1 Use a Figure and a Number Line to Add Fractions Add 3 5 1 5 : a) by drawing a fi gure to represent each fraction. b) using a number line. Solution a) Let’s shade 3 5 of a rectangle and 1 5 of a rectangle to fi nd the sum 3 5 1 5 . 3 shaded 1 1 shaded 5 4 shaded 5 5 5 How many total fi fths are shaded? 4 fi fths. Therefore, 3 5 1 5 4 5 . b) Now let’s use a number line to add these fractions just like we used a number line to add whole numbers in Section 1.2. To add 3 5 1 5 , start at 0 and move 3 5 unit to reach 3 5 . To add 1 5 unit, move 1 5 unit more to the right. We fi nish at 4 5 . 3 5 1 1 5 5 4 5 0 4 1 5 3 5 2 5 1 5 1 5 4 5 3 51 5 (or 5 ) 5 EXAMPLE 1 YOU TRY 1 Add 2 7 3 7 : a) by drawing a fi gure to represent each fraction. b) using a number line. Notice in Example 1 that the denominators of 3 5 and 1 5 are the same. When fractions have the same denominator, we call them like fractions. Definition Fractions with the same denominator are called like fractions. Fractions with different denominators are called unlike fractions. www.mhhe.com/messersmith SECTION 4.1 Adding and Subtracting Like Fractions 223
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