Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Objective: students add and subtract mixed numbers

Warm Up Add or subtract. 1. 2. 3. 4. 3 8 4 8 7 8 + 11 12 7 12 1 3 – 2 6 3 10 1 5 + –

Problem of the Day Which of these four expressions is the largest value? a. 13,579 + 1 2,468 1 b. 13,579 − 2,468 c. 13,579.2468 1 ÷ d. 13,579 2,468

Learn to add and subtract mixed numbers.

Additional Example 1: Measurement Application 3 8 5 8 Kevin is 48 inches tall. His brother Keith is 5 inches taller. How tall is Keith ? Add the integers and add the fractions. 3 8 5 8 8 48 + 5 = 53 + 8 = 53 + 1 Rewrite as 1. 54 inches tall. A mixed number is the sum of an integer and a fraction: 3 = 3 + . Helpful Hint 4 5

Add the integers and add the fractions. 72 + 15 87 + Check It Out: Example 1 2 3 Alvin weighs 72 lbs. His baby brother weighs 15 lbs. How much do they weigh together? 1 3 2 3 1 3 3 Add the integers and add the fractions. 72 + 15 = 87 + 3 as 1. = 87 + 1 Rewrite Together they weigh 88 pounds.

Additional Example 2A: Adding Mixed Numbers Add. Write the answer in simplest form. 2 3 2 3 9 + 12 Add the fractions and then add the integers. 9 2 3 + 12 = 21 + 4 3 Rewrite the improper fraction as a mixed number. Add = 21 + 1 1 3 = 22 1 3 Helpful Hint Add the fractions first in case an improper fraction needs to be rewritten.

Additional Example 2B: Adding Mixed Numbers Add. Write the answer in simplest form. 1 8 5 6 5 + 3 5 1 8 + 3 6 = 5 + 3 20 24 3 Find a common denominator. = 8 + 23 24 Add the fractions and then add the integers. = 8 23 24 Add.

Check It Out: Example 2A Add. Write the answer in simplest form. 4 5 2 5 7 + 10 Add the fractions and then add the integers. 7 4 5 + 10 2 = 17 + 6 5 Rewrite the improper fraction as a mixed number. = 17 + 1 1 5 = 18 1 5 Add.

Check It Out: Example 2B Add. Write the answer in simplest form. 1 4 3 8 4 + 4 4 1 + 4 3 8 = 4 + 4 3 8 2 Find a common denominator. = 8 + 5 8 Add the fractions and then add the integers. = 8 5 8 Add.

REGROUPING MIXED NUMBERS Sometimes when you subtract mixed numbers, the fraction portion of the first number is less than the fraction portion of the second number. In these cases, you must regroup before subtracting. REGROUPING MIXED NUMBERS WORDS NUMBERS Regroup. 1 8 7 = 6 + 1 + Rewrite 1 as a fraction with a common denominator. 8 = 6 + + 1 = 6 9 8 Add.

Remember! Any fraction in which the numerator and denominator are the same is equal to 1.

Additional Example 3A: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 2 3 1 3 4 – 2 Subtract the fractions and then subtract the integers. 4 2 3 – 1 = 2 + 1 3 = 2 1 3 Add.

Additional Example 3B: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 8 9 2 3 12 – 8 12 8 9 – 2 3 = 12 8 9 – 6 Find a common denominator. Subtract the fractions and then subtract the integers. = 4 + 2 9 = 4 2 9 Add.

Additional Example 3C: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 1 8 3 8 17 – 12 16 9 8 – 12 3 17 1 8 – 12 = 3 Regroup 17 1 8 = 16+ + . = 4 + 6 8 Subtract the fractions and then subtract the integers. = 4 6 8 = 4 3 Add and simplify.

Subtract the fractions and then subtract the integers. 3 4 5 – 2 1 = Check It Out: Example 3A Subtract. Write the answer in simplest form. 4 5 1 5 3 – 2 Subtract the fractions and then subtract the integers. 3 4 5 – 2 1 = 1 + 3 5 = 1 3 5 Add.

Find a common denominator. Check It Out: Example 3B Subtract. Write the answer in simplest form. 7 8 3 4 10 – 4 10 7 8 – 4 3 = 10 7 8 – 4 6 Find a common denominator. Subtract the fractions and then subtract the integers. = 6 + 1 8 = 6 1 8 Add.

Check It Out: Example 3C Subtract. Write the answer in simplest form. 1 4 3 4 14 – 10 13 5 4 – 10 3 14 1 4 – 10 = 3 Regroup 14 1 4 = 13+ + . = 3 + 2 4 Subtract the fractions and then subtract the integers. = 3 2 4 = 3 1 Add and simplify.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Add or subtract. Write each answer in simplest form. 1. 5 2. 9 3. 7 Lesson Quiz Add or subtract. Write each answer in simplest form. 1. 5 2. 9 3. 7 4. 10 10 5 12 1 4 1 6 + 5 2 3 7 12 20 1 4 + 10 7 8 3 4 5 1 8 – 2 2 9 5 6 5 7 18 – 4 1 2 5. A single roll of wallpaper unrolls to 15 yards 7 8 you hang 13 yards from the roll. How much wallpaper remains? 1 yards 5 8

Lesson Quiz for Student Response Systems 1. Add. Write your answer in simplest form. 6 + 6 A. 12 C. 10 B. 21 D. 6 1 3 1 7 10 21 4 7 5 6 1 10

Lesson Quiz for Student Response Systems 2. Add. Write your answer in simplest form. 7 + 5 A. 10 C. 12 B. 11 D. 13 2 5 1 3 11 15 11 15 11 15 11 15

Lesson Quiz for Student Response Systems 3. Subtract. Write your answer in simplest form. 5 – 4 A. 1 C. 5 B. 1 D. 7 5 6 1 4 7 12 1 3 3 5 1 12

Lesson Quiz for Student Response Systems 4. Subtract. Write your answer in simplest form. 11 – 2 A. 2 C. 9 B. 4 D. 9 2 7 1 6 5 42 1 21 5 42 5 42

Lesson Quiz for Student Response Systems 1 3 5. Bryan has a ribbon of length 14 inches. He uses 12 inches to wrap a gift. What length of the ribbon is left? A. 1 in. C. 1 in. B. 1 in. D. 1 in. 7 9 4 9 2 3 5 9 1 3