Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

20. Find the totals in the following list of the naval forces of the United States in 1917 :

[blocks in formation]

21. Find the totals in the following list showing the extent of a recent Naval Appropriation Bill:

[merged small][ocr errors][merged small][merged small]

TYPE
Battleships.
Battle cruisers.
Scout cruisers
Destroyers.
Fleet submarines
Coast submarines :

800-ton type

Smaller type
Neff submarine
Fuel ships
Ammunition ships
Hospital ship
Repair ship
Transport
Destroyer tenders
Submarine tender
Gunboat

Totals

[blocks in formation]

CHAPTER III

FRACTIONS AND FACTORS

A Fraction is an expression denoting one or more equal parts of a unit. It is an indicated division, usually written in the form

The number below the line is called the denominator. It shows into how many parts the whole number has been divided.

The number above the line is called the numerator. It shows how many parts have been taken to form the fraction.

The numerator and denominator are called the terms of the fraction.

A proper fraction is one whose numerator is less than its denominator. Thus, i, j, and 84

64 are proper

fractions. An improper fraction is one whose numerator is equal to, or greater than, its denominator. Thus, 4, s, and 42 are improper fractions.

A mixed number is a whole number with a fraction. Thus, 17, 27, and 34 are mixed numbers.

Mixed Numbers Expressed as Fractions Rule. - To express a mixed number as a fraction, multiply the whole number by the denominator, add the numerator, and write the result over the denominator.

EXAMPLE. Express 3ş as a fraction.
8 x 3 + 5 = 29, the numerator of the fraction required.
The denominator is 8.
Then 3 = 20

ORAL DRILL
Express as fractions the following mixed numbers :
1. 11

7. 116
13. 41 19. 63

25. 8 2. 13 8. 176

14. 51

20. 73 26. 91 3. 14 9. 111 15. 5

21. 82

27. 93 10. 11% 4. 13

16. 54 22. 8} 28. 9 11. 41 5. 1]

17. 53

23. 84 29. 107 6. 13 12. 44 18. 55

24. 8}

30. 1076

Exercise Express as fractions the following mixed numbers : 1. 47 7. 743 13. 973 19. 73 25. 924 2. 684

8. 593 14. 705 20. 874 26. 94} 3. 963 9.764 15. 27 21. 82 27. 693 4. 784 10. 38%

16. 49 22. 80 28. 53 5. 561 11. 823 17. 963 23. 966 29. 57% 6 645 12. 65 18. 804 24. 738 30.667

Improper Fractions Expressed as Mixed Numbers

Rule. — To express an improper fraction as a whole or mixed number, divide the numerator by the denominator.

EXAMPLE. Express 22 as a whole or mixed number.

34

ORAL DRILL Express as whole or mixed numbers the following fractions :

[blocks in formation]

7. 128

19. 25 6

75

25. 360

32

38

13. 25 6

30 14. 25 6

20. 25

Exercise Express as whole or mixed numbers the following fractions : 1. 128 2. 12.30 8. 128 3. 128 9. 128

21. 3.60

27.32 4. 120 16.256

28. 360 11. 256 5. 12

17. 25
23.360

29.
6. 123
12.256

24.3639 30. 3,950

32

26. 360

43

15. 256

35

10. 128

84

22. 3 6 0

15

2 5 6
45

360 85

18. 2.56

Greatest Common Divisor

The Greatest Common Divisor of two or more numbers is the greatest number that is exactly contained in all of them. It is also called the highest common factor.

Thus, 12 is the greatest common divisor of 24 and 36.

Greatest Common Divisor is commonly abbreviated G. C. D. or H. C. F.

The principal use of greatest common divisor is its application in reducing fractions to their lowest terms.

Prime Numbers. - If numbers have no common factor other than 1, they are said to be prime to each other.

The greatest common divisor of two or more numbers can frequently be found by inspection, but when this is impossible, observe the following rule.

Rule.-(1) Separate the numbers into prime factors, and (2) find the product of the prime factors common to the numbers.

EXAMPLE. Find the G. C. D. of 54, 72, and 108.

54 = 2 X 3 X 3 X 3
72 2 x 2 x 2 x 3 x 3

108 = 2 X 2 X 3 X 3 X 3
G.C.D. = 2 X 3 X 3 = 18

Exercise Find the G.C. D. of the following: 1. 4, 16

11. 10, 35, 85 2. 12, 78

12. 14, 21, 77 3. 15, 75

13. 18, 72, 81 4. 17, 51

14. 24, 60, 96 5. 19, 171

15. 32, 48, 96 6. 21, 105

16. 36, 54, 90 7. 23, 207

17. 39, 52, 91 8. 6, 8, 42

18. 63, 84, 126 9. 8, 28, 84 19. 33, 77, 121 10. 9, 33, 81 20. 30, 60, 250

21. 32, 48, 128 22. 51, 63, 132 23. 36, 84, 132 24. 60, 144, 576 25. 38, 190, 760 26. 32, 160, 808 27. 33, 132, 143 28. 50, 125, 250 29. 64, 128, 256 30. 64, 160, 640

Factors

A Factor of a number is a number which is exactly contained in that number. Thus, 2, 3, 4, and 6 are all factors of 12.

« ΠροηγούμενηΣυνέχεια »