E REDUCTION. 167. Reduction is the process of changing a number from one denomination to another without altering its value. 168. Reduction Descending is changing a number of one denomination to another denomination of less unit value, and is performed by multiplication; thus: $1 = 10 dimes = 100 cents = 1000 mills; 1 yard 3 feet = 36 inches. 1. Reduce 6 gal. 2 qt. 1 pt. to pints. OPERATION. 6 gal. 2 qt. 1 pt. 4 26 qt. 2 Ans. 53 pt. ANALYSIS. Since in 1 gal. there are 4 qt. in 6 gal. there 4 qt.X6-24 qt and the 2 qt. in the given number, added, makes 26 qt. in 6 gal. 2 qt. Since in 1 qt. there are 2 qt. in 26 qt. there 2 pt. X 26-52 pt. and the 1 pt. in 53 pints in the given com the given number added, make pound number. As either factor may be used as a multiplicand, ( 61 ), we may consider the numbers in the descending scale as multipliers. Hence the following RULE. I. Multiply the highest denomination of the given compound number by that number of the scale which will reduce it to the next lower denomination, and add to the product the given number, if any, of that lower denomination. II. Proceed in the same manner with the result obtained in each lower denomination, until the reduction is brought to the denomination required. EXAMPLES FOR PRACTICE. 2. In 8 lb. 10 oz. how many ounces? Ans. 138 oz. Ans. 2961d. 6. In 18s. 8d. 3 far. how many farthings? Ans. 899 far. 7. Reduce 3 lb. 9 oz. 12 pwt. to pennyweights. Ans. 6060 min. 10. Reduce 10 bu. 1 pk. 6 qt. to pints. Ans. 1308 pt. 11. Reduce 14 A. 3 R. 20 13. Reduce 4 yr. 7 mo. to hours. 14. Change 2 T. 11 cwt. to pounds. Ans. 39600 hr. Ans. 5100 lb. 15. Change 9 lb. 9 oz. 10 pwt. to grains. 16. Change 5 lb. 63 43 20 10 gr. to grains. 17. Change 3 mi. 6 fur. to feet. 18. In 40 chains how many links? Ans. 19800 ft. Ans. 4000 1. 19. In 28 sq. rd. 12 sq. yd. 4 sq. ft. how many square inches? X20. In 16 A. 4 sq. ch. 8 P. 80 links? Ans. 1113840 sq. in. sq. 1. how many square Ans. 1645080 sq. 1. Ans. 2224 pt. Ans. 2016 qt. 21. In 12 tons of round timber how many cubic inches? 22. In 8 bbl. 26 gal. how many pints? 23. Reduce 4 pipes to quarts. 24. Reduce 23 bu. 3 pk. to pints. 25. Reduce 8 S. 18° 40′ to minutes. 26. Reduce 15° to seconds. 27. Reduce 2 months to minutes. Ans. 1520 pt. Ans. 15520'. Ans. 54000". Ans. 86400 min. 28. Change 2 reams 10 quires to sheets. 29. In 40 score how many single things? Ans. 800. 30. In 14 great gross how many dozens? B1. In 30° 20′ 24" how many seconds? 32. In the 3 Autumn months how many hours? 33.. In the three Summer months how many minutes? 34. In 75 cords how many cubic feet? 169. Reduction Ascending is changing a number of one denomination to another of greater unit value, and is performed by Division; thus, 1000 mills 100 cents $1. 1. Reduce 53 pints to gallons. OPERATION. 2)53 4)26 qt.+1.pt. 6 gal.+2 qt.. Ans. 6 gal. 2 qt. 1 pt. = ANALYSIS. Dividing the given number of pints by 2, because there are as many quarts as pints, we obtain 26 qt. plus a remainder of 1 pt. We next divide 26 qt. by 4, because there are as many gallons as quarts, and we obtain 6 gal. and a remainder of 2 qt. This last quotient, with the several remainders annexed, forms the answer. 2. Reduce 4902 inches to rods. have 33 halves. Then dividing 816 by 33 we obtain 24 rd. plus a remainder of 24 halves to 12 ft. which, with the preceeding remainder annexed to the last quotient, gives the answer. RULE. I. Divide the given number by that number of the scale which will reduce it to the next higher denomina-. tion. II. Divide the quotient by the next higher number in scale; and so proceed to the highest denomination required. The last quotient, with the several remainders annexed in a reversed order, will be the answer. EXAMPLES FOR PRACTICE. 3. How many pounds in 3460 ounces? Ans. 216 lb. 4 oz. 4. How many shillings in 556 farthings? 5. How many yards in 1242 inches? Ans. 11s. 7d. Ans. 4 lb. 1 oz. 1 pwt. 3 gr. 8. Reduce 1597 quarts to bushels. Ans. 49 bu. 3 pk. 5 qt. 9. Reduce 107520 oz. avoirdupois to pounds. 10. In 28635 sec. how many hours? Ans. 7 hr. 57 min. 15 sec. 11. In 10000" How many degrees? Ans. 2o 46' 40". 12. In 11521 gr. apothecaries weight how many pounds? Ans. 2lb 1 gr → 13. In 3561829 seconds how many weeks? 14. Reduce 67893 cu. ft. to cords. Ans. 160 A. Ans. 160 mi. 15. In 1491 pounds how many hundred weight? 22. In 4060 how many score? 23. Reduce 1435 feet to fathoms. Ans. 6 bbl. Ans. 12 gross. Ans. 203 score. 24. Reduce 10000 sheets of paper to reams. Ans. 20 reams 16 quires 16 sheets. 25. Reduce 27878400 sq. ft. to square miles. PROMISCUOUS EXAMPLES IN REDUCTION. 1. Reduce 4 dollars 67 cents to cents. Ans. 467 cents. Ans. $3.724. Ans. $96.90. Ans. 8000 mills. 6. In 3 lb. 4 oz. 7 pwt. how many grains? 7. In 3 tons of cheese how many pounds? 8. How much will 4 cheese cost, each weighing 36 pounds, at 9 cents a pound? Ans. $12.96. 9. How much would 2 lb. 8 oz. 12 pwt. of gold dust be worth, at 72 cents a pwt.? Ans. $469.44. 10. Bought 1 T. 15 cwt. 36 lb. of sugar at 7 cents a pound; how ch did it cost? Ans. $247.52. 11. Paid $25.50 for one hogshead of molasses, and sold it all at 50 cents a gallon; how much was the whole gain? 12. How many pounds in 6 barrels of flour? 13. How many bushels of oats in a load weighing 1280 pounds? Ans. 40 bu. 14. How many bushels of wheat in a load weighing 2175 pounds? Ans. 36 bu. 15 lb. 15. A grocer bought 3 barrels of flour at $6 a barrel, and sold it out at 4 cents a pound; how much did he gain on the whole ? Ans. $5.52. \16. In a board 12 feet long and 2 feet wide, how many square feet? Ans. 24 sq. ft. 17. In a block of marble 6 feet long and 3 feet square, how my cubic feet? Ans. 54 cu. feet. 18. In a pile of wood 26 feet long 6 feet high and 3 feet wide, how many cubic feet? how many cords? Ans. 468 cu. ft.; or 3 Cd. 84 cu. ft. |