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

2. Warm Up Add or subtract. 1. 2. 3. 4. 3 8 4 8 7 8 + 11 12 7 12 1 3 – 26 3 10 1 5 + –

3. 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, 1 ÷
d. 13,579
2,468

4. Learn to add and subtract mixed numbers.

5. Additional Example 1: Measurement Application3 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 =
Helpful Hint 4 5

6. 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 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.

7. 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 = 1 3 = 22 1 3
Helpful Hint
Add the fractions first in case an improper fraction needs to be rewritten.

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

9. 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. = 1 5 = 18 1 5
Add.

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

11. 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 =
Rewrite 1 as a fraction with a common denominator. 8
= 6 + + 1
= 6 9 8
Add.

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

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

20. 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

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

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

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

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

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