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Adding and Subtracting
4-11 Mixed Numbers
Warm Up
Problem of the Day
Lesson Presentation
Course 2
4-11 Adding and Subtracting Mixed Numbers
Warm Up
Add or subtract.
1. 3 + 4 7
8 8 8
2. 11 – 7
12 12
1
3
3. 2 – 1
4.
Course 2
7
3 12 12
1 +1 – 3
3 6 10
1
5
4-11 Adding and Subtracting Mixed Numbers
Problem of the Day
Which of these four expressions is
the largest value?
1
a. 13,579 +
2,468
b. 13,579 − 1
2,468
c. 13,579.2468
1
÷
d. 13,579 2,468
Course 2
4-11 Adding and Subtracting Mixed Numbers
Learn to add and subtract mixed numbers.
Course 2
4-11 Adding and Subtracting Mixed Numbers
Additional Example 1: Measurement Application
3
5
Kevin is 48 inches tall. His brother Keith is 5
8
8
inches taller. How tall is Keith ?
48 3 + 5 5 = 53 + 8
8
8
8
= 53 + 1
Add the integers and add the
fractions.
8
Rewrite as 1.
8
Kevin is 54 inches tall.
Helpful Hint
A mixed number is the sum of an integer and a
fraction: 3 4 = 3 + 4 .
5
Course 2
5
4-11 Insert
Adding Lesson
and Subtracting
Mixed Numbers
Title Here
Try This: Example 1
2
Alvin weighs 72 3 lbs. His baby brother weighs
15 1 lbs. How much do they weigh together?
3
72 2 + 15 1 = 87 + 3
3
3
3
= 87 + 1
Add the integers and add the
fractions.
Rewrite 3 as 1.
3
Together they weigh 88 pounds.
Course 2
4-11 Adding and Subtracting Mixed Numbers
Additional Example 2A: Adding Mixed Numbers
Add. Write the answer in simplest form.
A. 9 2 +12 2
3
3
9 2 + 12 2 = 21 + 4
3
3
3
= 21 + 1 1
3
= 22 1
3
Course 2
Add the integers and
add the fractions.
Rewrite the improper
fraction as a mixed
number.
4-11 Adding and Subtracting Mixed Numbers
Additional Example 2B: Adding Mixed Numbers
Add. Write the answer in simplest form.
B. 5 1 + 3 5
8
6
5 1 + 3 5 = 5 3 + 3 20
8
6
24
= 8 + 23
24
= 8 23
24
Course 2
24
Find a common
denominator.
Add the integers and
add the fractions.
Add.
4-11 Adding and Subtracting Mixed Numbers
Try This: Example 2A
Add. Write the answer in simplest form.
A. 7 4 +10 2
5
5
7 4 + 10 2 = 17 + 6
5
5
5
= 17 + 1 1
5
= 18 1
5
Course 2
Add the integers and
add the fractions.
Rewrite the improper
fraction as a mixed
number.
4-11 Adding and Subtracting Mixed Numbers
Try This: Example 2B
Add. Write the answer in simplest form.
B. 4 1 + 4 3
4
8
4 1 + 4 3= 4 2 + 4 3
4
8
8
=8+ 5
8
= 85
8
Course 2
8
Find a common
denominator.
Add the integers and
add the fractions.
Add.
4-11 Adding and Subtracting 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
Regroup.
Rewrite 1 as a fraction with
a common denominator.
Add.
Course 2
NUMBERS
1
7 =6+1+
8
8
=6+ +
8
=69
8
1
8
1
8
4-11 Adding and Subtracting Mixed Numbers
Remember!
Any fraction in which the numerator and
denominator are the same is equal to 1.
Course 2
4-11 Insert
Adding Lesson
and Subtracting
Mixed Numbers
Title Here
Additional Example 3A: Subtracting Mixed Numbers
Subtract. Write the answer in simplest form.
A. 4 2 – 2 1
3
3
4 2 – 2 1 = 2 + 1 Subtract integers and
3
3
3 subtract fractions.
= 21
Add.
3
Course 2
4-11 Insert
Adding Lesson
and Subtracting
Mixed Numbers
Title Here
Additional Example 3B: Subtracting Mixed Numbers
Subtract. Write the answer in simplest form.
2
B. 12 8 – 8
3
9
128 – 8 2 = 12 8 – 8 6
9
9
9
3
= 4+ 2
9
=42
9
Course 2
Find a common
denominator.
Subtract integers and
subtract fractions.
Add.
4-11 Adding and Subtracting Mixed Numbers
Additional Example 3C: Subtracting Mixed Numbers
Subtract. Write the answer in simplest form.
C. 17 1– 12 3
8
8
9–
3
1
3
16
12
17 – 12 =
8
8
8
8
=4+6
8
3
6
4
=4 =
4
8
Course 2
1 = 16+ 8+ 1
Regroup 17
.
8
8 8
Subtract integers and
subtract fractions.
Add and simplify.
4-11 Insert
Adding Lesson
and Subtracting
Mixed Numbers
Title Here
Try This: Example 3A
Subtract. Write the answer in simplest form.
A. 3 4 – 2 1
5
5
3 4 – 2 1 = 1 + 3 Subtract integers and
5
5
5 subtract fractions.
= 13
Add.
5
Course 2
4-11 Insert
Adding Lesson
and Subtracting
Mixed Numbers
Title Here
Try This: Example 3B
Subtract. Write the answer in simplest form.
3
B. 10 7 – 4
4
8
107 – 4 3 = 10 7 – 4 6
8
8
8
4
= 6+ 1
8
=61
8
Course 2
Find a common
denominator.
Subtract integers and
subtract fractions.
Add.
4-11 Adding and Subtracting Mixed Numbers
Try This: Example 3C
Subtract. Write the answer in simplest form.
C. 14 1– 10 3
4
4
5–
3
1
3
13
10
14 – 10 =
4
4
4
4
=3+2
4
1
2
3
=3 =
2
4
Course 2
1 = 13+ 4+ 1
Regroup 14
.
4
4 4
Subtract integers and
subtract fractions.
Add and simplify.
4-11 Adding
Subtracting
Mixed Numbers
Insert and
Lesson
Title Here
Lesson Quiz
Add or subtract. Write each answer in
simplest form.
1.
2.
3.
4.
5
1
1
1012
5 +5
4
6
9 2 + 10 7 20 1
4
12
3
1
77 – 2 3 58
4
8
10 2 – 4 5 5 7
9
6 18
1
5. A single roll of wallpaper unrolls to 15 2 yards
you hang 13 7yards from the roll. How much
8
wallpaper remains? 1 5 yards
8
Course 2
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