12. William caught three fishes; the first weighed of a pound, the second í of a pound, and the third 1 of a pound : how much did they all weigh? 13. A merchant sold } of a yard of velvet to one lady, 4 of a yard to another, and $ of a yard to another : how much did he sell ? 14. A slate cost of a dollar, a reader į of a dollar, and a geography of a dollar: how much did all cost ? 15. If I sold of an acre to Mr. A., i to Mr. B., $ to Mr. C., and í to Mr. D., how much did I sell to all ? 16. John had į of a dollar in one pocket, 1 of a dollar in another pocket, and f of a dollar in his hand : how much had he ? 17. Mary gave I of a cake to her sister, 4 of a cake to her brother, and had 4 of a cake left: how much had she at first ? 18. A tailor cut 7 of a yard from a piece of cloth for one customer, šof a yard for another customer, and had # of a yard left : how much cloth had he at first ? 19. Thomas walked of a mile, Harry * of a mile, and Samuel as far as both Thomas and Harry: how many miles were walked by the three ? Find the sum of: 20. į and š; 3 and 4; 3 and 4; io and . WRITTEN EXERCISES. can = 30 common ART. 147.-1. Add }, , and to. Analysis.-Since only like fractions bo 44 40 added, }, { and to must 5 8 x 3 = 24 jó be changed to equiva4 10 x 3 lent fractions having a 4 denominator. 58 = 44, = 28, to = *t + 8 + 6 = 48 = 118 = 1, 17 and the sum of these 1.0. ART. 148.-Rule for Addition of Fractions.—Change the fractions to equivalent fractions having a common denominator, add their numerators and write their sum over the common denominator. When there are mixed numbers or integers, add the whole numbers and fractions separately, and then add their sums. NOTE.-If the sum be an improper fraction, change it to a whole or mixed number and reduce fractional results to their lowest terms. Find the sum of: 2. $ + 옥 + 1. 4. + 23 + 41. 3. & + + 13. 5. } + 2} + 111 6. A owns three lots, the first containing 53 acres, the second 114 acres, and the third 13 acres : how many acres does he own ? 7. A grocer has two casks of sugar, one containing 1637 pounds, and the other 1803 pounds : how many pounds in both ? 8. If I pay $1,2503 for a barn and expend $23016 in repairs, what is the total cost ? 9. A dealer purchased two boat-loads of coal. In the first there were 2754 tons, and in the second 2334 tons : how many tons did he purchase ? 10. The sales made by a commercial traveler amounted to $544 in one day, $481' the second day, and $603 the third day: how much did he sell in the three days? 11. Three bins contain respectively 847 bushels, 883 bushels, and 90: bushels : how much in the three bins ? 12. A farmer sold a horse for $175 , a colt for $353, and a cow for $494 : how much did he receive ? 13. A man earned $394 the first month, $411o the second month, and $374 the third month : how much did he earn ? 14. A grocer's sales amounted to $954 on Monday, $877 on Tuesday, $914 on Wednesday, and $8816 on Thursday : what was the total amount ? 15. A pedestrian walked 384 miles on Monday, 394 miles on Tuesday, 40} miles on Wednesday, and 424 miles on Thursday : how far did he walk ? 16. A farmer received $271% for some hay, $164 for some oats, $25 for some wheat, and $154 for some corn: how much did he receive for all ? 17. The value of a house is $4,250, of a lot $1,232, of a barn $2,151, and of the other buildings $948} : what is the value of all ? 18. Mr. B. owns four farms, containing 111f acres, 1193 acres, 205} acres, and 1937 acres : how many acres does he own ? 19. A clothier bought five pieces of cloth containing 21; yards, 334 yards, 378 yards, 394 yards, and 283 yards : how many yards did he buy? 20. A spent $194, B spent $11; more than A, and C spent $176 more than A and B : how much did they all spend ? 21. Illustrate by an original problem addition of frac Subtraction of Fractions. ORAL EXERCISES. ART. 149.–1. Albert having of a dollar spent of a dollar : how much had he left ? 2. Susan having of a quart of cherries, gave away of a quart of cherries: how much had she left ? 3. A man owned 1 of an acre and gave away in of an acre : how much had he left ? 4. Wilson gathered šof a bushel of pears and sold + of a bushel : how much remained ? 5. Jacob earned % of a dollar and spent iš of a dollar : how much did he save ? be ART. 150.—Principle.-Only like fractions can subtracted. 6. Aaron paid of a dollar for a knife and sold it for 3 of a dollar : what did he lose ? Solution. He lost the difference between of a dollar and } of a dollar. = % and į Po ; * - % = 16. He lost % of a dollar. %. If I pay 1% of a dollar for a book and sell it for of a dollar, how much will I lose ? 8. A man owning of a ship sold of it: what part of the ship did he still own ? 9. From io of a barrel of sugar, a grocer sold of a barrel : what part remained ? 10. A farmer planted of an acre with corn and } of an acre with potatoes : how much more did he plant with corn than with potatoes ? 11. Thomas earns of a dollar a day and Jarvis to 18. ART. 151.-1. From 8 take } ; from 131 take 114. 36 alent fractions having a common denominator. Analysis.-Reduce the fractional parts } and 2d Process. } to equivalent fractions having a common de13! = 133 nominator. As cannot be taken from ?, take 11= 113 1= from the integral part of the minuend and Ans. 12 add it to č. Then ? from leaves 6 and 11 from 12 leaves 1. ART. 152.-Rule for Subtraction of Fractions.-1. Change the fractions to equivalent fractions having a common denominator, subtract the numerator of the subtrahend from the numerator of the minuend, and write the dif ference over the common denominator. 2. If there are mixed numbers and the numerator of tie subtrahend is greater than the numerator of the minucnd, take 1 from the integral part of the minuend, reduce it to the required fractional form, add it to the fractional part of the minuend, and proceed as in 1 above. |