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Chapter 3—Fractions

3-10 Comparing Fractions

 When you complete the work for this section, you should be able to: Determine whether one fraction is smaller, equal, or larger than another.

Being able to compare the values of fractions is especially important in the U.S. system of measurement. The metric system virtually eliminates a real need for fractions and comparing values of fractions. Nevertheless, the concepts and thought processes involved in comparing fractional values can prove useful in other areas of modern mathematics.

 Consider this example: One piece of lumber is 5/8" thick and another is 3/4" thick. Which is thicker? Thinking in terms of a ruler, you can see that 3/4" is larger than 5/8" (even though the fraction 5/8 uses larger numbers).

Here is another situation that calls for comparing fractional values:

At 200° F, the area of a small metal plate is 23/32 in2. At 600° F, the area is found to be 55/64 in2. Does the metal expand or contract as its temperature rises? In other words, is 55/64 larger or smaller than 23/32?

Think about it as you work through the remainder of this lesson.

Comparing Fractions with Common Denominators

 Procedure When comparing two fractions that have a common denominator: Compare the numerators.  The fraction with the larger numerator is the larger fraction.

Examples:

 1.    Which is larger, 3/8 or 1/8 ? Denominators are the same. The numerator of 3/8 is larger than the numerator of 1/8. So 3/8 > 1/8 2.    Which is larger, 3/16 or 5/16 ? Denominators are the same. The numerator of 5/16 is larger than the numerator of 3/16. So 5/16 > 3/16 3.    Which is larger, 5/64 or 7/64 ? Denominators are the same. The numerator of 7/64 is larger than the numerator of 5/64. So 7/64 > 5/64

Examples and Exercises

 Comparing Fractions Having Common Denominators Indicate the fraction that has the larger value.

Comparing Fractions that Do Not Have Common Denominators

 Procedure When two fractions do not have the same denominator: Adjust the fractions so that they have a common denominator. Compare the numerators. The fraction with the larger numerator is the larger fraction.

Examples:

 1.    Which is larger, 3/8 or 1/4 ? After rewriting the fractions so they have a common denominator:  3/8 or 2/8 The numerator of 3/8 is larger than the numerator of 2/8. So 3/8 > 1/4 2.    Which is larger, 22/27 or 4/9 ? Rewriting the fractions to have a common denominator: 22/27 or 12/27 The numerator of 22/27 is larger than the numerator of 12/27. So 22/27 > 4/9 3.    Which is larger, 4/5 or 3/4 ? Rewriting the fractions to have a common denominator: 16/20 or 15/20 The numerator of 16/20 is larger than the numerator of 15/20. So 4/5 > 3/4

Examples and Exercises

 Comparing Fractions Not Having Common Denominators Indicate the fraction that has the larger value.

Comparing Mixed Fractions

 Procedure When comparing mixed fractions, the one with the larger whole-number part is the larger number — provided the fraction part is a proper fraction. Rewrite any improper fraction as a proper fraction. Compare the whole-number values. The fraction with the larger whole-number part is the larger value.

Examples:

 1.    Which is larger, 5 1/8 or 2 3/4 ? The fraction parts for both values are proper fractions, and whole-number 5 is greater then whole-number 2, so: 5 1/8 is greater than 2 3/4 2.    Which is larger, 16 3/4 or 18 1/8 ? The fraction parts for both values are proper fractions, and whole-number 18 is greater than whole-number 16. Thus: 18 1/8 > 16 3/4 3.    Which is larger, 110/5 or 2 3/4 ? The fraction part 10/5 is not a proper fraction -- it is actually equal to 2. So when 110/5 is rewritten as a proper fraction, it becomes 3. Now, which is larger,   3 or  2 3/4 ?  Of course 3 is larger than 2 3/4. So: 110/5 is larger than 2 3/4

Examples and Exercises

 Comparing Mixed Fractions Indicate the fraction or mixed fraction that has the larger value.