164 Chapter 3 Fractions and Mixed Numbers: Addition and Subtraction Section 3.1 Addition and Subtraction of Like Fractions 1. Addition and Subtraction of Like Fractions In Chapter 2 we learned how to multiply and divide fractions. The main focus of this chapter is to add and subtract fractions. The operation of addition can be thought of as combining like groups of objects. For example: 3 apples 1 apple 4 apples three-fifths one-fifth four-fifths 3 5 The fractions and are said to be like fractions because their denominators are the same.That is, the fractions have a common denominator. In general, two or more like fractions may be added or subtracted according to the following procedure. Adding and Subtracting Like Fractions Step 1 Add or subtract the numerators. Step 2 Write the sum or difference over the common denominator. Step 3 Simplify the fraction to lowest terms, if possible. Adding Like Fractions Example 1 Add. Write the answer as a fraction or whole number. a. b. Solution: a. Add the numerators. Write the sum over the common denominator. Simplify to lowest terms. 1 4 7 15 6 3 42 b. Add the numerators. Simplify to lowest terms. 2 2 3 10 15 3 10 15 2 15 1 15 7 2 1 15 3 2 6 4 5 4 1 5 4 7 15 2 15 1 15 1 4 5 4 15 3 5 1 5 4 5 = 1 5 3 5 4 5 Answers 1. 2. 23 12 2 3 Write the sum over the common denominator. Concepts 1. Addition and Subtraction of Like Fractions 2. Order of Operations 3. Applications of Addition and Subtraction of Fractions Avoiding Mistakes Notice that when adding fractions, we do not add the denominators. We add only the numerators. Skill Practice Add. Write the answer as a fraction or whole number. 1. 2. 7 12 5 12 11 12 2 9 4 9
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