Ferrell's Elementary Arithmetic by John Appley Ferrell

Author:John Appley Ferrell
Language: eng
Format: epub
Published: 1903-03-25T05:00:00+00:00

=40.

Explanation: (1) Cancel 5 out of 50 and 15, leaving 10 above and 3 below. (2) 96 contains 8 12 times; cancel 8 and 06, placing 12 above. (3) 12 contains 3 4 times; cancel 3 and 12, and place 4 above. (4) 4x 10=40.

6. How many times will 48 X 27 X15 contain 9 X 6 X10 ?

4

^ 8 3

?x(3x;0

=36.

Explanation: (1) 6 in 48 8 times. Cancel 6 and 48, and place 8 above. (2) 9 in 27 3 times. Cancel, and write 3 above. (3) 5 is common to 15 and 10. Cancel, and write 3 above and 2 below. (4) 2 in 8 4 times. Cancel, and write 4 above. (5) 4x3x3 = 36.

EXERCISE LXVII.

i. Divide 6X10 by 12.

2, Divide 9x24 by 36.

12X9X5 _ 45X18X4 _

^' 15X9 -^ '^ ^' 9X20 -^ '^

30X56X80 _. . 36X64X100 _

^' 100X12X28"^ ' 25x16x8 "^ ^'

36X50X28 _. . 42X52X108 _

^- 70X18X10"^ ^^ ^^* 78X60 "^ ^^

72X95X48 _. . 200X39X9X 21^

^' 24X19X15 ^ ^ 50X12X27" ^ ^

14X26X72 _ 210X340X1260 ^

^' 13X24X21"^ ^ 280X25X252 ^ ^

C. GREATEST COMMON DIVISOR.

75. Definition and Process.— The Greatest Common Divisor of two or more numbers is the largest number that is contained in each of them an integral number of times. The G. C. D. of two or more numbers is the product of all the 'prime factors common to the numbers. When the numbers are small enough to be factored mentally, factoring should be employed in finding the G. C. D.

EXAMPLES.

1. Find the G. C. D. of 210 and 150.

Factors of 210 are 3, 2, 5, 7. Factors of 150 are 3, 2, 5, 5. 3, 2 and 5 are common. .-. 3x2x5 = 30, G.C.D.

2. Find the G. C. D. of 55 and 77.

55 = 11x5. 77 = 7x11. .'. 11, being the only common factor, is the G.O.D.

S. Find the G. C. D. of 24, 48, and 72.

24 = 2x2x2x3.

48 = 2x2x2x2x3.

72 = 2x2x2x3x3.

2, 2, 2, 3 are common factors.

.-. 2x2x2x3=24, G.O.D.

4. Find the G. C. D. of 15, 45, and 60.

6 )15, 45, 60 3) 3, 9, 12

1, 3, 4 3 and 5 are all the common factors. .-. 3x5=15, G.O.D.

Note.— In this process, use only such divisors as will divide all the numbers.

EXERCISE LXVIII.

Find the G, C. D, of the following :

1. 10, 25, 50. r. 120, 150, 210.

2. 14, 85, 63. 8. 48, 128, 80.

3. 21, 68, 105. 9. 70, 42, 84.

4. 86, 60, 84. 10. 12, 18, 86, 66.

5. 80, 75, 90. 11. 24, 56, 72, 96.

6. 48, 12, 56. 12. 89, 65, 104, 156.

D. LEAST COMMON MULTIPLE.

76. Definition and Process.—The Least Common Multlx^le of two or more numbers is the smallest number that contains each of them an integral number of times. The L. C. M. of two or more numbers contains every prime factor of the several numbers the greatest number of times that it occurs in any one of them

EXAMPIiES.

1. Find the L. C. M. of 15, 12, and 10.

15 = 3x5.

12 = 3x2x2.

10 = 5x2.

The L.C.M. must contain 3 once, 5 once, and 2 twice.

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