5-2 Adding and Subtracting with Unlike Denominators

Learn to add and subtract fractions with unlike denominators.

5-2 Adding and Subtracting with Unlike Denominators

Vocabulary

least common denominator (LCD)

5-2 Adding and Subtracting with Unlike Denominators

The Pacific Ocean covers of Earth’s surface. The Atlantic

Ocean covers of Earth’s surface. To find the fraction of

Earth’s surface that is covered by both oceans, you can add

and , which are unlike fractions.

1

3__

1

3__

1

5__

1

5__

5-2 Adding and Subtracting with Unlike Denominators

Fractions that represent the same value are equivalent.

Remember!

To add or subtract unlike fractions, first rewrite them as equivalent fractions with a common denominator.

5-2 Adding and Subtracting with Unlike Denominators

Additional Example 1: Cooking Application

Mark made a pizza with pepperoni covering of the

pizza and onions covering another . What fraction of

the pizza is covered by pepperoni and onions?

1

4__

1

3__

1

4__

1

3__

_____+ Find a common denominator for 4 and 3: 4 x 3 = 12.

?

1

4__ 1

3__

1

4__ 1

3__Add + .

5-2 Adding and Subtracting with Unlike Denominators

Additional Example 1 Continued

Write equivalent fractions with 12 as the common denominator.

1

4__

1

3__

_______+

3

12__

4

12__

_____Add the numerators. Keep the common denominator.

1

4__ 1

3__

7

12__

112

112

112

112

112

112

112

The pepperoni and onions cover of the pizza.7

12__

5-2 Adding and Subtracting with Unlike Denominators

Check It Out: Example 1Tori made a pizza with peppers covering of the pizza

and ham covering another . What fraction of the pizza

is covered by ham and peppers?

1

3__

1

2__

1

3__ 1

2__

?1

3__

1

2__

_____+ Find a common denominator for 3 and 2: 3 X 2 = 6.

1

3__ 1

2__Add + .

5-2 Adding and Subtracting with Unlike Denominators

Check It Out: Example 1 Continued

Write equivalent fractions with 6 as the common denominator.

1

3__

1

2__

_______+

2

6__

3

6__

_____Add the numerators. Keep the common denominator.

5

6__

1

3__ 1

2__

16

16

16

16

16

The peppers and ham cover of the pizza.5

6__

5-2 Adding and Subtracting with Unlike Denominators

You can use any common denominator or the least common denominator to add and subtract unlike fractions. The least common denominator (LCD) is the least common multiple of the denominators.

5-2 Adding and Subtracting with Unlike Denominators

Additional Example 2A: Adding and Subtracting Unlike Fractions

Add or subtract. Write each answer in simplest form.

Method 1: Multiplying denominators.

7

10__ 3

8__

–7

10__ 3

8__

–56

80__ 30

80__

Multiply the denominators. 10 • 8 = 80

Write equivalent fractions with a common denominator.

Subtract.

Write the answer in simplest form.

26

80__

13

40__

–

5-2 Adding and Subtracting with Unlike Denominators

Additional Example 2B: Adding and Subtracting Unlike Fractions

Add or subtract. Write each answer in simplest form.

Method 2: Use the LCD.

– 11

12__ 3

8__

–11

12__ 3

8__

–22

24__ 9

24__

Multiples of 8: 8, 16, 24, … The LCD is 24.

Write equivalent fractions with a common denominator.

Subtract. 13

24__

Multiples of 12: 12, 24, …

5-2 Adding and Subtracting with Unlike Denominators

Additional Example 2C: Adding and Subtracting Unlike Fractions

Add or subtract. Write each answer in simplest form.

Method 3: Use mental math.

5

16__ 1

8__

+5

16__ 1

8__

+5

16__ 2

16__

Think: 16 is a multiple of 8, so the LCD is 16.

Rewrite with a denominator of 16.

Add. 7

16__

1

8__

+

5-2 Adding and Subtracting with Unlike Denominators

Additional Example 2D: Adding and Subtracting Unlike Fractions

Add or subtract. Write each answer in simplest form.

Method 3: Use mental math.

5

16__ 1

8__

–5

16__ 1

8__

–5

16__ 2

16__

Think: 16 is a multiple of 8, so the LCD is 16.

Rewrite with a denominator of 16.

Subtract. 3

16__

1

8__

–

5-2 Adding and Subtracting with Unlike Denominators

Check It Out: Example 2A

Add or subtract. Write each answer in simplest form.

Method 1: Multiplying denominators.

– 8

10__ 2

6__

–8

10__ 2

6__

–48

60__ 20

60__

Multiply the denominators. 10 • 6 = 60

Write equivalent fractions with a common denominator.

Subtract.

Write the answer in simplest form.

28

60__

7

15__

5-2 Adding and Subtracting with Unlike Denominators

Check It Out: Example 2B

Add or subtract. Write each answer in simplest form.

Method 2: Use the LCD.

– 4

7__ 1

3__

–4

7__ 1

3__

–12

21__ 7

21__

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, …The LCD is 21.

Write equivalent fractions.

Subtract. 5

21__

Multiples of 7: 7, 14, 21, …

5-2 Adding and Subtracting with Unlike Denominators

Check It Out: Example 2C

Add or subtract. Write each answer in simplest form.

Method 3: Use mental math.

3

12__ 1

6__

+3

12__ 1

6__

+3

12__ 2

12__

Think: 12 is a multiple of 6, so the LCD is 12.

Rewrite with a denominator of 12.

Add. 5

12__

1

6__

+

5-2 Adding and Subtracting with Unlike Denominators

Check It Out: Example 2D

Add or subtract. Write each answer in simplest form.

Method 3: Use mental math.

3

12__ 1

6__

–3

12__ 1

6__

–3

12__ 2

12__

Think: 12 is a multiple of 6, so the LCD is 12.

Rewrite with a denominator of 12.

Subtract. 1

12__

1

6__

–