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Observe that this work is not different from that given under example II., page 111., except that the number of zeros to be annexed to the numerator is always two. Why?

I. Reduce to hundredths.

9

14. 25

19. to

1. 1 / 2 6. 1 11. 10 16.
2. } 7. 1 12.

17.
3.

8. $ 13. 11 18.

9.
5. 1 / 4 10. 24
(a) Find the sum of the twenty decimals.
(b) Find the sum of the twenty common fractions.

1

15. 3

14

20. 5

17

II. Reduce to hundredths.

1. 115
4. 118

7. 14
2. 10
5. 115

8. 18
3. 117
6. 3-5

9. 18
(a) Find the sum of the nine decimals.
(b) Find the sum of the nine common fractions.

175

is not always the most simple.

Multiply the numerator and the denominator by 21.

Fractions.

III. Reduce to hundredths. NOTE.-Such fractions as the following may be easily reduced to hundredths by dividing the numerator and the denominator of each by that number which will change the denominator to 100.* 1. 7 5.

9.
2.

6. 2036
7. 138

8. 103
(a) Find the sum of the twelve results.
(b) Find the sum of the twelve common fractions.

45 400

36 300

10. 40

4.6 500

94 500

11.

300

85 300

12. 139

300

IV. Reduce to hundredths. NOTE.—Multiply the numerator and the denominator of each fraction by that number which will change the denominator to 100*.

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6 + 40+

5. 18

8.

81 150

69 167 1 54 350

6. 16

9. 196

40

1. 118+

4.

7. 188
2.
3.

(a) Find the sum of the nine decimals. * Every common fraction can be changed to hundredths by annexing two zeros to the numerator and dividing by the denominator; but this method of reduction

* Take of the numerator and 3 of the denominator.

Fractions.

205. DENOMINATE FRACTIONS. 1. One half inch is what part of a foot ? 2. Two and I inches are what part of a foot ? 3. Five and { inches are what part of a foot ? 4. One half foot is what part of a rod ? 5. Three and one half feet are what part of a rod ? 6. Ten and one half feet are what part of a rod ? 7. Sixty-four rods are what part of a mile? 8. Ninety-six rods are what part of a mile ? 9. One hundred eighty rods are what part of a mile? 10. One and one half quarts are what part of a peck ? 11. Two and one half quarts are what part of a gallon ? 12. Twenty-four quarts are what part of a bushel ? 13. Fourteen ounces are what part of a pound? 14. Seven and one half ounces are what part of a pound? 15. One and one fourth ounces are what part of a pound? 16. Six hundred pounds are what part of a ton ? 17. Four hundred fifty pounds are what part of a ton ? 18. Six hundred twenty-five pounds are what part of a ton? 19. Seventy-five square rods are what part of an acre? 20. Forty-five square rods are what part of an acre ? 21. One hundred square rods are what part of an acre ? 22. Thirty-two cubic feet are what part of a cord ? 23. Fifty-six cubic feet are what part of a cord ? 24. One hundred cubic feet are what part of a cord ? 25. Seven and one half minutes are what part of an hour? 26. Forty minutes are what part of an 8-hour day? 27. Ninety minutes are what part of an 8-hour day?

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Multiplying both members of the equation (See page 77, Art. 170, Statement 5) by 2, the denominator of the fraction in the equation, we have

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* Observe that the equation might have been cleared of fractions by multijl. ing both its members by 6, the l. c. m. of 2 and 3.

Algebra.

207. PROBLEMS LEADING TO EQUATIONS CONTAINING

ONE UNKNOWN QUANTITY WITHOUT FRACTIONS.

then

EXAMPLE
John and Henry together have 60 oranges, and Henry
has three times as many as John. How many has each ?
Let x = the number John has,

3 x the number Henry has,
and x + 3 x = the number they together have.

But they together have 60.
Therefore x + 3 x 60.
Uniting

60.
Dividing

15. Multiplying 45. Therefore John has 15 oranges and Henry has 45 oranges.

4 x

X =

3 x =

PROBLEMS. 1. The sum of two numbers is 275, and the greater is four times the less. What are the numbers ?

2, Robert has a certain sum of money and Harry has five times as much ; together they have $216. How many dollars has each ?

3. One number is four times another, and their difference is 270. What are the numbers ?

4. Peter has a certain number of marbles and William has 8 more than Peter ; together they have 96 marbles. How many has each ?

5. Sarah has a certain number of pennies and her sister has nine more than twice as many ; together they have 93. How many has each ?

6. Two times Reuben's money plus three times his money equals 175 dollars. How many dollars has he?

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