Course 1

5-3 Adding and Subtracting Mixed Numbers5-3 Adding and Subtracting Mixed Numbers

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

5-3 Adding and Subtracting Mixed Numbers

Warm UpAdd or subtract. Write each answer in simplest form.

1. – 2. +

3. + 4. –

712__ 1

2__ 3

11__ 2

3__

16__ 3

4__ 11

12__ 1

3__

112__ 31

33__

1112__ 7

12__

Course 1

5-3 Adding and Subtracting Mixed Numbers

Problem of the Day

The sum of every row, column and diagonal is the same. Complete the

magic square. 1

34__ 11

12___11 3

__

11

6__

121 1__

56__

23__ 1

4__1

Course 1

5-3 Adding and Subtracting Mixed Numbers

Learn to add and subtract mixed numbers with unlike denominators.

Course 1

5-3 Adding and Subtracting Mixed Numbers

Additional Example 1A: Adding and Subtracting Mixed Numbers

Find the sum. Write the answer in simplest form.

1

8__ 5

6__

31

8__ 3

6

48__ Multiply the denominators.

8 · 6 = 48

+15

6__ + 1

40

48__

______ ______Write equivalent fractions with a denominator of 48.

4 = 446

48__ 23

24__ Add the fractions and then

whole numbers, and simplify.

3 + 1

Course 1

5-3 Adding and Subtracting Mixed Numbers

Additional Example 1B: Adding and Subtracting Mixed Numbers

Find the difference. Write the answer in simplest form.

2

3__ 1

4__

52

3__ 5

8

12__ The LCD of 3 and 12 is 12.

–11

4__ – 1

3

12__

______ ______Write equivalent fractions with a denominator of 12.

4 5

12__ Subtract the fractions and

then the whole numbers.

5 – 1

Course 1

5-3 Adding and Subtracting Mixed Numbers

Additional Example 1C: Adding and Subtracting Mixed Numbers

Find the sum. Write the answer in simplest form.

1

2__ 4

5__

21

2__ 2

5

10__ The LCD of 2 and 10 is 10.

+44

5__ + 4

8

10__

______ ______Write equivalent fractions with a denominator of 10.

6 = 713

10__ 3

10__ Add the fractions and then

the whole numbers, and simplify. 6 = 6 + 1

13

10__ 3

10__

2 + 4

Course 1

5-3 Adding and Subtracting Mixed Numbers

Additional Example 1D: Adding and Subtracting Mixed Numbers

Find the difference. Write the answer in simplest form.

2

3__ 2

9__

62

3__ 6

6

9__ Think: 9 is a multiple of 3, so 9

is the LCD.

–32

9__ – 3

2

9__

______ ______Write equivalent fractions with a denominator of 9.

3 4

9__ Subtract the fractions and

then the whole numbers.

6 – 3

Course 1

5-3 Adding and Subtracting Mixed Numbers

Check It Out: Example 1A

Find the sum. Write the answer in simplest form.

1

4__ 1

6__

21

4__ 2

6

24__ Multiply the denominators.

4 · 6 = 24

+31

6__ + 3

4

24__

______ ______Write equivalent fractions with a denominator of 24.

5 = 510

24__ 5

12__ Add the fractions and then

whole numbers, and simplify.

2 + 3

Course 1

5-3 Adding and Subtracting Mixed Numbers

Check It Out: Example 1B

Find the difference. Write the answer in simplest form.

1

2__ 3

7__

41

2__ 4

7

14__ The LCD of 2 and 7 is 14.

–13

7__ – 1

6

14__

______ ______Write equivalent fractions with a denominator of 14.

3 1

14__ Subtract the fractions and

then the whole numbers.

4 – 1

Course 1

5-3 Adding and Subtracting Mixed Numbers

Check It Out: Example 1C

Find the sum. Write the answer in simplest form.

7

8__ 2

3__

27

8__ 2

21

24__ The LCD of the denominators is

24. +4

2

3__ + 4

16

24__

______ ______Write equivalent fractions with a denominator of 24.

6 = 737

24__ 13

24__ Add the fractions and then

the whole numbers, and simplify. 6 = 6 + 1

37

24__ 13

24__

2 + 4

Course 1

5-3 Adding and Subtracting Mixed Numbers

Check It Out: Example 1D

Find the difference. Write the answer in simplest form.

3

4__ 1

8__

73

4__ 7

6

8__ Think: 8 is a multiple of 4, so 8

is the LCD.

–21

8__ – 2

1

8__

______ ______

Write equivalent fractions with a denominator of 8.

5 5

8__ Subtract the fractions and

then the whole numbers.

7 – 2

Course 1

5-3 Adding and Subtracting Mixed Numbers

Additional Example 2: Measurement ApplicationThe 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__

101

4__ 10

2

8__ Find a common denominator. Write

equivalent fractions with the LCD, 8, as the denominator.

+51

8__ + 5

1

8__

______ ______Add the fractions and then the whole numbers. 15

3

8__

The total length of the kitten’s body and tail is 15 inches.

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

Helpful Hint

3

8__

Add 10 + 5

Course 1

5-3 Adding and Subtracting Mixed Numbers

Check It Out: Example 2The 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__

22

3__ 2

4

6__ Find a common denominator. Write

equivalent fractions with the LCD, 6, as the denominator.

+21

6__ + 2

1

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.5

6__

Add 2 +2 .

Course 1

5-3 Adding and Subtracting Mixed Numbers

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?

1112__ 2

3__ 1

6__ 3

8__

78__ 3

10__ 2

5__ 1

6__

23__3

4__

31

4__ 16

13

24__

87

40__ 6

7

30__

14 hours5

12__