26. 18-71. 25. 431÷9. 27. 56÷18. 29. 3÷2×31. 28. 8 of 34. 30. of 887,8%. will produce 644 ? 31. What number multiplied by 32. What number divided by 123 will give 93? 33. The dividend is 4 times 33, the divisor of 70; what is the quotient? 34. If 175 bushels of potatoes are raised on 21 acres, what is the average yield an acre? 35. At $ a pound, how many pounds of tea can be bought for $37? For $28? For $404? 36. At $4 a bushel, how many bushels of clover-seed can be bought for $174? For $3743? For $758? 37. If 1 man consume of a pound of meat, how many men will consume of 93 pounds? of 32 pounds? 38. At $14 a bushel, how many bushels of wheat will pay for of a barrel of flour, at $10 a barrel? 39. If 9 bushels of corn weigh 528 pounds, what is the average weight of a bushel? 40. How many pounds of coffee can be bought for $45}, at $3 a pound? At $? At $? At $5? 10 16 41. If of a lot is worth $1200, what is the whole worth? 42. How many tons of hay, at $164 a ton, will $2031 buy ? 43. How many acres of land will $2187 purchase, at $1314 an acre? At $843? At $757? 44. If a man spend $3 a day for cigars, in what time will he spend $25? $50? $125? $75? 45. Allowing 13 bushels to an acre, how many acres can be sown with 1564 bushels of wheat? 112 bushels ? 46. If of a farm cost $3155, what is the cost of the whole? Find the value of 47. 33 of 25% of 88; of 2 × 25 ÷ 23 — 24. 48. 31 × 2 × 1; of (-2% +18) ÷ (§ —† +{ }). 0 26 = 15÷8} = 185 ÷ 35 = 185 × = EXPLANATION. This example simply means that 15g is to be divided by 8. Similar expressions are sometimes called Complex Fractions, and performing the division is called reducing a complex fraction to a simple one. When the terms of the dividend or divisor are connected by + or -, these operations must be performed before that of division. The following sets of numbers will give all the exercise upon fractional numbers that may be desired. Thus, take the first set, and ; find in their simplest form their sum, difference, product, and lastly, the quotient of the first divided by the other. Treat each set in the double columns in like manner. 185. The relation of one number to another is expressed by the quotient obtained by dividing the number compared by the number with which it is compared. 186. PRINCIPLE. Only like numbers, whether integral or fractional, can be compared with each other. 187. To find what part one integer is of another. 1. What part of 5 is 4? ANALYSIS. 1 is of 5, and 4 is 4 times of 5, or 3 of 5. Hence, etc. Of 8 is 7? Of 9 is 2? 2. What part of 7 is 3? 3. What part of 6 cts. is 4. What part of 60 is 40? 5. If a watch cost $60, and a chain $15, what part of the cost of the watch equals the cost of the chain? 6. If a chest of tea is worth $36, what part of a chest can be bought for $9? For $6? $12? $4? $18? $27? 188. To find what part a fraction is of an integer. 1. What part of 7 is ? ANALYSIS. 1 is of 7, and of 1 is of, or of 7; or, ÷7= 2 2. What part of 8 is ? is ? is ? ? ? ? ? 3. What part of $12 is $4? Of 10 weeks is of a week? 0915 4. What part of 15 acres is 14 or acres? Of 8 is 21? 5. What part of $20 is $? $? $q? $3? $J? 6. If flour bought at $7 a barrel is sold at $81, what part of the cost equals the gain? 189. To find what part a fraction is of a fraction. 1. What part of 3 is 2? ANALYSIS. 1 is of, and 3 of 1 is of, or = . Or, 1+1=1. Hence, etc. ་ 2. What part of 4 is ? Of is ? Of § is 4? Of } is } ? 3. What part of is? Of 14 is 3? 4. What part of $83 is $51? 5. Ella had $10, and spent $3. left? Of 55 miles is 33 miles? 6. At $13 a pound, what part of a pound will $3 buy? 7. A man bought of an acre of land, and sold of an acre; what part of of an acre had he left? 190. To find a number when a fractional part is given. 1. 24 is of what number? ANALYSIS. If of a number is 24, of it is of 24, or 6; hence, the number is 5 times 6, or 30. of what 5. Frank gave 60 cents for a knife, which was he paid for a sled; what did the sled cost him? 6. If of a ton of hay is worth $95, what is 1 ton worth? 18 7. 24 is of how many times 6? ANALYSIS. If of a number is 24, } of it is 6; hence, the number is 5 times 6, or 30; and 6 in 30, 5 times. 12. A lady paid $50, which was of what she paid for 10 yards of silk; what was the cost of the silk a yard? 13. of 56 is 4 of how many times 20? 9? 8? 10? 12? 14. of of 40 is of of how many times 8? 6? 7? 15. of 32 is of 4 times what number? ANALYSIS. of 32 is 24, and 24 is § of 28; 28 is 4 times of 28, which is 7. Hence, etc. 16. of 72 is of 5 times what number? 17. A merchant sold of a piece of cloth for $45, at $3 a yard; how many yards in the piece? 18. Paid $10 for a pair of pantaloons, which was ‡ of 3 times what I paid for a coat; what did the coat cost? 19. A grocer, after selling of a barrel of sugar, had 60 pounds left; how many pounds did the barrel contain? 191. 1. The sum of two fractions is, and one of them is ; what is the other? What their difference? 2. From what number must 41 be taken to leave 7? 3. The greater of two numbers is 94, and their difference 21; what is 3 times the less number? 4. The minuend is 123, and the subtrahend 7; what is of their difference? 5. What number divided by will give a quotient of 35? 6. What is the product of 24 and 4 of 13? 7. The product of two factors is of 35, and one of the factors is 4; what is of 3 times the other factor? 8. The divisor is 44, and the quotient 31; what is 4 times of the dividend? 9. Find the sum of 4 of 3 and . Their difference. Their product. The quotient of the greater by the less. 10. Add 3 to both terms of the fraction . Is its value increased, or diminished, and how much? |