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9. A girl who was taking lessons on the piano practiced as follows during one week: Monday, 14 hr.; Tuesday morning, 1 hr.; Tuesday afternoon, hr.; Wednesday, 11⁄2 hr.; Thursday, 3 hr.; Friday, 14 hr.; Saturday morning, 1 hr.; Saturday afternoon, & hr. How many hours did she practice during the week?

10. A boy had 10 mi. to travel. If he traveled 34 mi. on foot and rode the remainder of the distance, how far did he ride?

125. Oral Exercises.

1. Subtract 6 from 93.

MODEL: 92

64

23

The sum of and the fraction of the difference is 13. Find what must be added to to make 1 and

add it to . and are 1. and are . Carry 1 to 6. 7 and 2 are 9.

The numerator of the fraction in the difference may be found by subtracting 4 (the numerator of the fraction in the subtrahend) from 5 (the denominator of the fraction in the minuend), and adding 2 (the numerator of the fraction in the minuend). Explain why this method will give the correct result. Use this method in subtracting.

2. Subtract without the use of a pencil:

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3. Find the sum of each of the above exercises.

4. A dressmaker had two pieces of cloth containing 8 yd. and 63 yd., respectively. She used 10 yd. in making a dress. How much cloth was left?

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1. If A represents a unit divided into 2 equal parts, what does B represent? C? D? E? F?

2. The fractional unit of B is ; what is the fractional unit of C? D? E? F? What part of the fractional unit of A is the fractional unit of B? C? D? E? F? How many of the fractional units of B does it take to make one of the fractional units of A? How many of C? of D? of E? of F?

3. The fractional unit is what part of the fractional unit?. is what part of ?

4. The denominator of the fractional unit is 2 times. the denominator of the fractional unit. It shows that the unit has been divided into twice as many equal parts. It will therefore take 2 of the fractional units sixteenths to make one of the fractional units eighths. §•

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= 6

5. The fractions 1, 4, 4, are the same in value. They differ in form. Changing the form of a fraction without changing its value is called reduction.

6. The fraction is equal to the fraction. Compare their numerators. 8 is times 4.

nominators. 16 is times 8.

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Compare their deHow may be derived

from? How may be derived from?

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5

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8

7. Compare in a similar way the terms of the fractions and; and ; and 2. What effect upon the value of a fraction has multiplying both terms by the same number?

8. A fraction is an indicated division. is the same as 6)3. The denominator of the fraction is the divisor, and the numerator is the dividend. What effect upon the quotient has multiplying both the dividend and the divisor by the same number? Is multiplying both the numerator and the denominator of a fraction by the same number the same as multiplying both the dividend and the divisor by the same number? =-12-16.

9. The fraction 10 is equal to the fraction §. Compare their numerators. 5 is what part of 10? Compare their denominators. 8 is what part of 16? Compare in a similar way with; with. What effect upon the value of a fraction has dividing both terms by the same number? ===

16

10. What effect upon the quotient has dividing both dividend and divisor by the same number? Is dividing both numerator and denominator of a fraction by the same number the same as dividing both dividend and divisor by the same number?

Multiplying or dividing both terms of a fraction by the same number does not alter the value of the fraction.

11. Change the form of the following without changing their value, 12, 4, 18, 3, 18, 38, 15.

8 5 12 7

20 9

12. By what must the terms of the fraction & be multiplied to reduce the fraction to 10ths? to 15ths? to 20ths?

13. How many 12ths are there in 1? in ? in ?

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1. Change to 12ths. As the denominator 12 is 4 times the denominator of, the numerator of the required fraction must be 4 times the numerator of .

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Another method.

12. 3 is contained in 12 four times.

=

12.

1 = }}; } = } of 12, or 12; } = 2 times, or 12.

2. State how you would find the number that 3 must be multiplied by to change to 20ths.

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2 3

2 3
6

3. Change to 12ths: 1, 3, 4, 5, 1, 4, 8, 8, 8.

4. Change to 18ths:

5. Change to 24ths:

6. Change to 20ths:

7. Change to 36ths:

8. Change to 30ths:

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8 5

14

6

15, 16, 8, 3, 2, 1, 11, 3, 1o.

9. Write eight fractions and change them to 48ths.

10.

When the terms of a fraction have been made larger by reduction, the fraction is said to have been reduced to higher terms.

128. Oral Exercises.

1. Express each in a different form without changing the value: §, 34, 13, 1, 2, 21, 1, 8, 73, 42, 28,

2. Find the sum of 34, 24, and 7.

3. Find the difference:

4.

20. 1.

992/ 181 25 441

30 7-9 178 188

Show that of 2 yd. is equal to of 1 yd.; that of 8 ft. is the same as § of 1 ft.

129. Oral Exercises.

1. Show by a diagram that of a line is equivalent to of the line; that ft. ft.; that ft. + ft. = 7 ft., 3 1

or 11 ft.

=

= 12

2. Show with objects that of 12 objects = 12 of 12 objects; that of 12 objects of 12 objects; that of 12 objects + 1 of 12 objects = 12 of 12 objects + 2 of 12 objects, or 11 of 12 objects.

3. Why is it necessary to change and to 12ths before finding their sum?

4. Show by a diagram that the difference between ft. and 1 ft. is 151⁄2 ft.

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5. If of a group of objects contains 6 objects, show the number of objects in of the group.

6. Show with objects that if of a group of objects is 6 objects, the whole group contains 9 objects.

7. Show by a diagram that if % of the length of a line is 4 ft., the entire length of the line is 10 ft.

8. If 6 objects represent of the number of books on a certain shelf, represent by objects of the number of books on the shelf. Represent all the books.

9. What is the least number of boys that may be separated either into groups of 3 boys or of 4 boys?

10. What is the least number of equal parts into which a rectangle can be divided so that either or of the rectangle may be shown?

11. What is the least number of girls that can be separated into groups containing as many girls as are indicated in the denominator of any one of the following: 1, 3, 1, §. ?

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