10.5 Addition and Subtraction with unlike denominators Steps: 1.Find a least common denominator (LCD) 2.Rename fractions 3.Add or subtract numerators.

10.5 Addition and Subtraction with unlike denominators

Steps:

1. Find a least common denominator (LCD)

2. Rename fractions

3. Add or subtract numerators

REVIEW:

2 1

7 3

21 21 21

3

3 7

7

6 7 13

How to get a LCD with RE1. Factor the denominators

2. Take one of each factor– If there are duplicates take the one with the

highest exponent

Rename Fractions with LCD• Compare the LCD to the denominator of

each fraction• Multiply the numerator and denominator of

the fraction by a number or polynomial to make your denominator match your LCD

7 2

1 1x x

111111

xxxxxx

7 1x 2 1x 9 5x

Example 1

xx 2

3

2

2

xxxxxx 222222

4x 3 2x 7 6x

Example 2:

2

1 4a

a a

2 2 2

4a

a a a

2

2 2a

a

a

a

a2

2 4a

a

Example 3:

2

3 12

2 4

x x

x x

2

2

x

x

3 12

2 2 2

x x

x x x

+12

2 2

x

x x

23 6x x

23 6

2 2

x x

x x

3 2

2 2

x x

x x

3

2

x

x

Example 4:

5 3

1 1 1

x

x x x

1

1

x

x

5 3 3

1 1

x x

x x

8 3

1 1

x

x x

Example 5:

3 3x x

2

5 4

9 3

x

x x

5 4

3 3 3

x

x x x

5

3 3

x

x x

3

3

x

x

4 12x

12

3 3

x

x x

Example 6:

Example 7

You try! Raise your hand when you are done! First person done with the correct answer

will earn a math buck!$$$

4

1

x

x

1 1x x

1

1

x

x

2 2 3

1 1

x x

x x

1x

2 3 4

1 1

x x

x x

4 1

1 1

x x

x x

Example 8

You try! Raise your hand when you are done! First person done with the correct

answer will earn a math buck!$$$

14

1 1 1

xx

x x x

4

1 1

x

x x

1

1

x

x

2 2 1x x

2 2 1

1 1

x x

x x

1

1

1

1

x

x

x

x

2

4 1

1 1

x x

x x

Example 9

You try! Raise your hand when you are done! First person done with the correct answer

will earn a math buck!$$$

2

5 4 4

y

y y y

5 4

y

y y

5

5

y

y

2 10y

3 10

5 4

y

y y

Example 10

You try! Raise your hand when you are done! First person done with the correct answer

will earn a math buck!$$$

2

16t

222

ttt

2

136

t

t

Example 11

You try! Raise your hand when you are done! First person done with the correct answer

will earn a math buck!$$$

yx

yx

xy 22

3

222222 yxyxyx

22

23

yx

yxyx

Assignment:

Page 448 (2-34) even