Fractions. 196. TO REDUCE COMPLEX FRACTIONS TO SIMPLE FRACTIONS. Observe that every reduction of a complex fraction may be regarded as a problem in division. J is read, divided by . + = 4 of 4 = 11 = 4. (a) Find the sum of the four fractions. Observe that a complex fraction may be reduced to a simple fraction by multiplying its numerator and denominator by some number that will in each case give an integral product. When this number can be easily discovered by inspection this is a convenient method of reduction: thus == X 2 1 2 14 Fractions. 197. PRACTICAL APPLICATION OF THE PRECEDING RULES. Page 84, problems 1 and 2. 1. A man owned a farm of 375 acres; he gave to his eldest son 275 acres of his farm. What part of the farm did the son receive? 2. Peter Lundy earned $650 in one year; of this sum he expended $520. What part of his earnings did he expend? Page 85, problems 1 and 2. 3. A lady owned § of an acre of land. How many 160ths of an acre did she own? 4. Benton walked of a mile. Express the distance he walked in 160ths of a mile. Page 91, problems 1 and 6. 5. In a certain furnace of a ton of coal was consumed 20 in one day, and of a ton the next day. What part of a ton was consumed in the two days? 6. Mr. Luker has three lots of land; in the first lot there are of an acre; in the second, of an acre, and in the third, of an acre. How many acres in all? Page 91, Art. 186, problems 3 and 4. 7. Of of a mile of board fence of a mile was burned. What part of a mile remained? 8. Mr. Reynolds had put into the bank of his annual salary; he drew from this money a sum equal to of his salary. What part of his salary remained in the bank? Page 92, Art. 187, I., problems 4 and 5. 9. From 523 tons of hay, were sold and delivered 31% How many tons remained of the unsold hay? tons. 10. On Monday James rode on his wheel 473 miles; on Tuesday he rode 18 miles. How much further did he ride Monday than Tuesday? Page 93, Art. 188, I., problems 1 and 5. 11. If a street car makes a round trip in of an hour, in how long a time can it make 4 such trips? 12. If yd. of ribbon are required to trim a hat, how much ribbon will be required to trim 8 such hats? Page 93, Art. 188, II., problems 1 and 5. 13. At 3 dollars a cord, what is the cost of 7 cords of wood? 14. If Henry rides his wheel at the rate of 4 miles an hour, how far does he ride in 5 hours? 2 Page 94, Art. 189, I., problems 1 and 4. 15. If of a yd. of ribbon is cut into 4 equal pieces, what part of a yard is each piece? 16. John hoes 4 rows of corn in of an hour. In what part of an hour does he hoe 1 row? Page 94, Art. 189, II., problems 1 and 5. 17. A horse traveled 17 miles in 3 hours. his rate per hour? What was 18. A farmer divided a field containing 18, acres into 4 equal lots. How many acres in each lot? Page 96, Art. 190, I., problems 1 and 5. 19. At $345 an acre, what is the cost of acre? 20. At $263 an acre, what is the cost of 4 acre? Page 96, Art. 190, II., problems 1 and 9. 6 21. A piece of land in the form of a rectangle is of a mile long and of a mile wide. The piece is what part of a square mile? 22. At a dollar per yard, what is the cost of 4 of a yard of silk? Page 96, Art. 190, III., problems 1 and 9. 23. A strip of land 372 rods long and a rod wide contains how many square rods? 24. At $153 an acre, find the cost of of an acre. Page 96, Art. 190, IV., problems 1 and 8. 25. At $4623 a mile, what is the cost of grading 24 miles of road? 26. How many square feet in a piece of land 275 ft. by 4 ft. ? Page 102, I., problems 1 and 5. 27. At a dollar a bushel, how many bushels of potatoes can be bought for 46 dollars? 28. At of a dollar a bushel, how many bushels of apples can be bought for 375 dollars? Page 102, II., problems 1 and 5. 29. At of a dollar a yard, how many yards of cloth can be bought for } of a dollar? 30. At of a dollar a yard, what part of a yard of cloth can be bought for of a dollar? 12 Page 102, III., problems 1 and 6. 31. If a rectangular diagram on the blackboard contains 5 square feet and is of a foot wide, how long is it? Make the diagram. 32. At $ a bushel, how many bushels of meal can be bought for $243 ? Page 102, IV., problem 1. 33. A strip of land contains 325 square rods, and is 24 rods wide. How long is it? Page 103, II., problem 1. 34. Five-sixths of an hour is what part of 5 hours? |