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pk. are neither bush. nor #pk.; but bush.= $pk. (Art. 148), and then pk.pk.pk. Hence,

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RULE. Reduce the fractions, if necessary, first to the same denomination, then to a common denominator; after which write the sum of the new numerators over the common denominator.

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10

11. Add together T5, 5, 5, 15, and 1.

1259

67 1259

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Ans. 23.

Ans. 43.

}+&+&=18+28+48 (Art. 147, Rule 2) = 18, Aus.

15. Add together 3 and §.

3+8=38+33 (Art. 147, Rule 1) = 13=133, Ans.

16. Add together, 3, and 4.

17. Add together 2, 1, and g.

16

+ ✩+9=1+1+1=1=11, Ans.

18. Add 1, 6, 12, and 18.

89

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152. Rule for adding fractions? Can unlike numbers be added? Of what kind is the sum of two or more numbers?

23. Add s. to 3d.

s.+3d.=24d. +3d. = 73d.+1}d.={}d.=57d., Ans.. or, fs.d.35. +1s. =365.+s. 1s., 2d Ans.

== 1st Ans.

24. Add ggal. to qt.

25. Add together bush. pk. and ğqt.

26. Add together ton cwt. and qr.

=

Ans. qt. or gal.

(c) To add two fractions that have a common numer

ator:

Multiply the sum of the denominators by either numerator, and lace the product over the product of the denominators.

27. What is the sum of 3 and ?

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and ?

=17, Ans.

and?

28. What is the sum of

29. What is the sum of

(d) To add mixed numbers:

Add the sum of the fractions to the sum of the integers
30. What is the sum of 3 and 43?

1+3=38+18=47=17; 3+4=7;
..3+437+1=86, Ans.

31. What is the sum of 54, 35, and 123?
32. What is the sum of 18, 5, and 24g?
33. What is the sum of 15%, 24, 74, and 1⁄2?
34. What is the sum of 3, 61%, 412, and 243 ?

35. What is the sum of of 3 of 63, 4,

8巷

Ans. 2113.

and 43?

36. What is the sum of 38, 63, and of &?

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37. What is the sum of 3, 4, 85, and 25 ? 38. How many are 83+33 +83 +14 ?

152. Mode of adding two fractions that have like numerators? adding mixed numbers?

Mode of

PROBLEM 15.

153. To subtract a less fraction from a greater:

RULE. Prepare the fractions as in addition, and then write the difference of the numerators over the common denominator.

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11. From (a)

take 3.

—=1-18=f, Ans. (See Art. 152, a).

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X-X=8—4—3}-1}}}, Ans.

22. From of take of fr

23 From of 14 take

of 19.

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Ans.

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153. Rule for subtracting one fraction from another? How are the fractions prepared in addition?

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30. From s. take d. (See Art. 152, b).

(b) s. d.2d.d.§gd.d.§3d.138d., Ans.

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60

or, 4s. d. 4s.—s. = 40s. s. s., 2d Ans.

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31. From qt. take pt.

32. From ton take cwt.

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4

Ans.

=

420

qt. or 14pt.

33. From acre take a rod.

Ans. 188a. or 6723rd.

448

NOTE. The answer to these examples may be in any denomination of the table.

34. From of a week take of an hour.

(c) To subtract when the fractions have a common numerator:

Multiply the difference of the denominators by either numerator, and write the product over the product of the denominators.

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(d) To take a mixed number from a whole or mixed

number.

38. From 6 take 23.

632841, Ans. (See Art. 152, d).

153. Mode of subtracting when the fractions have a common numerator?

39. From 8 take 271.

8-217-714-275, Ans.

In Ex. 38, take from , and 2 units from 6 units; but in Ex 39 we cannot take from,.. reduce one of the 8 units to 11, and add it to the, making 15, and then take the

, and the 2 units from the remaining 7 units.

from

93—33=87 — 3 — 843-335=517, Ans.

40. From 93 take 3.

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5. Subtract 1815 from 2517.

76. Reduce 233 to an improper fraction.

7. Reduce 8 to a fraction whose denominator is 27.

S. Reduce 9 to 6 fractional forms.

9. Divide by f

10. Divide 16 by 23.

11. Divide by 3.

12. Reduce of a day to hours, minutes, and seconds. 13. Reduce 3pk. 5qt. 1pt. to the fraction of a bushel.

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21. Reduce of of 1 to a simple fraction.

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153. Mode of taking a mixed number from a whole or mixed number?

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