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Find the least common multiple of:

3. 15, 20, 30

13.

16, 24, 32

4. 18, 24, 36

14. 20, 35, 42

5. 14, 21, 42

15.

27, 45, 63

6. 27, 54, 63

16.

28, 40, 56

7. 32, 48, 96

17.

36, 48, 64

8. 36, 54, 63

18.

32, 52, 65

9. 64, 72, 108

19. 50, 60, 70

10. 72, 84, 120

20.

55, 75, 88

11. 54, 81, 135

21. 60, 72, 96

12. 8, 12, 16, 20

22. 84, 108, 120

Find the g. c. d. and the 1. c. m. of each of the following:

23. 45, 105, 180

27. 42, 70, 126

24. 36, 132, 192

28. 48, 80, 144

25. 54, 108, 198

29.

66, 134, 220

26. 39, 91, 130

30. 60, 135, 180

FRACTIONS

1. Divide 1 into 5 equal parts; into 10 equal parts; into 15 equal parts.

2. What is meant by,, or, of 1?

§

3. What is meant by? by ft.? by yd.? 4. In 10 there are how many whole units?

An integer or an integral number is a whole number.

5. How many integral units are there in 5? in 10 ft.? in 5 yd.? in 4 mi. ? in $10?

6. If 1 ft. is divided into 12 equal parts, what is each part called? How many twelfths of a foot does it take to equal a foot?

A fractional unit is one of the equal parts into which an integral unit has been divided; as, 1, 1, 1, 1b, 12, etc.

A fraction is one or more fractional units; as, 1, 4, 7, 8, 10. 7. How many fractional units are there in ? in? in? in? in ? in? in 12? How many are there in ? in? in ? in ? in &?

8. Observe that the sum of the fractional units of an integral unit equals the integral unit. Thus, 1=1; f=1; =1; 8=1; 18=1.

9. In the fraction, what is 3 called and what does it show?

10. In the fraction, what is 4 called and what does it show?

Since the denominator (p. 23) of a fraction shows into how many equal parts the integral unit has been divided, as, tenths, thirds, fourths, it shows the size of the fractional unit.

Since the numerator (p. 23) of a fraction shows the number of fractional units taken, as, two thirds,, it names the number of the fractional units.

11. Observe that the unit of measure in 12 yd. is 1 yd.; thus, 12 yd. means 12 x 1 yd; $8 means 8 x $1. What does 16 acres mean? 6 dozen ?

12. Name the different units of measure in problem 11. 13. Observe that the unit of measure in 12 in. is1⁄2 in.; thus, in. means 7 × in.; $ means 4 x $. What does acre mean? dozen?

2

14. What are the different units of measure in problem 13? 15. With what kind of a unit do we measure or compare whole numbers?

16. With what kind of a unit do we measure or compare fractions?

17. What is a proper fraction? (see p. 59). Explain why the fractional forms, 8, 1, 4, 4, are not proper fractions. 18. What is an improper fraction? (see p. 59). A mixed number? (see p. 35).

REDUCTION OF FRACTIONS

Changing a mixed number to an improper fraction.

1. Change 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, each to the fractional unit 4ths; to 5ths; to 6ths; to 7ths. Thus, 1=1, 2, etc.

2. Change 11, 13, 23, 35, 27, 8, 9, 105, each to the fractional units indicated by the fraction of the mixed numbers. Thus, 11-3.

=

3. What kind of fractions are 1⁄2, 1, 12?

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Written Work

1. Change 11 to an improper fraction.

117

15

165

7

172

15

To change a mixed number to an improper fraction, multiply the whole number by the denominator. To this product add the numerator, and write the sum over the denominator.

Since 1 unit 1, 11 units = 11 × 1 = 185; 185 + 18:

=

122.

[blocks in formation]

Changing an improper fraction to a mixed number.

1. Name the integers and the fractions in 5, 15, 4 ft., 4 lb., $20, 25 yd., 10 oz., 23 in.

2. How much greater than 1 are ? ? ? ? 15? 12? 18? 18?

3. In changing ft. to integers and fractions, think first how many fourths it takes to make one whole unit. Then

7

= how many whole units and & remaining?

HAM. INT. ARITH. - 10.

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Written Work

1. Change 145 to a mixed number.

Since 1 =

8)145

8 eighths, in 145 eighths there are as many 1's as 8 eighths are contained times in 145 eighths, or 18}. 18 Therefore 145 = 18.

Change to mixed numbers:

2. 25

8. 86

3. 37

9.65 oz.

4. 46

5. 29

6.- 65

7. 75

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1

Changing the size of fractional units without changing the value of the fraction.

10. $75

11. lb.

12. 14 hr.

13. 124 min.

?

14.

흑표
12

15.

15 mi.

16.

rd.

17.

2 bu.

18. 110 in.

19.

116 A.

10

1.

2. }=}=}=12=18.

3.

== 12=16-20-24-28-32.

4. In changing to, we multiply both terms of the fraction by 3. Does this affect the value of ? Draw a figure to show that and are the same in value.

5. In changing to we divide both terms of the fraction by 3. Does this change its value? Illustrate by the figure drawn for example 4.

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

7

6. Change, 1, 1, 3, 8, 12, §, f2, each to twenty-fourths.

10 15

7. Change, 12, 13, 14, 18, 14, 35, each to sixths.

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