By J. Kampe de Feriet, C.-F. Picard
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Additional info for Theories de l'information; actes des Rencontres de Marseille-Luminy, 5 au 7 juin 1973
The sum of the digits in the numerator is 24. The sum of the digits in the denominator is 30. Since these sums are both divisible by 3, each number is divisible by 3. Since these numbers meet the divisibility tests for 2 and 3, they are each divisible by 6. Example: 43, 672 Simplify to simplest form: 52, 832 Solution: Since both numbers are even, they are at least divisible by 2. However, to save time, we would like to divide by a larger number. The sum of the digits in the numerator is 22, so it is not divisible by 3.
A) (B) (C) (D) (E) 3 5 21 32 11 16 55 64 7 8 Solution: To compare the last four, we can easily use a common denominator of 64. 21 42 = 32 64 11 44 55 7 56 = = 16 64 64 8 64 7 7 3 7 The largest of these is . Now we compare with using Method II. 7 · 5 > 8 · 3; therefore, 8 8 5 8 is the greatest fraction. com 29 30 Chapter 2 Exercise 5 Work out each problem. Circle the letter that appears before your answer. 1. Arrange these fractions in order of size, from largest to smallest: (A) (B) (C) (D) (E) 2.
3. com 5. 2 7 of . 3 12 7 (A) 8 7 (B) 9 8 (C) 7 8 (D) 9 7 (E) 18 5 Divide 5 by . 12 25 (A) 12 1 (B) 12 5 (C) 12 Find (D) 12 (E) 12 5 Operations with Fractions 3. SIMPLIFYING FRACTIONS All fractional answers should be left in simplest form. There should be no factor that can still be divided into numerator and denominator. In simplifying fractions involving very large numbers, it is helpful to tell at a glance whether or not a given number will divide evenly into both numerator and denominator. Certain tests for divisibility assist with this.