40. 1. 9 is 1 fourth of what number? ANALYSIS. 9 is 1 fourth of 4 times 9; 4 times 9 is 36. Therefore 9 is 1 fourth of 36. 2. 7 is 1 fifth of what number? 11. 9 times 4, and 3 fourths of 4 are how many? 12. 6 times 9, and 7 ninths of 9 are how many? 13. 10 times 12,and 5 twelfths of 12 are how many? 14. 14 times 2, and 1 half of 2 are how many? 15. 8 times 11, and 7 elevenths of 11 are how many? 16. 5 times 20, and 13 twentieths of 20 are how many? 17. 64 are how many times 8?5?12? 18. 47 are how many times 9? 10?8?6? 19. 81 are how many times 8? 9? 11? 12? 20. 35 are how many times 7?6?8? 9? 21. 75 are how many times 5? 6? 7? 9? 25? 22. 3 fourths of 16 are how many times 6? ANALYSIS. 3 fourths of 16 are as many times 6 as 6 is contained times in 3 times 4 of 16; 1 fourth of 16 is 4, and 3 times 4 is 12; 6 is contained in 12, 2 times. Therefore 3 fourths of 16 are 2 times 6. 23. 6 tenths of 100 are how many times 5? 24. 5 twelfths of 72 are how many times 3? 4? 6?8? 25. 7 ninths of 63 - 3 eighths of 24 are how many times 4?5?6?7? 8? 26. 11 twentieths of 80 +7 fifteenths of 45 are how many times 6? 7? 9? 12? 13? 41. 1. If 1 fourth of a yard of cloth cost 12 cents, what will 1 yard cost? ANALYSIS. If 1 fourth of a yard cost 12 cents, 4 fourths, or 1 yard, will cost 4 times 12 cents; 4 times 12 cents are 48 cents. Therefore, if 1 fourth of a yard cost 12 cents, 1 yard will cost 48 cents. 2. If 1 fifth of a pound of tea cost 10 cents, what will 1 pound cost? 3. If 1 third of a gallon of molasses cost 20 cents, what will 1 gallon cost? 4. 20 is 1 third of what number? 5. 10 is 1 fifth of what number? 6. If 1 half of a cord of wood cost 2 dollars, what will 1 cord cost? what will 2 cords cost? 7. A man gave 2 shillings for his dinner, which was 1 twelfth of all the money he had; how much money had he ? 8. A drover sold some sheep, and gained by the sale 15 dollars, which was 1 fourth of what the sheep cost him; what was the cost of the sheep? 9. If 1 sixth of a ton of hay cost 3 dollars, what will 3 sixths cost? 5 sixths? 1 ton ? 10. If a man can walk 6 miles in 1 eighth of a day, how far can he walk in 1 day? in 2 days? in 3 days? 11. James had 40 plums, and divided 1 fourth of them equally among 5 of his companions; how many did he give to each ? 12. 6 is 1 eighth of what number? 13. 15 is 1 fifth of what number? 14. 40 is 1 third of what number ? 15. 1 fourth of 40 is how many times 5? 7? 16. 1 sixth of 90 is how many times 4? 5?6? 17. I have 16 dollars, which is 1 third of what I paid for 12 sheep; how much did I pay a head? 18. A man plowed 36 acres of his farm; 3 fourths of this was just equal to 1 third of the whole number of acres in his farm; how many acres in his farm? 19. A pole stands 12 feet in the water, which is 1 fifth of the length of the pole; how long is the pole ? 20. Bought a watch and chain; for the chain I gave 15 dollars, which was 1 fourth of what I paid for the watch; what did they both cost me? 21. If 1 twelfth of an acre of land cost 5 dollars, what will 2 acres cost? 42. 1. If 3 fourths of a barrel of flour cost 6 dollars, what will one barrel cost? ANALYSIS. If 3 fourths of a barrel of flour cost 6 dollars, 1 barrel will cost 4 times 1 third of 6 dollars; 1 third of 6 dollars are 2 dollars, and 4 times 2 dollars are 8 dollars. Therefore, &c. 2. If 4 fifths of a barrel of ale cost 8 dollars, what will 1 barrel cost? 3. If 5 ninths of a month's wages amount to 25 dollars, what will a month's wages amount to? 2 months'? 4. What will 1 barrel of flour cost, if 5 sevenths of a barrel cost 10 dollars? 5. Sold a cow for 25 dollars, which was 5 fourths of what she cost me; what did she cost me ? 6. Bought 4 barrels of vinegar at 6 dollars a barrel, which was but 3 ninths of its real value; what was its real value per barrel? 7. A speculator bought some pork for 90 dollars, which was 9 elevenths of what he sold it for; how much did he gain ? 8. A tailor bought two pieces of cloth, the shorter piece containing 24 yards; 5 eighths the number of yards in the shorter piece is 20 yards less than the number of yards in the longer piece; how many yards in both pieces? 9. If 7 tenths of an acre of land yield 28 bushels of wheat, what will 1 acre yield? what will 3 acres yield? 10. 16 is 4 fifths of what number? ANALYSIS. 16 is 4 fifths of 5 times 1 fourth of 16; 1 fourth of 16 is 4, and 5 times 4 is 20. Therefore, 16 is 4 fifths of 20. 11. 25 is 5 eighths of what number? 22. 5 sixths of 24 is 2 thirds of what number? ANALYSIS. 5 sixths of 24 is 2 thirds of 3 times 1 half of 5 times 1 sixth of 24; 1 sixth of 24 is 4, and 5 times 4 is 20; 1 half of 20 is 10, and 3 times 10 is 30. Therefore, & sixths of 24 is 2 thirds of 30. 23. 3 fourths of 16 is 6 sevenths of what number? 24. 4 fifths of 30 is 8 elevenths of what number? 25. 6 fourths of 28 is 7 ninths of what number? 26. 9 twelfths of 60 is 5 thirds of what number? 27. 8 ninths of 18 is 1 fourth of what number? 28. 11 fifteenths of 45 is 3 halves of what number. 29. 6 tenths of 100 is 5 twelfths of what number? 30. 3 twentieths of 80 is 2 sixteenths of what number? 31. 9 eighths of 64 is 8 fifths of what number ? 32. Of a certain farm, 36 acres are woodland, and 5 sixths of the woodland is 3 fifths of the number of acres of cleared land; how many acres of cleared land, and how many acres does the farm contain? 33. Mr. Smith gave 5 sevenths of all the money he had for a horse; he then paid 12 dollars for a saddle and bridle, which was 3 fourths of all the money he had left; how much money had he at first? 34. A person, being asked his age, answered that if he were twice as old, 1 third of his age would be 20 years; how old was he? 43. A FRACTION is one or more of the equal parts of a unit. Fractions are expressed by figures in the following manner, viz.: 4, 1 1. 69 1 , one fifth. one sixth. one seventh. , 1. one eighth. 1, one tenth. 9 three fourths, seven eighths. 1, nine tenths. 11, eleven twelfths. 12 13 20, ,thirteen twentieths. 44, four and 1 seventh. 90, nine and 5 eighths, &c. 1. The number below the short horizontal line is called the denominator. 2. The number above the line is called the numer ator. 3. The denominator shows into how many parts the whole thing is divided. |