DECIMAL TABLES OF WEIGHTS AND MEASURES, CLOTH MEASURE.--Quarters, and nails reduced to the deco imal of a yard. qr. dec, 1 is 25 3 is •75 1 is .0625 3 is •1875 Q" 2. " •125 na. na. Time.---Days reduced to the decimal of a year, allowing 365 days to a year. days. dec. days. dec. days: dec. days. dec. | 1 is •0027+1 6 .is 3 .01637 20.is •05467 70 is •19111 %" •00457 7 “ •01917 30.“ •0819+ 80.“ .21847 3 •0081 | 8 -02187 40 « •1092ti 90' 24577 4.'" •010911 96.0245+ 50 16.6 •13657|100 •27301 5.“ .01361|10" •02737 60“ .1638+|110“ •3003 lin. dec. dec. LONG MEASURE.---Links reduced to the decimal of a rod, allowing 25 links to a rod. lin. lin. dec. lin. dec. 1 is .04 6 is •24 11 is •44 .64 2 •08 7 •28 12 •48 17 •68 3 •12 8 •32 •72 •16 9 .36 14 6 56 19 •76 56.20 110 40-- 115. « •60 20 •80: 16 is USE OF THE PRECEDING TABLES. If it were required to reduce 3 qrs. 17 lb. 6 oz. to the decimal of an hundred weight; look in Avoirdupois weight you will find 3 qrs. to be ·75 which take off; then look for 14 lbs. (the table not being carried so high) look for 14 lb. and 3 lb. the decimals of which take off; then look for 6.oz, and take off its decimal; and add the several decimals together the sum will be the decimal sought: is •75 14 Ib. 3 qr: • 125 3 lb. 10267 6 OZ. .9050 Ans. REDUCTION. DEFINITION.Reduction teaches to reduce one denomination to another, and retain the same value. REDUCTION DESCENDING, Reduction is called 'descending when it is required to reduce a larger to a smaller denomiņation, and it is then performed by multiplication. RULE. Multiply the highest denomination given, by such a number as will reduce it to the next lower, observing to bring in the parts of the same name, thus continue till you have reduced it to the de. nomination required. Examples dols.cts.m. 100 44416 cts. 10 Ans. 444165 mills.. 2. In 57 dollars. 93-cents 5 mills, how many mills? Ans. 57935 mills. 3. In 4 cwt. 2 qrs. 20 lb. how many pounds, Avoirdupois weight? Ans. 524 lb. 4. In 20-acres, 29 rds. how many square rds.? Ans. 3229 rds.' 5. How many inches from Exeter to Dover; it being 18 miles ? Ans. 1140480 in, 6. How many inches will reach round the world ; it being 360 degrees, each degree containing 69 miles ? Ans. 1585267200 in. 7. How many solid feet in 20 cords of wood ? Ans. 2560 sd. ft. Ans. 2016 pts. 8. How many pints are in 1 tun of wine? 9. How many hours in 32 years, 2 months 12 days; allowing 13 months to a year? Ans. 289920 h. 10. In 29 yards, 2 quarters, 3 nails, how many Dails? Ans. 475 na. REDUCTION ASCENDING. DEFINITION.--Reduction is called ascending when it is required to reduce a smaller, to a larger denomination; and it is then performed by division. Rule. Divide the given denomination by such a number as will make one of the next higher ; and the last quotient by such a number as will make one of the next, &c. until you have reduced it-tothe denomination required. Examples. 10)444165 10) 441 dimes 6 cts. Ans. 444 dol. 16 cts. 5 m. Ans. $57. 93 cts. 5 mo Ans. 4 cwt. 2 qrs. 20 lb. 14. In 3229 rods, how, many acres, square meas Ans. 20 acres, 29 rods. 5. In 1140480 inches, how many miles, long measure ? Ans. 18 miles. 6. In 1585267200 inches how many degrees, each containing 69 miles?. Ans. 360 deg 7. How many cords of wood are in 2560 solid feet? ure? Ans 20, cords. th qu be 8. In 2016 pints of wine, how many tuns. Ans. 1 tun: 9. In 289920 hours, how many years ; allow. ing 13 months to a year? Ans. 33' years, 2 mo. 12 d. 10. In 475 nails, how many yards? Ans. 29 yds. 2 qr. 3. Dai 1 the N of a for a dols the got COMPOUND DIVISION. DEFINITION. Compound Division teaches, by having the price of several things given, to find the price of one. CASE I. When the quantity is an even number: RULE..Divide the price by the quantity, (if there are decimals in the price, point them off according to the rule of division of decimals) the quotient will be the price of one, in dollars and parts. Examples. 1. If 24 bushels of rye cost 821, how much is 1 bushel of it worth? Dol. Cts: 2. If 340 bushels of rýe cost 8456-25 cts. I demand the price of 1 bushel ? Ans. 81, 341346 3. If 2020 lb., of cheese cost 8.181.80 cts. what did it cost per pound? Ans. $0:09 cts. CASE 11. quantity, such as cwt. gr. &c. RULE.Reduce the smaller denominations to the deco imal of an cwt. (by case 2d in reduction of decimals) then divide the price by the quantity, as in case ist; the quotient, pointed according to the rule of decimals, will be the answer, Examples 1. If 2 cwt. 3 qr. of sugar cost $45.26 cts. I demand the price of l twt. Cwt. gr. cwt. D. cts. Note.--In this question 3 qr. reduced to the decimal of a cwt, is equal to •75, which I annexed to the 2 cwt. for a divisor; and divided $45.26 cts, by it, and got 16 dols. in the quotient; I then annexed three cyphers to the remainder, and continued the division, and thereby got the remaining part of the quotient, viz. 458,175 2. If 15 cwt. 2 qr. of rice were sold for $54.25 cts, ; I demand the price of 1 cwt. Ans. $3.5 dimes. 3. If 3 cwt. 2 qr. 14 lb, of iron cost $16.6705 ; I dea mand the price per cwt. Ans. $4.6 dimes. CASE III. When Cout. grs. and lb. are given to find the price per 1b. RULE. Find the price per cwt. by case ad ; then di.. vide the price per cwt, by 112, the quotient will be the price per Ib. Examples. 1. If 3 cwt, 2 gr. 14 lb. of iron cost $16.67 cts, 5 m. I demand the price per pound. Cwt.qr. 16. D. c. m. D. d. 3 2 14=3•625)16.675(4.6=1123041 Tit. Ans. 1 4500 czot c. m. 21750 21750 2. If 20.cwt. 3 qrs. 14 lb. of iron, cost $43-50 cts. what did it cost per lb, ? Ans, 03 sts, st m. |