Solution.--1 yard will cost of or dollars. Explanation: is to be divided into 3 equal parts. Each part will be, for 4+z+3. 2. At 2 dollars a pound what part of a pound of packing can be bought for of a dollar? Solution. For 1 dollar a pound can be bought. For of a dollar of a pound or of a pound can be bought. Then, for of a dollar, 3 times, or of a pound, can be bought. 3 Explanation: Were it required to find how many pounds at $2 per pound could be bought for $6, then 6 would be divided by 2. Hence, to find what part of a pound $3 will pay for, must be divided by 2. To divide by 2, multiply the denominator. 3. At of a cent per apple, how many apples can be bought for 4 cents? Solution. For of a cent an apple can be bought. Then for or 1 cent, 3 times, or apples, can be bought. Hence, for 4 cents, 4 times & apples can be bought, or 6 apples. 4. At of a cent for 1 apple, how many apples can be bought for of a cent? Solution. For of a cent, an apple can be bought, cent, or 1 cent, of an apple can be bought. Then for and for 3 of a of a cent, of , or of an apple, can be bought, and for å of a cent 3 times, or of an apple, can be bought. g equals 14. 5. Divide by 4. Solution.- is the same as of 4. divided by 4 is. Then, divided by of 4 is 5 times, or 18. 15 RULE: Invert the terms of your divisor and proceed as in multipli cation. NOTE.-Express integers in the form of fractions. Reduce mixed numbers to improper fractions. Indicate the operation and apply rule for cancellation whenever practicable. 5. If 4 yards of toweling for grease extractors cost of a dollar, what will 1 yard cost? Answer, $3. 6. At a cent each, how many apples can be bought for 3 cents? Answer, 6. 8. At of a dollar per gallon, how many gallons of oil can be bought for? Answer, 43. 10 9. If 1 orange cost 3 cents, what part of an orange can be purchased for a cent? Answer . 10. At of a dollar per yard, how many yards of cloth can you buy for $6? Answer, 8. 11. At of a dollar per foot, how many feet of cable can you buy for of a dollar? Answer, 34. 83143-13- 4 12. If 7 pounds of iron washers cost of a dollar, what will 1 pound cost? Answer, $25. 13. Divide 4 by 11. Solution. Reducing 4 and 13 to improper fractions, we have and Dividing by the result is 27, or 3. 14. Divide 2 by 6. Answer, 3. 15. Divide 22 by 54. 16. Divide 2 by 17. Divide 44 by 8. 18. Divide 6 by 23. 19. Divide of by 16. Answer, 4. 1 × 2 × 4 × 5 2 × 3 × 3 × 4 Explanation: Invert the terms of both and as in the case of the divisor being a common fraction. 20. Divide of & by of 4. 21. Divide of 5 by of 17. 5 22. Divide of 3 of 12,8% by 18 10 41 Answer, 113. 23. Divide of by of of 5. Answer, . 24. Divide of of 12 by of 41 of 20. Answer, 12. 10 XXVII. What part one number is of another is found by division. Solution.-1 is of 3. Then, 2 is 2 times, or 3. XXVIII. Complex fractions are reduced to simple fractions by division. Solution.-Reducing 14 and 23 to improper fractions we have & and 3. Dividing by the result is 18. 15 2. Reduce to a simple fraction. Answer, 39. 3. Reduce to a simple fraction. Answer, . 2 6 4. Reduce to a simple fraction. Answer, 11. 3 31 5. Reduce to a simple fraction. Answer, 174. 45 52 97 to a simple fraction. Answer, . 8. Reduce to a mixed number. Answer, 4. 227 9. Reduce to a mixed number. Answer, 15. 58 10. Reduce to a simple fraction. Answer, 12. MISCELLANEOUS EXAMPLES. 517 1. At dollar per pound, how many pounds of packing can be bought for $34? Answer, 61. 2. At of a dollar each, how many monkey wrenches can be bought for $23 Answer, 35. 3. At 34 dollars each, how many micrometers can be bought for $414 ? Answer, 11. 4. By what must be multiplied that the product may be 10? Answer, 26. 8. There were 793 tons of coal burned in 6 boilers in 211⁄2 hours. How much was burned in each boiler per hour? Answer, 33. 238 9. The revolution counter at the end of an hour registered 10,115 revolutions of the shaft. The engine had been run 59 minutes. What was the average revolutions per minute? Answer, 170. 10. A piece of work tapers inch in 12 inches. What is the taper per inch? Answer, 2. 11. A-inch steel plate containing 24 square feet weighs 48312% pounds. What is its weight per square foot? Answer, 2012 12. A man, in shaping a piece of work with a planer, regulated the machine so that at each cut of the tool a chip of inch was taken. The surface of the work to be planed measured 24 inches by 36 inches. The work was clamped lengthwise of the table. How many times must the table travel back and forth under the tool to plane the whole surface? Answer, 384 times. 13. How many rivets are contained in a keg containing 1593 pounds? All rivets are the same size and weigh of a pound each. Answer, 850 rivets. 