5.3 Adding and Subtracting Mixed Numbers

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Presentation transcript:

5.3 Adding and Subtracting Mixed Numbers I can add and subtract mixed numbers with unlike denominators

Additional Example 1A: Adding and Subtracting Mixed Numbers Find the sum. Write the answer in simplest form. 1 8 __ 5 6 __ 3 + 1 3 + 2 = 5 Estimate the sum. 1 8 __ 6 48 __ Multiply the denominators. 8 · 6 = 48 3 3 5 6 __ 40 48 __ Write equivalent fractions with a denominator of 48. +1 + 1 ______ ______ Add the fractions and then whole numbers, and simplify. 46 48 __ 23 24 __ 4 = 4 4 is close to the estimate of 5. The answer is reasonable. 46 48 __

Check It Out: Example 1C Find the difference. Write the answer in simplest form. 3 4 __ 1 8 __ 7 – 2 8 – 2 = 6 Estimate the difference. Think: 8 is a multiple of 4, so 8 is the LCD. 3 4 __ 6 8 __ 7 7 Write equivalent fractions with a denominator of 8. 1 8 __ 1 8 __ –2 – 2 ______ ______ 5 8 __ Subtract the fractions and then the whole numbers. 5 5 8 __ 5 is close to the estimate 6. The answer is reasonable.

Additional Example 2: Measurement Application The length of Jen’s kitten’s body is 10 inches. Its tail is 5 inches long. What is the total length of its body and tail? 1 4 __ 1 8 __ 1 4 __ 8 Add 10 + 5 Find a common denominator. Write equivalent fractions with the LCD, 8, as the denominator. 1 4 __ 2 8 __ 10 10 1 8 __ 1 8 __ +5 + 5 ______ ______ Add the fractions and then the whole numbers. 3 8 __ 15 3 8 __ The total length of the kitten’s body and tail is 15 inches. You can use mental math to find an LCD. Think: 8 is a multiple of 4 and 8. Helpful Hint

Check It Out: Example 2 The length of Regina’s mouse’s body is 2 inches. Its tail is 2 inches long. What is the total length of its body and tail? 2 3 __ 1 6 __ 2 3 __ 1 6 Add 2 +2 . Find a common denominator. Write equivalent fractions with the LCD, 6, as the denominator. 2 3 __ 4 6 __ 2 2 1 6 __ 1 6 __ +2 + 2 ______ ______ 5 6 __ Add the fractions and then the whole numbers. 4 5 6 __ The total length of the mouse’s body and tail is 4 inches.

Lesson Quiz Find each sum or difference. Write the answer in simplest form. 1. 2. 3. 4. 5. Miles worked 5 hours on Friday and 8 hours on Saturday. How many total hours did he work? 3 1 4 __ 16 13 24 __ 8 7 40 __ 6 7 30 __ 3 __ __ 2 4 3 5 12 __ 14 hours