Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Comparing Fractions *

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1 OpenStax-CNX module: m9 Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Comparing Fractions * Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License.0 Abstract This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to compare fractions. By the end of the module students should be able to understand ordering of numbers and be familiar with grouping symbols and compare two or more fractions. Section Overview Order and the Inequality Symbols Comparing Fractions 2 Order and the Inequality Symbols Our number system is called an ordered number system because the numbers in the system can be placed in order from smaller to larger. This is easily seen on the number line. On the number line, a number that appears to the right of another number is larger than that other number. For example, is greater than 2 because is located to the right of 2 on the number line. We may also say that 2 is less than. To make the inequality phrases "greater than" and "less than" more brief, mathematicians represent them with the symbols > and <, respectively. * Version.: Aug 20, 200 :0 pm

2 OpenStax-CNX module: m9 2 Symbols for Greater Than > and Less Than < > represents the phrase "greater than." < represents the phrase "less than." > 2 represents " is greater than 2." 2 < represents "2 is less than." Comparing Fractions Recall that the fraction indicates that we have of parts of some whole quantity, and the fraction indicates that we have of parts. Since of parts is more than of parts, is greater than ; that is, > We have just observed that when two fractions have the same denominator, we can determine which is larger by comparing the numerators. Comparing Fractions If two fractions have the same denominators, the fraction with the larger numerator is the larger fraction. Thus, to compare the sizes of two or more fractions, we need only convert each of them to equivalent fractions that have a common denominator. We then compare the numerators. It is convenient if the common denominator is the LCD. The fraction with the larger numerator is the larger fraction.. Sample Set A Example Compare 9 and. Convert each fraction to an equivalent fraction with the LCD as the denominator. Find the LCD. 9 = 2 = } The LCD = 2 = 9 = 9 = = 0 = = 2 Since 0 < 2, 0 < 2 Thus 9 <. Example 2 Write 6,, and in order from smallest to largest. 0 Convert each fraction to an equivalent fraction with the LCD as the denominator. Find the LCD. 6 = 2 0 = 2 = 6 = = = = = 2 = Since 2 < 2 < 26, 2 < 2 < }The LCD = 2 = 0 < 0 6 < Writing these numbers in order from smallest to largest, we get, 0 6,. Example Compare 6 and 6.

3 OpenStax-CNX module: m9 To compare mixed numbers that have dierent whole number parts, we need only compare whole number parts. Since 6 <, 6 < 6 Example Compare and 2 To compare mixed numbers that have the same whole number parts, we need only compare fractional parts. = 2 2 = 2 2 }The LCD = 2 = = 2 = = 2 2 = 2 = Since <, < < Hence, 2 <.2 Practice Set A Exercise (Solution on p..) Compare and. Exercise 2 (Solution on p..) Compare 9 and 0 Exercise (Solution on p..) Write,, and in order from smallest to largest Exercise (Solution on p..) Compare 6 and 9 2. Exercise (Solution on p..) Compare 9 and 6 Exercises Arrange each collection of numbers in order from smallest to largest. Exercise 6 (Solution on p..), Exercise 6, 2 Exercise (Solution on p..), 6 Exercise 9 9, 2 Exercise 0 (Solution on p..), 2 Exercise 2,, 6

4 OpenStax-CNX module: m9 Exercise 2 (Solution on p..) 2,, Exercise, 2, 6 Exercise (Solution on p..), 9, Exercise, 6 2 Exercise 6 (Solution on p..), 2, Exercise Exercise (Solution on p..), Exercise Exercise 20 (Solution on p..) 9 2, 9 Exercise 2 2, 6 Exercise 22 (Solution on p..) Exercise 2 20, Exercise 2 (Solution on p..) 2 2 9, 2 Exercise 2, Exercises for Review Exercise 26 (Solution on p..) () Round 26,006,2 to the nearest ten million. Exercise 2 () Is the number 2,6 divisible by 2? by? by? Exercise 2 (Solution on p..) () Convert 2 to an improper fraction. Exercise 29 () Find the value of Exercise 0 (Solution on p..) () Find the value of +.

5 OpenStax-CNX module: m9 Solutions to Exercises in this Module Solution to Exercise (p. ) < Solution to Exercise (p. ) < 9 0 Solution to Exercise (p. ),, Solution to Exercise (p. ) 9 2 < 6 Solution to Exercise (p. ) 9 < 6 Solution to Exercise (p. ) < Solution to Exercise (p. ) < 6 Solution to Exercise (p. ) < 2 2 < < < 9 < < 2 < < 9 2 < 9 9 < < 2 20,000,000 2 or 09