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17. If I buy 27 quarters of a yard of calico, how many yards are there?

18. I have 3 silver dollars. ought I to receive for them?

Ans. 63 yards. How many half-dollars

Ans. 6 half-dollars.

19. A boy wished to give his sister

How could he most easily divide it? =

of an apple.

20. If I owe a man of a dollar, how many quarters will pay him?

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21. How many dimes are equal to

Ans. 3 quarters.

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18 of a dollar? 22. How many dimes are equal to of a dollar?

23. How many dimes are equal to 28 of a dollar?
24. How many dimes are equal to 23 of a dollar?
25. How many pints in 28 of a quart?
26. How many quarts in of a gallon?
27. How many days in 23 of a week?
28. How many days in g of a week?
29. How many hours in of a day?

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MODEL FOR RECITATION.

(1) PROBLEM.—What is the sum of 4; %, and §?

(2) ADDITION.-1 seventh+3 sevenths+5 sevenths are 9 sevenths; 9 sevenths=1 (unit) and 2 sevenths (of a unit).

(3) RESULT.-Hence, the sum of 4; 3, and § is 14

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1+1+1; }+{+}; !+&+3:

Ans. 11; 1; 12; 1.

13. Find the value of ++; }+&+}; }+&+9;

+3+/

Ans. 1; 1; 14; 1.

7

14. Find the value of ++; +å+ ̃; √1⁄2+12

3

1

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Ans 2. Ans. 1

15

Ans.

18. Copy and recite the following exercises:

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(3) ADDITION.-3 sixths and 4 sixths are 7=1}. (4) RESULT.-Hence, the sum of 1 and 2 is 11.

REMARK.-The fractions of (1) are reduced to sixths, because 6 is the smallest number that can be divided by the denominator

2 and 3 without a remainder. For a similar reason the fractions of (2) are reduced to twelfths, and those of (3) to eighteenths. (See 51.)

RULE.

(1.) If all the fractions have the same denominator, add their numerators, and place the result over the common denominator; reduce the resulting fraction, if it admits of reduction. Otherwise,

(2.) Find the smallest whole number that can be divided by each denominator without a remainder.

(3.) Reduce each fraction to another fraction which shall have the whole number just found for a denominator (See 51.)

(4.) Add the numerators, of the resulting fractions, and proceed as in (1).

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(1) PROBLEM.-What is the sum of 173; 29, and 4752?

(2) REDUCTION-3 fourths equal 18 twenty-fourths; 5 eighths equal 15 twenty-fourths; 5 twelfths equal 10 twenty-fourths.

(3) ADDITION.—10, 15, and 18 are 43 (twenty-fourths); 43 twenty-fourths equal 1 unit and 19 twenty-fourths (of a unit) over; 1, 8, 17, 24 (units); 2, 6, 8, 9 (tens).

(4) RESULT.-Hence, the sum is 9412.

34. Find the value of 3+4; 5+63; 71+81; 8+ 93; 131+247. Ans. 7; 12; 15,7; 18,5; 38g. 35. Find the value of 17+19; 261+417; 1951+ 3765; 13261+523. Ans. 367; 682; 57117; 18498. 36. Find the value of 49+81; 76+191; 53+5+81; 271+65+105. Ans. 57; 267; 662; 103. 37. Find the value of 31 +43 +195; 2171+293+13,552; 1871+6158+216. Ans. 271; 2607; 10191. 38. Find the value of 3+5+7+11+13,51⁄2·

Ans. 418.

Ans. 623.

39. Find the value of 187+191+178+253 +678 + 40+15+19511+6723+203+137. 40. A boy gathered 34 quarts of cherries on Monday, 5 quarts on Tuesday, and 6 quarts on Wednesday. How many quarts did he gather in the three days? Ans. 15 quarts.

41. If you give of a dollar for a yard of calico, 73 dollars for a yard of broadcloth, and 15 dollars for a dozen chairs, how many dollars do you expend for all the articles? Ans. $2317. 42. If I ride 73 miles in one day, 5 miles in another, and 83 miles in another, how many miles do I ride during the three days? Ans. 21,4 miles.

SUBTRACTION OF FRACTIONS.

55. To subtract one fraction from another.

EXAMPLES.

1. Copy and read the following exercises: -1=1 = 1; 2-2=2=4; &−&=&; &—&=&; 1

=

12

5

Read thus: 1 eighth from 3 eighths leaves 2 eighths,

or 1 fourth.

2. Copy, complete, and read the following:

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9

3

3. Copy, complete, and read the following: A-Å

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14 14

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RECITATION.

(1) PROBLEM.-What is the difference between § and?

(2) REDUCTION.-6 ninths equal 2 thirds (see 50), and

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