Warm Up – Get Your Clicker Please Lesson Presentation Lesson Quizzes

Add or subtract. Write each answer in simplest form. Warm Up Add or subtract. Write each answer in simplest form. 1. 2. 3. 4. 1 12 __ 31 33 __ 11 12 __ 7 12 __

Learn to 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 __

Additional Example 1B: Adding and Subtracting Mixed Numbers Find the difference. Write the answer in simplest form. 2 3 __ 1 4 __ 5 – 1 6 – 1 = 5 Estimate the difference. 2 3 __ 8 12 __ The LCD of 3 and 4 is 12. 5 5 1 4 __ 3 12 __ Write equivalent fractions with a denominator of 12. –1 – 1 ______ ______ 5 12 __ Subtract the fractions and then the whole numbers. 4 5 12 __ 4 is close to the estimate 5. The answer is reasonable.

Additional Example 1C: Adding and Subtracting Mixed Numbers Find the difference. Write the answer in simplest form. 2 3 __ 2 9 __ 6 – 3 7 – 3 = 4 Estimate the difference. 2 3 __ 6 9 __ Think: 9 is a multiple of 3, so 9 is the LCD. 6 6 2 9 __ 2 9 __ Write equivalent fractions with a denominator of 9. –3 – 3 ______ ______ 4 9 __ 3 Subtract the fractions and then the whole numbers. 4 9 __ 3 is close to the estimate 4. The answer is reasonable.

Check It Out: Example 1A Find the sum. Write the answer in simplest form. 1 4 __ 1 6 __ 2 + 3 2 + 3 = 5 Estimate the sum. 1 4 __ 6 24 __ Multiply the denominators. 4 · 6 = 24 2 2 1 6 __ 4 24 __ Write equivalent fractions with a denominator of 24. +3 + 3 ______ ______ 10 24 __ 5 12 __ Add the fractions and then whole numbers, and simplify. 5 = 5 5 12 __ 5 is close to the estimate 5. The answer is reasonable.

Check It Out: Example 1B Find the difference. Write the answer in simplest form. 1 2 __ 3 7 __ 4 – 1 5 – 2 = 3 Estimate the difference. 1 2 __ 7 14 __ 4 4 The LCD of 2 and 7 is 14. 3 7 __ 6 14 __ Write equivalent fractions with a denominator of 14. –1 – 1 ______ ______ 1 14 __ Subtract the fractions and then the whole numbers. 3 1 14 __ 3 is close to the estimate 3. The answer is reasonable.

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 Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

Lesson Quiz for Student Response Systems 1. Identify the difference in the simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 2. Identify the sum in the simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 3. Identify the sum in the simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 4. Identify the difference in the simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 5. Shiloh bought pounds of bananas and pounds of apples. How many pounds of fruits did she buy? A. C. B. D.