5-3 Adding and Subtracting Mixed Numbers Warm Up Problem of the Day Course 1 Warm Up Problem of the Day Lesson Presentation

Add or subtract. Write each answer in simplest form. Warm Up Add or subtract. Write each answer in simplest form. 1. – 2. + 3. + 4. – 7 12 __ 1 2 __ 1 12 __ 3 11 __ 2 3 __ 31 33 __ 1 6 __ 3 4 __ 11 12 __ 11 12 __ 1 3 __ 7 12 __

Problem of the Day The sum of every row, column and diagonal is the same. Complete the magic square. 1 __ 3 1 3 __ 11 12 ___ 4 1 6 __ 5 6 __ 12 1 __ 2 3 __ 1 4 __

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 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 ______ ______ 46 48 __ 23 24 __ Add the fractions and then whole numbers, and simplify. 4 = 4

Additional Example 1B: Adding and Subtracting Mixed Numbers Find the difference. Write the answer in simplest form. 2 3 __ 1 4 __ 5 – 1 2 3 __ 8 12 __ The LCD of 3 and 12 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

Additional Example 1C: Adding and Subtracting Mixed Numbers Find the sum. Write the answer in simplest form. 1 2 __ 4 5 __ 2 + 4 1 2 __ 5 10 __ 2 2 The LCD of 2 and 10 is 10. 4 5 __ 8 10 __ Write equivalent fractions with a denominator of 10. +4 + 4 ______ ______ 13 10 __ 3 10 __ Add the fractions and then the whole numbers, and simplify. 6 = 7 13 10 __ 3 10 __ 6 = 6 + 1

Additional Example 1D: Adding and Subtracting Mixed Numbers Find the difference. Write the answer in simplest form. 2 3 __ 2 9 __ 6 – 3 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.

Check It Out: Example 1A Find the sum. Write the answer in simplest form. 1 4 __ 1 6 __ 2 + 3 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

Check It Out: Example 1B Find the difference. Write the answer in simplest form. 1 2 __ 3 7 __ 4 – 1 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

Check It Out: Example 1C Find the sum. Write the answer in simplest form. 7 8 __ 2 3 __ 2 + 4 7 8 __ 21 24 __ 2 2 The LCD of the denominators is 24. 2 3 __ 16 24 __ Write equivalent fractions with a denominator of 24. +4 + 4 ______ ______ 37 24 __ 13 24 __ Add the fractions and then the whole numbers, and simplify. 6 = 7 6 = 6 + 1 37 24 __ 13

Check It Out: Example 1D Find the difference. Write the answer in simplest form. 3 4 __ 1 8 __ 7 – 2 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

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 __ 1 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. Helpful Hint You can use mental math to find an LCD. Think: 8 is a multiple of 4 and 8.

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. 7 – 4 2. 9 + 7 3. 6 + 1 4. 10 – 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 __ __ 11 __ 2 __ 1 __ 3 12 3 6 8 __ 7 __ 3 8 7 40 __ __ 2 1 6 7 30 __ __ 8 10 5 6 3 __ __ 2 4 3 5 12 __ 14 hours