ADDITION. 3. Mr. A. sold of his farm at one time, and 2 at another What part of it did he sell? What is the sum of 4 time. and ? 4. James caught a fish in the morning that weighed 3 of a pound, and another in the afternoon that weighed of a pound. What did both weigh? What is the sum of and ? 5. Marian gave $ for a book and $1 for some writing How much did she pay for both? What is the sum paper. of 1 and 1? 6. Ella gave of her apple to a poor beggar and Julia gave him of hers. How many fourths did he receive? What is the sum of 3 and ? and 7. I bought of an acre of ground for a site for a house, 1-80 of an acre for a site for a barn. How much land did I buy? What is the sum of and ? Of and 1? Of and? 8. Mr. A. gave $331⁄2 to one man and $3 to another. How much did he give to both? 9. A merchant sold of a bushel of clover seed to one How much did he farmer, and of a bushel to another. sell to both? 10. Sarah paid $2 for eggs and $3 for butter. How much did both cost her? 11. I paid $ for turnips and $g for squashes. How much did I pay for both? 12. A merchant sold of a yard of silk to one lady and of a yard to another. How much did he sell to both? 13. A boy earned $3 in the forenoon and $1 in the afterHow much did he earn that day? noon. 10 14. What is the sum of and? and ? and ? 15. What kind of fractions can be added without changing their form? 16. What must be done to dissimilar fractions before they can be added? How are dissimilar fractions made similar? 175. PRINCIPLES.-1. Only similar fractions can be added. 2. Dissimilar fractions must be reduced to similar fractions before adding. WRITTEN EXERCISES. 176. 1. What is the sum of, and ? PROCESS. 36 ANALYSIS. Since the frac § + 3 + 3 = 3 8 +37+3=85 tions are not similar, before adding we must change them to similar fractions, or equivalent fractions having a common denominator. 30 The least common denominator of the given fractions is 36; and &=38, 1=37, and 3%. Hence the sum of the given fractions must be equal to the sum of 38, 37, and 3%, which is 93, or 13. 369 2. What is the sum of 51, 63 and 24? 6 PROCESS. 512=512 63=612 ANALYSIS. Since the numbers are composed of both integers and fractions, we may add each separately and unite the sums. Thus, the sum of the fractional parts is 3, or 111; the sum of the integers is 13; and the sum of both, 1411. RULE. Reduce the given fractions to similar fractions, add their numerators and write the sum over the common denominator. When there are mixed numbers, or integers, add the fractions and integers separately and then add the results. If the sum be an improper fraction, reduce to an integral or mixed number. 14. 74, 8, 65, 37, 578. 15. 21, 17, 231, 31, 213. 16. 35, 47, 6, 95, 27. 5 17. A farmer received $183 for hay, $65 for a cow, and $1613 for a horse. How much did he receive for all? 18. A man earns $675 per month, and each of his two month? sons $233 per month. How much do all earn per 19. A pedestrian walked 45 miles on Monday, 47% on Tuesday, 505 on Wednesday. How far did he walk? 20. A has 5 acres of land, B has 10 acres more than A, C has as much as both A and B. How many acres have B and C together? SUBTRACTION. 177. 1. Mary earned 5 ninths of a dollar and spent 2 ninths. How many ninths of a dollar had she left? 2. Mr. A. owning 1⁄2 of a flouring mill, sold & of it. How many sevenths did he then own? 3. From subtract . From subtract 5. From subtract 4. From subtract. From 5. Mr. B. owned a lot containing had he left after selling of an acre? subtract of an acre. How much 6. A boy paid $3 for a whip, but sold it after a time for $1. How much did he lose? 7. Find the difference between and .and. 8. What kind of fractions can be subtracted without changing their form? 9. What must be done to dissimilar fractions before they can be subtracted? How are dissimilar fractions made similar? 178. PRINCIPLES.-1. Only similar fractions can be subtracted. 2. Dissimilar fractions must be reduced to similar fractions before subtracting. WRITTEN EXERCISES. 179. 1. What is the difference between 11 PROCESS. and 2/? ANALYSIS. Since the fractions are not similar, before subtracting we must change them to similar fractions. The common denominator of the given fractions is 36; and 11=3%, and 3=3%. Hence the difference between the given fractions is equal to the difference between 3 and, which is 35. 2. What is the difference between 234 and 45. PROCESS. 234 23=2215 48 419 419 182 ANALYSIS.-Since the numbers are composed of both integers and fractions, we may subtract each separately. We first reduce the given fractions to similar fractions. Since we can not take 12 from, we unite with the 1, or 12, taken from 23, making 15. Then 2215-419-1852, the remainder. RULE. Reduce the fractions to similar fractions. Find the difference of the numerators and write it over the common denominator. When there are mixed numbers or integers, subtract the fractions and integers separately. Mixed numbers may be reduced to improper fractions and subtracted according to the first part of the rule. 21. If from a bin containing 5063 tons of coal, 418 tons are taken, how many tons still remain ? 22. A lady having $25, paid $2 for a pair of gloves, $15% for a bonnet, and $33 for some lace. How much money she left? had 23. A man owned a farm of 412 acres. He sold three parcels of land from it, the first containing 60 acres, the second 45 acres, and the third 116 acres. How many acres did he sell, and how many had he remaining? 24. A clerk earned $50 per month. He paid $20 for board, $5 for washing, and $43 for other expenses. How much did he save per month? MULTIPLICATION. CASE I. 180. To multiply a fraction by an integer. 1. At $1 a yard what will 3 yards of cambric cost? 2. If a man can earn $3 per hour, how much can he earn in 5 hours? How much can he earn in 8 hours? 3. James gave of an apple to each of 5 children. How many apples did he give to all? How much is 5 times ? 4. How many fifths are there in 6 times ? In 7 times ? 5. If Mr. A. spends $2 per day, how much will he spend in 5 days? How much in 10 days? |