From Higher to Lower Denominations.-Multiply the highest denomination given, by that number which it takes of the next lower denomination to make one of this higher; add to the product the number, if any, of the next lower denomination. Proceed in like manner with the result obtained, until the whole is reduced to the required denomination. From Lower to Higher Denominations.-Divide the given quantity by the number of units of its own denomination which make one of the next higher. Proceed in like manner with the quotient thus obtained, till the whole is reduced to the required denomination. The last quotient, with the several remainders, if any, annexed, will be the answer. PROOF.-Reverse the operation; that is, reduce the answer back to the denomination from which it was derived. EXAMPLES. 1. Reduce 2 bu. to pints. 2. Reduce 172 pt. to bushels. 5. Reduce 1 bu. 1 pk. 1 qt. to quarts. 128 pt. 2 bu. 2 pk. 6 qt. 336 pt. 6 bu. 1 pk. 4 qt. 41 qt. 1200 pt. 28 bu. 5 qt. 1 pt. 790 pt. 660 bu. 1 pk. 4 qt. 1511 pk. 6 qt. 8. Reduce 12 bu. 1 pk. 3 qt. to pints. 9. Reduce 21132 qt. to bushels. 10. Reduce 24188 pt. to pecks. 11. Bought 10 bushels of plums at 5 cents a quart: what did they cost? $16. 12. Bought 8 bu. 3 pk. of blackberries at 8 cents a quart, and sold them for 10 cents a quart: how much did I gain? $5.60 13. A man sold 108 bu. 3 qt. of corn at the rate of one cent a pint: what did it bring? $69.18 14. How many bushels of wheat can be purchased for $17.30, at 2 cents a pint? 13 bu. 2 pk. 1 pt. 15. In fifteen cars of wheat containing 300 bushels each, how many quarts? 144000 qt. 16. A dealer bought a load of apples for $10.50. The price paid per bushel was 42 cents. How much did he gain by selling all at 20 cents a peck? 17. In 100000 pt. how many bushels? $9.50 1562 bu. 2 pk. 18. How many bags, each containing 2 bu. 2 pk., will be needed to contain 62 bu. 2 pk.? 25. 19. A dealer bought 40 barrels of apples, each containing 2 bu. 1 pk., at $2 a barrel. He retailed them at 30 ct. a peck: how much did he gain? $28. 20. How many pecks of potatoes in eighty-seven pints? 5 pk. 3 qt. 1 pt. 67. Avoirdupois Weight is used in weighing ordinary articles that are bought and sold by weight, such as groceries, metals, drugs by wholesale, etc. NOTES.-1. The standard avoirdupois pound of the United States is determined from the Troy pound, and contains 7000 gr. Troy. 2. At the Custom-house and in some trades, 2240 pounds are considered a ton. MENTAL EXERCISES. 1. How many ounces in one half a pound? 2. How many ounces in one quarter of a pound? How many in two quarters? How many in three quarters? 3. How many ounces in 3 pounds? In 2 lb.? In 4 lb. ? 4. How many pounds in 32 ounces? In 96 oz.? In 80 oz.? In 48 oz.? EXAMPLES. 1. Reduce 1 T. to ounces. 2. Reduce 32000 oz. to tons. 3. Reduce 325 lb. to ounces. 4. Reduce 1000224 oz. to tons. 32000 oz. 1 T. 5200 oz. 31 T. 514 lb. 5. Reduce 316450 ounces to denominations of higher orders. 197 cwt. 78 lb. 2 oz. 6. Reduce 14 T. 1512 lb. 14 oz. to ounces. 7. Reduce 360 cwt. 5 lb. to ounces. 8. Reduce 8374160 oz. to tons. 9. Reduce 14 lb. 10 oz. to ounces. 10. Reduce 17460 lb. to tons. 472206 oz. 576080 oz. 261 T. 1385 lb. 234 oz. 8 T. 1460 lb. 11. Bought 2345 lb. of hay, at one cent a pound: what did it cost? $23.45. 12. What is the cost of 3014 lb. of sugar, at 15 cents a pound? $452.10. 13. What is the cost of 20094 lb. of iron, at 4 cents a pound? $803.76. 14. A man bought 15 cwt. of lead, at 10 cents a pound, and paid for it with sugar, at 15 cents a pound: how much sugar did it take? 1000 lb. 15. At 25 cents a pound, what quantity of grapes can be bought for $450? 1800 lb. 16. How many pounds will 36 books weigh, if the weight of each book is 20 oz.? 45 lb. 17. The United States Postal Department charges 1 cent an ounce for all matter of the "third class." What would be the postage on a parcel of this nature weighing 3 lb. 3 oz.? 18. Reduce 171 T. to ounces. 19. Reduce 2 T. 12 cwt. 8 lb. 4 oz. to ounces. 20. In one load of hay there were 1480 other, 1520 pounds. How much in both? 51 ct. 560000 oz. 83332 oz. pounds; in an 1 T. 1000 lb. NOTES.-1. The yard is the standard unit of length. The standard yard for the United States is kept at Washington. A copy is deposited at the capital of each State. 2. The yard and its subdivisions are used in measuring cloth, ribbon, lace, etc. MENTAL EXERCISES. 1. How many inches in 2 feet? In 4 ft.? In 3 ft.? In 5 ft.? 2 How many feet in 48 inches? In 72 in.? In 120 in.? In 96 in.? 3. How many feet in 5 yards? In 7 yd.? In 6 yd.? In 12 yd.? 4. How many yards in 12 feet? In 21 ft.? In 18 ft.? In 27 ft.? 5. How many yards in 5 rods? |