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3. Mr. A. sold of his farm at one time, and i at another time. What part of it did he sell? What is the sum of and ?
4. James caught a fish in the morning that weighed 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 $1 for a book and $1 for some writing paper. How much did she pay for both ? What is the sum of į and
6. Ella gave Å of her apple to a poor beggar and Julia gave him of hers. How many fourths did he receive? What is the sum of i and į?
7. I bought 1 of an acre of ground for a site for a house, and of an acre for a site for a barn. How much land did I buy? What is the sum of į and ? Of } and ? Of } and 1?
8. Mr. A. gave $1 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 farmer, and of a bushel to another. How much did he sell to both ?
.10. Sarah paid $1 for eggs and $7 for butter. How much did both cost her?
11. I paid $g for turnips and $ for squashes. How much did I pay for both ?
12. A merchant sold of a yard of silk to one lady and x of a yard to another. How much did he sell to both?
13. A boy earned $g in the forenoon and $1 in the afternoon. How much did he earn that day? 14. What is the sum of 5 and 117? and 15? * 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.
176. 1. What is the sum of ã, and z?
ANALYSIS.—Since the frac4+ 4+ =38++36=tions are not similar, before
adding we must change them to similar fractions, or equivalent fractions having a common denominator. The least common denominator of the given fractions is 36; and
I=31, and s=. Hence the sum of the given fractions must be equal to the sum of 36, 37, and 3%, which is $i, or 137.
2. What is the sum of 51, 63 and 24?
ANALYSIS.-Since the numbers are composed of 51=512
both integers and fractions, we may add each sep
arately and unite the sums. Thus, the sum of the 63=612
fractional parts is 13, or 11); the sum of the inte23=2 gers is 13; and the sum of both, 141).
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.
Find the sum
3. Of 5, 4, 3, 5 and 11. 4. Of }, }, }, } and . 5. Of į, , , } and 12: 6. Of }, 3, 4, 5 and 1%.
7. Of , 14, 15 and 31. 8. Of 21, 4, 31 and 56. 9. Of 274, 8f and 403. 10. Of 134, 151 and 2013.
Add the following:
14. 74, 8, 652, 37, 545. 15. 4, 4, 231, 34, 213. 16. 35, 413, 6, 9g, t.
17. A farmer received $184, for hay, $65} for a cow, and $1614 for a horse. How much did he receive for all?
18. A man earns $675 per month, and each of his two sons $23; per month. How much do all earn per month?
19. A pedestrian walked 453 miles on Monday, 47on Tuesday, 503 on Wednesday. How far did he walk?
20. A has 54 acres of land, B has 103 acres more than A, C has as much as both A and B. How many acres have B and C together?
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 of a flouring mill, sold of it. How many sevenths did he then own?
3. From subtract From subtract. From i
4. From 1 subtract is. From subtract is.
5. Mr. B. owned a lot containing of an acre. How much had he left after selling of an acre?
6. A boy paid $g for a whip, but sold it after a time for $1. How much did he lose ?
7. Find the difference between and 1 and 1.
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
179. 1. What is the difference between 11 and 3? PROCESS.
ANALYSIS.-Since the fractions are not 1- = -386
similar, before subtracting we must change them to similar fractions.
The common denominator of the given
fractions is 36; and 11=it, and =36. Hence the difference between the given fractions is equal to the difference between 33 and 36, which is 5
2. What is the difference between 231 and 46.
ANALYSIS.—Since the numbers are 231=23=22 15
composed of both integers and frac
tions, we may subtract each sepa45= 412
rately. 18 0
We first reduce the given fractions
to similar fractions. Since we can not take 12 from 12, we unite with the is 1, or 1%, taken from 23, making 13. Then 2215 — 419=1811, 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.
9. From take 36 10. From í take 8. 11. From take is. 12. From take 4s. 13. From 17 take 7. 14. From zł take 16.
15. From 1034 take 13. 16. From 663 take 333. 17. From 2101 take 1095. 18. From 112 take 75.. 19. From 606 take 701. 20. From 589; take 67%.
21. If from a bin containing 5063 tons of coal, 418.1 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 $3 for some lace. How much money
had she left?
23. A man owned a farm of 412 acres. He sold three parcels of land from it, the first containing 60% acres, the second 452 acres, and the third 1161 acres. How many acres did he seh, and how many had he remaining?
24. A clerk earned $50] per month. He paid $200 for board, $54 for washing, and $43 for other expenses. How much did he save per month?
180. To multiply a fraction by an integer.
2. If a man can earn $1% per hour, how much can he earn in 5 hours? How much can he earn in 8 hours ?
3. James gave s of an apple to each of 5 children. How many apples did he give to all? How much is 5 times f? 4. How many
fifths are there in 6 times 4 ? In 7 times ? 5. If Mr. A. spends $24 per day, how much will he spend in 5 days? How much in 10 days?