Section 3.4 Addition and Subtraction of Mixed Numbers 189 Addition and Subtraction of Mixed Numbers Section 3.4 1. Addition of Mixed Numbers In this section, we learn to add and subtract mixed numbers. To find the sum of two or more mixed numbers, add the whole-number parts and add the fractional parts. Adding Mixed Numbers Example 1 Add. 1 5 9 Solution: 2 Add the whole numbers. 323 The sum is . 3 2 3 1 5 9 1 9 3 2 6 9 1 9 Add the fractional parts. 3 When we perform operations on mixed numbers, it is often desirable to estimate the answer first.When rounding a mixed number, we offer the following convention. Skill Practice Add. 1. 7 Answers 1. 2. Estimate: 10; actual sum: 913 22 9 1 5 TIP: To understand why mixed numbers can be added in this way, recall that and . Therefore, 3 2 3 3 6 9 6 9 1 5 9 2 1 9 1 5 9 2 1 9 219 2 19 159 1 59 Concepts 1. Addition of Mixed Numbers 2. Subtraction of Mixed Numbers 3. Applications of Mixed Numbers Skill Practice Estimate the sum and then find the actual sum. 2. 6 1 11 3 1 2 2 15 2 1 15 Rounding a Mixed Number Step 1 If the fractional part of a mixed number is greater than or equal to (that is, if the numerator is half the denominator or greater), round to the next-greater whole number. For example, and both round to 7. 1 2 612 Step 2 If the fractional part of a mixed number is less than (that is, if the numerator is less than half the denominator), the mixed number rounds down to the whole number. For example 6 7 rounds to 6. 16 6 9 16 1 2 Adding Mixed Numbers Estimate the sum and then find the actual sum. Solution: To estimate the sum, first round the addends. 42 1 12 rounds to 42 17 7 8 rounds to 18 60 The estimated value is 60. 42 1 12 17 7 8 Example 2
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