190 Chapter 3 Fractions and Mixed Numbers: Addition and Subtraction To find the actual sum, we must first write the fractional parts as like fractions. The LCD is 24. 5923 42 1 12 42 1 2 12 2 42 2 24 17 7 8 17 7 3 8 3 21 24 59 17 23 24 The actual sum is . This is close to our estimate of 60. 24 Adding Mixed Numbers with Carrying Example 3 Estimate the sum and then find the actual sum. Solution: 7 5 6 7 5 6 3 rounds to 8 3 3 5 rounds to 4 3 5 12 The estimated value is 12. To find the actual sum, first write the fractional parts as like fractions. The LCD is 30. 3 43 30 7 5 6 7 5 5 6 5 7 25 30 3 5 3 3 6 5 6 18 30 10 3 43 30 Notice that the number is an improper fraction. By convention, a mixed number is written as a whole number and a proper fraction. We have Therefore, 1113 10 43 30 10 1 13 30 11 13 30 The sum is . This is close to our estimate of 12. 30 43 30 113 30. We have shown how to add mixed numbers by writing the numbers in columns. Another approach to add or subtract mixed numbers is to write the numbers first as improper fractions. Then add or subtract the fractions, as you learned in Section 3.3. To demonstrate this process, we add the mixed numbers from Example 3. Skill Practice Estimate the sum and then find the actual sum. 3. 5 29 8 Answers 3. Estimate: 13; actual sum: 4. Write the improper fraction as , and 11 8 1313 add the result to 2. The result is 31. 8 9 8 45 2 5 7 8 9 Concept Connections 4. Explain how you would rewrite as a mixed number containing a proper fraction.
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