10. How many eighths are there in † and §? 11. How many tenths are there in 1, 1, and ? 12. What kind of fractions can be added without chang ing their form? 13. What must be done to dissimilar fractions before they can be added ? 14. Add and ; and ; and ; and §; and ; and ; and 151⁄21⁄2; } and 71⁄2; } and †1⁄2. 15. Add and }; and ; and §; † and §; † and 1. 16. Add and }; † and §; } and 3; 3 and §; 2 and . 17. I paid $ } for milk and $1 for lettuce. did I pay for both? How much 18. James paid $3 for a fishing-rod and $ for a line. What part of a dollar did both cost him? 19. Lucy worked of a day at a picnic. at both? of a day at her lessons and spent What part of the day did she spend 20. A farmer's son sold dozen eggs to one man, & dozen to another, and dozen to another. How many dozen did he sell in all? 21. A lad was presented with some money on his birthday. The next day he spent † of it, the day following, 1⁄2 of it, and on the third day he spent of it. What part of the money did he spend? WRITTEN EXERCISES. 135. 1. What is the sum of §, 4, and ? =路 =27. EXPLANATION. - Since the fractions are not similar, they must be changed to similar fractions before they are added. The least common denominator of the given frac = = tions is 40, and § 25, 3 = 38, and 32. Hence the sum of the given fractions will be the sum of 25, 8, and 3, which is 17, or 24. 136. From the above solutions, it is evident that: In adding fractions, dissimilar fractions are first changed to similar ones, then their numerators are added, and the sum is placed over the common denominator. 1. If the sum is an improper fraction, it should be reduced to an integer or mixed number. 2. When there are mixed numbers or integers to be added, the integers and fractions should be added separately and then those results added. 18. A farmer sold a load of hay for $83, a load of oats for $223, and a load of wheat for $533. How much did he receive for all? 19. James picked 5 bushels of apples from one tree, 711 bushels from another, 63 bushels from another, and 85 bushels from another. How many bushels did he pick in all ? 20. Three barrels of sugar contained respectively 225% pounds, 232 pounds, and 24017 pounds. What was the weight of the whole? 21. A school-room is 32 feet long and 293 feet wide. What is the distance around the room? 22. An express train starts from Boston at 1 P.M., reaches Springfield 23 hours later, and Albany 4 later still. At what o'clock does it arrive in Albany? hours SUBTRACTION OF FRACTIONS. 137. 1. Bertie earned $ and spent $3. How much had he left? 2. Susie had g of a pound of candy, but she ate % of a pound. How much had she left? 3. There were & of a bushel of oats in a bin. If of a bushel was taken out, how much remained? 5. If I have $g and give away $4, what part of a dollar shall I have left? 6. A man who had of a cord of wood sold of a cord. What part of a cord had he left? 7. One pitcher held of a quart of milk, and another held of a quart. How much more did the one hold than 9. What kind of fractions can be subtracted without changing their form? 10. What must be done to dissimilar fractions before they can be subtracted? 5 11. 1-3=? 1-? 1-3=? 1-3=? 1-7=? 12. =? — } = ? } } = ? }}=? 11-8=? ?ᄒᄒ -? 12 13. 臺-髫=? 玉-号=?景-壬=?告-景=? 吾-ㄠ=? 1-1/2 = ? 14. A lad earned one day $ and spent $3. How much had he left? 15. A mechanic's wages were $3 per day, but he paid $ per day for his board. How much did he save daily? 16. A boy agreed to work for a man 5 days, but lost 1 days by sickness. How many days did he work? 17. A boy raised vegetables which he sold for $3. The cost of seed and other expenses were $11. How much was his net profit ? 18. A man bought a hat for $21, a vest for $24, and a linen coat for $14. How much change should he receive from the merchant, if he paid for them with a ten-dollar bill? WRITTEN EXERCISES. 138. 1. What is the difference between 15 and? EXPLANATION. Since the fractions are not similar, they must be made similar before they can be subtracted. The least common denominator of the given fractions is 48; 1=1, and 2=28. Hence, the difference between the 1 given fractions is the difference between 1 and 2§, which is 13. 2. What is the difference between 15 and 85? 153 = 15,2 = 1422 8 = 812= 819 = 61 EXPLANATION. Since the numbers are composed of integers and fractions, each may be subtracted separately. Reducing the fractions to similar fractions, it is evident that 19 cannot be subtracted from 192, hence 1, taken from 15, is united with. 1, or 12,+ 11⁄2 = }}. Subtracting 819 from 141, there is a remainder of 611. 139. From the solution of the above examples it is seen that: In subtracting fractions, dissimilar fractions are changed to similar ones, then their numerators are subtracted, and the difference is written over the common denominator. When there are integers or mixed numbers to be subtracted, the integers and fractions should be subtracted separately. 24. A box of soap weighed 75 pounds. The weight of the box alone was 3 pounds. How much did the soap weigh? 25. From a farm of 120 acres there were sold 367 acres. How much was left? 26. A flag-staff 50% feet high was broken off by a storm, so that it measured 437 feet. How much was broken off? 27. A grocer had 1284 pounds of sugar in one barrel, and 98 pounds in another. How much more was in the one barrel than the other? 28. A clerk earned $75 per month. His expenses during that time were as follows: board, $221; washing, $53; and other expenses $163. How much did he save per month? for 29. A man spent of his money for a house, furniture, and for horses and carriages. What part of his money had he left? 18° 30. The sum of two numbers is 11,5 bers is 83. What is the other number? One of the num 31. From a web of cotton cloth containing 58 yards, 8 yards were cut off at one time, and 153 yards at another time. How many yards remained? 32. Mr. Allen left of his property to his wife, to his sons, to his daughter, and the remainder to charitable institutions. What part of his property was left to charitable institutions? |