From the foregoing operations the following rules for dividing by a fraction are obtained: RULE I. Reduce the dividend and the divisor to like fractional units, then divide the numerator of the dividend by the numerator of the divisor. RULE II.—“Invert the divisor and proceed as in multipli cation." Observe that the inverted divisor shows the number of times the divisor is contained in 1: then in 6 it is contained 6 times as many times; in 4, 4 times as many; in }, } as many; in, as many, etc. *18 thirds + 2 thirds = 9. 1. 3 thirds + 2 thirds = = 1) = 2. 35 fortieths + 24 fortieths = 111. 21. 5 fifths + 3 fifths = 1} = §. Fractions. 196. TO REDUCE COMPLEX FRACTIONS TO SIMPLE FRACTIONS. is read, divided by 7.3 of ;= = 9. = (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 Fractions. 197. PRACTICAL APPLICATION OF THE PRECEDING RULES. Page 224, problems 1 and 2. 1. B owned a farm of 375 acres; he gave to his son 275 acres. What part of the farm did the son receive? earned $650 in one year; of this sum he exWhat part of his earnings did he expend? 2. Mr. L. pended $520. Page 225, 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 226, Art. 179, problems 1 and 6. 5. In a certain furnace 5 of a ton of coal was consumed 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, 13 of an acre. How many acres in all? 20 Page 231, 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? tons. Page 232, Art. 187, I., problems 4 and 5. 9. From 525 tons of hay, were sold and delivered 31% How many tons remained of the unsold hay? 10. On Monday James rode 473 mi.; on Tuesday, 18 mi, How much further did he ride Monday than Tuesday? Page 233, Art. 188, I., problems 1 and 5. 12 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 233, Art. 188, II., problems 1 and 5. 13. At 31 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? Page 234, 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. part of an hour does he hoe 1 row? Page 234, Art. 189, II., problems 1 and 5. 17. A horse traveled 17 miles in 3 hours. his rate per hour? In what What was 18. A farmer divided a field containing 183 acres into 4 How many acres in each lot? Page 236, I., problems 1 and 5. equal lots. 19. At $345 an acre, what is the cost of 20. At $263 an acre, what is the cost of acre? Page 236, II., problems 1 and 9. of a 21. A piece of land in the form of a rectangle is 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 3 of a yard of silk? |