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Adding and Subtracting Mixed Numbers. 4-11. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 4-11. Adding and Subtracting Mixed Numbers. Course 2. Warm Up Add or subtract. 1. 2. 3. 3 8. 4 8. 7 8. +. 7 12. 11 12. 1 3. –. 1 12. 7 12. 2 3.

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slide1

Adding and Subtracting Mixed Numbers

4-11

Course 2

Warm Up

Problem of the Day

Lesson Presentation

slide2

4-11

Adding and Subtracting Mixed Numbers

Course 2

Warm Up

Add or subtract.

1.

2.

3.

3

8

4

8

7

8

+

7

12

11

12

1

3

1

12

7

12

2

3

1

3

1

6

3

10

1

5

4.

+

slide3

4-11

Adding and Subtracting Mixed Numbers

Course 2

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

slide4

4-11

Adding and Subtracting Mixed Numbers

Course 2

Learn to add and subtract mixed numbers.

slide5

4-11

Adding and Subtracting Mixed Numbers

Helpful Hint

A mixed number is the sum of an integer and a fraction: 3 = 3 + .

Course 2

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 ?

8

8

3

8

5

8

Add the integers and add the fractions.

+

5

48

+

=

53

8

8

53 + 1

=

Rewrite

as 1.

Kevin is 54 inches tall.

4

5

4

5

slide6

4-11

Adding and Subtracting Mixed Numbers

Course 2

Insert Lesson Title Here

Try This: Example 1

2

3

Alvin weighs 72 lbs. His baby brother weighs 15 lbs. How much do they weigh together?

1

3

3

3

2

3

+

1

3

Add the integers and add the fractions.

15

72

87

+

=

3

3

as 1.

87 + 1

Rewrite

=

Together they weigh 88 pounds.

slide7

4-11

Adding and Subtracting Mixed Numbers

4

3

2

3

2

3

9

=

12

21 +

+

1

3

= 21 + 1

1

3

=

22

Course 2

Additional Example 2A: Adding Mixed Numbers

Add. Write the answer in simplest form.

2

3

2

3

A. 9

+

12

Add the integers and add the fractions.

Rewrite the improper fraction as a mixed number.

slide8

4-11

Adding and Subtracting Mixed Numbers

3

24

1

8

20

24

5

6

+ 3

5

= 5 + 3

23

24

= 8 +

23

24

= 8

Course 2

Additional Example 2B: Adding Mixed Numbers

Add. Write the answer in simplest form.

1

8

5

6

B. 5

+

3

Find a common denominator.

Add the integers and add the fractions.

Add.

slide9

4-11

Adding and Subtracting Mixed Numbers

6

5

4

5

2

5

7

=

10

17 +

+

1

5

= 17 + 1

1

5

=

18

Course 2

Try This: Example 2A

Add. Write the answer in simplest form.

4

5

2

5

A. 7

+

10

Add the integers and add the fractions.

Rewrite the improper fraction as a mixed number.

slide10

4-11

Adding and Subtracting Mixed Numbers

2

8

1

4

3

8

3

8

+ 4

4

= 4 + 4

5

8

= 8 +

5

8

= 8

Course 2

Try This: Example 2B

Add. Write the answer in simplest form.

1

4

3

8

B. 4

+

4

Find a common denominator.

Add the integers and add the fractions.

Add.

slide11

4-11

Adding and Subtracting Mixed Numbers

1

8

1

8

= 6 + 1 +

7

1

8

8

8

+

= 6 +

9

8

= 6

Course 2

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.

Rewrite 1 as a fraction with a common denominator.

Add.

slide12

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

slide13

4-11

Adding and Subtracting Mixed Numbers

2

3

1

3

1

3

=

4

2

2 +

=

1

3

2

Course 2

Insert Lesson Title Here

Additional Example 3A: Subtracting Mixed Numbers

Subtract. Write the answer in simplest form.

1

3

2

3

2

A. 4

Subtract integers and subtract fractions.

Add.

slide14

4-11

Adding and Subtracting Mixed Numbers

8

9

6

9

8

9

2

3

=

8

12

12

8

2

9

=

4 +

2

9

= 4

Course 2

Insert Lesson Title Here

Additional Example 3B: Subtracting Mixed Numbers

Subtract. Write the answer in simplest form.

2

3

8

9

8

B.

12

Find a common denominator.

Subtract integers and subtract fractions.

Add.

slide15

4-11

Adding and Subtracting Mixed Numbers

9

8

1

8

1

8

8

8

3

8

1

8

3

8

= 16+

16

+

Regroup 17

.

12

– 12 =

17

6

8

= 4 +

3

4

6

8

4

= 4

=

Course 2

Additional Example 3C: Subtracting Mixed Numbers

Subtract. Write the answer in simplest form.

1

8

3

8

17

12

C.

Subtract integers and

subtract fractions.

Add and simplify.

slide16

4-11

Adding and Subtracting Mixed Numbers

4

5

1

5

3

5

=

3

2

1 +

=

3

5

1

Course 2

Insert Lesson Title Here

Try This: Example 3A

Subtract. Write the answer in simplest form.

1

5

4

5

2

A. 3

Subtract integers and subtract fractions.

Add.

slide17

4-11

Adding and Subtracting Mixed Numbers

7

8

6

8

7

8

3

4

=

4

10

10

4

1

8

=

6 +

1

8

= 6

Course 2

Insert Lesson Title Here

Try This: Example 3B

Subtract. Write the answer in simplest form.

3

4

7

8

4

B.

10

Find a common denominator.

Subtract integers and subtract fractions.

Add.

slide18

4-11

Adding and Subtracting Mixed Numbers

5

4

1

4

1

4

4

4

3

4

1

4

3

4

= 13+

13

+

Regroup 14

.

10

– 10 =

14

2

4

= 3 +

1

2

2

4

3

= 3

=

Course 2

Try This: Example 3C

Subtract. Write the answer in simplest form.

1

4

3

4

14

10

C.

Subtract integers and

subtract fractions.

Add and simplify.

slide19

4-11

Adding and Subtracting Mixed Numbers

5

12

10

1

4

20

1

8

5

7

18

5

5

8

1 yards

Course 2

Insert Lesson Title Here

Lesson Quiz

Add or subtract. Write each answer in simplest form.

1. 5

2. 9

3. 7

4. 10

1

4

1

6

5

+

7

12

2

3

+ 10

3

4

7

8

– 2

2

9

5

6

– 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?