16 14. If 60 barrels of machine oil cost $6144, how much will 1 gallon of the oil cost? Answer, 32 cents. 15. A ship can make 19 miles per hour. How many hours will it take to make a journey of 2493 miles? Answer, 1339 hours. 16. What is the average weight of a bag of coal if 27 bags weigh 17,7083 pounds? Answer, 655 pounds. 17. Four men, in emptying a bunker of 87 tons of coal, shovel 11 tons per hour. How long will it take them to empty the bunker? Answer, 748 hours. 18. A tank contains 5677 gallons of oil. How many days will it last if 23 gallons are used each day? Answer, 24 days. 19. The stroke of an engine is 2 feet. How many revolutions of the shaft will it take for the piston to travel a mile? Answer, 1,200 revolutions. 20. How many steps will it take to walk 1 mile if each step is 21 feet long? Answer, 2,112 steps. FRACTIONAL COMPOUND NUMBERS. 7 1. Add $161, $91, $5, $218. Answer, $33%. 2. I paid for books $94, for paper $416, for a slate $3, for pens $13. What amount did I expend? Answer, 15%. 3. Having $504, I paid a bill of $273. How much had I left? Answer, $231. 4. From $32.324 take $15.12. Answer, $17.194. 5. From $5.814 take $1.183. Find the cost of Answer, $4.624. 6. 9 gauge glasses at 12 cents each. Answer, $1.12. 7. 21 tons of coal at $64 per ton. Answer, $1314. 8. 15 pounds packing at $3.184 per pound. Answer, $47.814. 9. 5 yards of linen at $0.62 10. 12 pounds of line at 18 11. 13 copper gaskets at 16 per yard. Answer, $3.434. 12. 17 dozen books at $3.75 per dozen. Answer, $66.25. 13. At 18 cents per yard, how many yards of muslin can be bought for $2.25? Answer, 12 yards. 14. At 37 cents per dozen, how many dozen pencils can you buy for $5.814? Answer, 15 dozen. 15. If 5 yards of cloth cost $11.564, what will 1 yard cost? Answer, $2.314. 16. Seven men share equally $31.064. What is the share of each man? Answer, $4.433. 17. Reduce 5 miles to inches. Answer, 316,800 inches. 18. Reduce 2 miles, 2 rods, 2 feet, to feet. Answer, 10,595 feet. 19. In what time will a body move from the earth to the moon, at the rate of 31 miles per day, the distance being 238,545 miles? Answer, 21 years, 30 days. XXIX. A fraction is reduced to lower denominations by multiplication. 1. Reduce 24 peck to the fraction of a pint. Solution. To reduce of a peck to the fraction of a pint, multiply by 8 and by 2. The result is of a pint. 2. Reduce 3. Reduce of a bushel to the fraction of a quart. Answer, . of a pound to the fraction of an ounce. Answer, 4. 4. Reduce of a rod to the fraction of a foot. Answer, 28. 28 20 7 33 5. Reduce 1280 of an acre to the fraction of a square rod. Answer, J. 6. Reduce of a dollar to the fraction of a cent. Answer, . 7. Reduce of a day to the fraction of a minute. Answer, 11. 1584 XXX. In reducing a fraction to a lower denomination, when the result is a mixed number, proceed only with the reduction of the fractional part. This is called finding the value of a fraction in integers. 1. Find the value of of a day in integers. Solution. To reduce of a day to hours, multiply by 24. The result is 9 hours. To reduce of an hour to minutes, multiply by 60. The result is 36 minutes. of a day is, then, 9 hours 36 minutes. 2. Reduce quart to the fraction of a bushel. Answer, 4. 3. Reduce foot to the fraction of a rod. Answer, 185. 4. Reduce 5. Reduce 6. Reduce 7. Reduce 8. Reduce 3 Answer, 1280 ounce to the fraction of a pound. pound to the fraction of a ton. pint to he fraction of a bushel. Answer, 320. ounce to the fraction of a hundredweight. Answer, 2. inch to the fraction of a rod. Answer, 24. 2800. 9. Reduce & minute to the fraction of a day. Answer, 1620 10. Reduce ounce to the fraction of a hundredweight. Answer, 35340 2 XXXI. To find what part one compound number is of another, reduce them to the same denomination and proceed as in Article XXVII. 1. 2 feet 3 inches is what part of a yard? 2 ft. 3 in. =27 in. Solution.-2 feet 3 inches equals 27 inches. 1 yard equals 36 inches. 27 inches are 7 of 36 inches. 3 equals 3. 37 2 feet 3 inches then is of 1 yard. 3 2. 2 feet 6 inches is what part of 6 feet 8 inches? Answer, . 3. 2 pecks 4 quarts is what part of a bushel? Answer, 4. 2 yards 9 inches is what part of 8 yards 2 feet 3 inches? An 9 swer, 35 5. What part of a day is 13 hours 30 minutes? Answer, 1. 6. What part of a mile is 145 rods? Answer, 22. а 8 7. What part of a yard is 2 feet 8 inches? Answer, §. 8. What part of a pound is 73 ounces? Answer, 4. 9. 2 quarts 1 pints is what part of 1 bushel 1 quart 13 pints? Answer, 2. 16 10. 1 yard 1 foot 1 inches is what part of 3 yards 2 feet 89 inches? Answer, 1918. 5423 |