, 16Ft. 8in., 14Ft. 6in., 17Ft. 9in. 2′′, how many feet do they contain? Ans. 48 Ft. 11in. 2". SUBTRACTION OF DUODECIMALS. Perform the operation as in compound subtraction carrying 12 when necessary. 3. If from a room measuring 475Ft. 7in. 2" I partition off 81Ft. 2in. 5" 10" 6"""', how long will the room still be? Ans. 394 ft. 4in. 8"' 1''' 6'''' MULTIPLICATION OF DUODECIMALS, Case 1. When the feet of the multiplier are not more than 12. Rule. 1. Set the multiplier in such a manner that the feet thereof may stand under the lowest denomination of the multiplicand, and in multiplying carry one for every 12 from one denomination to another, and place the result of the lowest denomination in the multiplicand under its multiplier. Case 2. When the feet of the multiplier exceeds 12. Rule. Multiply by the component parts as in compound multiplication and take parts for the inches as in practice. Questions. By what rule do you work in inultiplication of duodecimals when the feet in the multiplier do not exceed 12? How do you proceed when the feet of the multiplier exceeds 12? Examples. 1. Multiply 5Ft. 6in. by 2Ft. 4in, Ft.in. 24 1 10 0 11 O Ft. 12 10 0 Ans. 2. Multiply 54Ft. 10in. by 5Ft. 7in. Ans. 306 ft. lin. 10′′ 3. What is the contents of a door measuring in length 6 Ft. 9in. 3′′, and in width 3Ft. 5in. Ans. 23 ft. lin. 7" 3"" Case 2. 1. Multiply 208 Ft. 8in. 4′′, by 24Ft. 3in, 9′′.` in. Ft. in. " 2. A partition is 81 Ft. 10in. 4" long and 14Ft. 7in. 5" high, how many yards does it contain? Ans. 132yd. 11 ft. 4in. 10" 3. How many square feet of roof will 1000 shingles cover, when the shingles are 2Ft. 5in. 7′′ 2′′ in length, and 5in. 3" 6" 5"""' in width? Ans. 1094 ft.2in. 4′′ 11′′ 5"'" PROMISCUOUS EXAMPLES. 1. A. is 25 years old, B. 15 years older than A. and C. is 12 years older than B., the ages of B. and C. are required? Ans. B. 40 years C. 52 years. 2. A. B. and C. have 220 dollars 50 cents and are desirous to share it in the proportion of A., B., and C. the rest, but B. is willing his share shall be divided equally between A. and C., it is required what will A. B. and C. receive individually according to the first proportion, and what will be the shares of A. and C. each after B's. relinquishing his share? Ans. A. will receive $44.10, B. $36.75, C.8139.65, A. will receive after B. relinquishes, B. $62.47 5 3. A person sells a piece of cloth at 56 dollars 25 cents and thereby loses 7 per cent. what was the first cost? Ans. $60.81. 4. If A. travel by mail at the rate of 8 miles an hour, and when he is 50 miles on his way, B. start from the same place that A. did, and travel on horseback the same road at 10 miles an hour, how long and how far will B. travel to come up with A.? Ans. 25 hours, and 250 miles. 5. Bought a quantity of cloth for 750 dollars, 5 of which I found to be inferior which I had to sell at 1 dollar 25 cents per yard, and by this I lost 100 dollars, what must I sell the rest at per yd. that I shall lose nothing by the whole? Ans. $3.151. 6. If 1000 bricks lie 6 inches from each other in a straight line and a person be employed to gather them up one by one, and place them on a pile which is one foot from the first brick, how far will he have walked when he shall have placed the last brick on the pile? Ans. 94M. 7 fur. 186yds. 2 ft. 7. Three bricklayers A. B. and C. can raise the walls. of a house in 20 days, B. C. and D. in 24, C. D. and A. in 30, and A. B, and D. can do it in 36 days, in what time can A. B. C. and D. do it together, and in what time can each do it by himself? Ans. 197 Together, A. 108 days, B. 3615 days, C. 434 days, D. 1080 days. 8. If I would exchange 1055l. 15s. for dollars at 9s. per piece, ducats at 11s. 4d. per piece and crowns at 12s. 2d. per piece, and would have 6 dollars for 4 ducats and 3 dollars for 4 crowns, haw many of each sort must I have? $1111 7 Ans. ducats 511, 21 crowns 400. 9. A. and B. dissolve partnership and equally divide their gain, A's share which was 332 dollars 50 cents lay for 21 months, B's. for 9 months only, the adventure of B. is required? Ans. 775.83. 10. If 4 years should be added to a lease of 12 years yet to come, the advance rent being 720 dollars 25 cents per annum, what should be paid down for the additional 4 years, discount being allowed at 5 per cent. per annum, compound interest? Ans. 1422.14 8m. 11. A gate-keeper is to receive 6 cents for every wagon, 4 cents for every gig, 2 cents for every horseman, and 1 cent for every footman that passes the gate, at the year's end he found that 3150 gigs had passed, and that 7 gigs passed when 5 wagons did, and 4 horsemen passed when 6 footmen did and 5 footmen passed when 3 gigs did what number of wagons, horsemen, and footmen passed, and how much did the gate-keeper receive? Gigs Ans. Footmen 3150. 2250. 5250. 3500. Amount of toll $383.50. 12. If a water hogshead holds 110 gallons, and the pipe which fills the hogshead discharges 15 gallons in 3 minutes and the tap will discharge 20 gallons in 5 minutes, and these were both left running one hour, how many gallons would the hogshead contain, and if the tap was then stopped in what time would the hogshead be filled? Ans. 60 gallons, and filled in 10 min. |