FRACTIONAL PARTS OF NUMBERS Finding what part one number is of another. 1. What part of 1 is 2? What part of 4 is 3? of 6 is 5 ? Express the answers also in the form of division. Thus, į= 1+ 2; 4= 3 = 4; 5 = 5 +6. 2. What part of is ? of is 4? = }=2+3 = 3; 4- 5 = 4+5=1. How, then, can you find what part one number is of another? Divide the smaller number by the larger number. Written Work 1. What part of 108 is 48 ? We divide the smaller number 48 4 48 by 108, which gives the fraction 48 : 108 108 4. This reduced to its lowest terms equals . 2. What part of 41 is & ? 9 3 9 3 2 1 We reduce the mixed number to 41 24 6 the improper fraction f. We then 2 divide by as in example 1, page 173. The result is 3. What part of : = 21 х 3. 48 is 36 ? 5. 117 is 104 ? 7. 4 is ? 4. 96 is 16 ? 6. 144 is 128 ? 8. 14 is 11? 9. If John had 60 cents and spent 20 cents, what part of his money did he spend ? 10. The distance between two stations is 72 miles. What part of the distance are 18 miles ? 11. What part of a yard are 18 inches ? 12. Ruth draws a line on the blackboard } a foot long and Martha draws one ; of a foot long. What part of the length of Martha's line is the length of Ruth's ? Finding a number when the value of a fractional part of the number is given. 1. What is the number of which 4 is 3 ? If 4 of the number, i of the number, or the number, = 2 x 4, or 8. 2. 6 is of what number? If 6 is two thirds of a number, one third of the number equals one half of 6, or 3, and three thirds of it or the number equals 3 x 3, or 9. 3. 8 is of what number? 5. 21 is of what number? 4. 9 is of what number? 6. 64 is g of what number? = Written Work 1. 240 is of what number? 80 Since 240 is of a number, of 3 4 the number equals 1 of 240, and 4 of it equals of 240, which is 320. 240 = Divide the number by the fractional part. 2.965 is of what number? 5. 909 is % of what number? 3. 872 is of what number? 6. 672 is I of what number? 4. 342 is of what number? 7. 539 is 12 of what number? 8. A boy sold 32 newspapers, which was of the number he had to sell. How many did he have at first ? 9. The admissions to a fair, which were of the total receipts, amounted to $135. What were the total receipts ? 10. One year 220,000 Italians arrived in the United States. If they were id of all the immigrants, how many immigrants arrived that year ? REVIEW OF FRACTIONS 1. The sum of two fractions is 1. One fraction is ; what is the other? 2. The product of two fractions is f. One fraction is 1}; what is the other? 3. If of an acre of land costs $ 45, how much will 5 acres cost? 4. A boy, after spending of his money, had $1.60 remaining. How much money had he at first? 5. If butter is selling at 28 cents a pound, how much will 31 pounds cost? 6. A man owned of a farm and sold } of his share for $1250. At that rate how much was the whole farm worth? 7. If 12 acres yield 120 bushels of potatoes, how many bushels will 3 acres yield at the same rate? SUGGESTION. - 3 are how many times 11? 8. Compare and į ; and ; 4 and 1. 9. At 162 cents a pound, how many pounds of meat can be bought for $1? $2? $4? $5? 10. What part of 60 is 10? 15? 20? 40? 11. I sold a bicycle for $15; this was of what I paid for it. How much did I pay for it? 12. If 20 dozen eggs are worth $5.60, how much are 50 dozen worth? 13. If a telegram of 10 words costs 25 cents, how much will a telegram of 30 words cost at 2¢ for each extra word ? 14. Compare 6 and 18; 8 and 48; 36 and 12. 15. How does a city lot worth $6000 compare with another worth $5000? 16. If James's age is 16 years and his father is 21 times as old, what is the difference in their ages? James's age is what part of his father's? 17. How much will 9 lemons cost at the rate of 40 cents a dozen? How much will 11 dozen cost? 3 dozen? 18. A field is 40 rods long. The width is of its length. What is the distance around the field ? 19. A traveler walked 251 miles the first day, 304 miles the second day, 294 miles the third day, 273 miles the fourth day, and 25 miles the fifth day. How far did he travel in the 5 days, and what was his average rate per day? 20. An errand boy receives $4 a week. In how many weeks can he earn enough to pay for a pair of shoes at $24, a suit at $ 10, a hat at $11, and 3 shirts at $ each ? 21. Divisor 25%; quotient 200. Find the dividend. 22. Multiply the sum of 41 and 3 by 8. 23. At $14 a yard, how many yards of Brussels carpet can be bought for $30? 24. A lady bought 127 yards of muslin at 8 cents a yard, 41 yards of ribbon at 4 cents a yard, 8 yards of dress goods at 75 cents a yard, and gave in payment a ten-dollar bill. How much change should she receive ? 25. The sum of three numbers is 418; the first is 1981, and the second 2063. What is the third ? 26. Mr. Jones sold of his farm for $8890. At the same rate what was the value of the remainder? 27. Mr. White paid $2700 for a three-eighths interest in a store. How much was the entire store worth? 28. A teacher spends $ 1062.50 a year, which is of his salary. How much is his salary? 29. A dealer bought 960 bushels of wheat at 84 cents a bushel. He sold I of it at 88 cents a bushel, of it at 87 cents a bushel, and the remainder at 89 cents a bushel. What was his entire gain? 30. Compare j and ; and b; 2 and 1. 31. Thomas buys a necktie for $1, a pair of gloves for $13, and 2 shirts at $$ apiece. How much change should he receive from a five-dollar bill? 32. If a man's wages are $3] a day, and his daily expenses $14, how many weeks of 6 days each must he labor to save $105? 33. Two men are 29 miles apart and travel toward each other, the one at the rate of 31 miles an hour and the other at 34 miles an hour. In how many hours will they meet? 34. Find the cost of 74 pounds of mackerel at 16 cents, 61 pounds of codfish at 12 cents, and 6 cans of salmon at the rate of 2 for a quarter. 35. What is the cost of 80 pounds of sugar at 644, 484 pounds of tea at 36%, and 124 pounds of coffee at 16¢? What is the cost of 21 pounds of coffee at 28%, ) pound of pepper at 248, 38 pounds of butter at 28%, and 17 gallons of vinegar at 32¢? 37. Mrs. Baker willed to her daughter of her estate, which amounted to $2400. To her son she left of her estate, and the rest to her sister. How much did the son and the sister each receive? 38. A man spent $22}; then earned $18.75, and then had $50. How much had he at first? 39. What is the cost of 3 barrels of sugar weighing 300 pounds, 310 pounds, 312 pounds, respectively, at 52¢ a pound ? 36. |