Chapter 7 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common...

Chapter 7 Section 3

Objectives

1

Copyright © 2012, 2008, 2004 Pearson Education, Inc.

Least Common Denominators

Find the least common denominator for a group of fractions.

Write equivalent rational expressions.

7.3

2


Objective 1


Slide 7.3-3



Adding or subtracting rational expressions often requires a least

common denominator (LCD), the simplest expression that is

divisible by all of the denominators in all of the expressions. For

example, the least common denominator for the fractions and

is 36, because 36 is the smallest positive number divisible by both 9

and 12.

2

9

5

12

We can often find least common denominators by inspection. For

example, the LCD for and is 6m. In other cases, we find the

LCD by a procedure similar to that used in Section 6.1 for finding the

greatest common factor.

1

6

2

3m

Slide 7.3-4


Finding the Least Common Denominator (LCD)

Step 1: Factor each denominator into prime factors.

Step 2: List each different denominator factor the greatest number of times it appears in any of the denominators.

Step 3: Multiply the denominator factors from Step 2 to get the LCD.

When each denominator is factored into prime factors, every prime factor must be a factor of the least common denominator.

Slide 7.3-5

Find the least common denominator for a group of fractions. (cont’d)


Find the LCD for each pair of fractions.

Solution:

7 1,

10 25

4 6

4 11,

8 12m m

10 2 5

4 48 2 2 2m m

25 5 5

6 612 2 2 3m m

432 m 622 3 m

52 25

2LCD 5 2

3 63D 2LC m

50

624m

Slide 7.3-6

EXAMPLE 1 Finding the LCD


Find the LCD for

Solution:

3 5

4 5 and .

16 9m n m

3 316 2 2 2 2m n m n 5 59 3 3m m

342 nm 2 53 m

4 2 52 3LCD m n 5144m n

When finding the LCD, use each factor the greatest number of times it appears in any single denominator, not the total number of times it appears.

Slide 7.3-7

EXAMPLE 2 Finding the LCD


Solution:

4 1,

1 1x x

Find the LCD for the fractions in each list.

2 2

6 3 1,

4 16

x

x x x

4x x

4 4x x

LCD 4 4x x x

4x x

44 xx

Either x − 1 or 1 − x, since they are opposite expressions.

Slide 7.3-8

EXAMPLE 3 Finding LCDs


Objective 2


Slide 7.3-9



Writing A Rational Expression with a Specified Denominator

Step 1: Factor both denominators.

Slide 7.3-10

Step 2: Decide what factor (s) the denominator must be multiplied by in order to equal the specified denominator.

Step 3: Multiply the rational expression by the factor divided by itself. (That is, multiply by 1.)


Rewrite each rational expression with the indicated denominator.

Solution:

3

4

93

4 9

3

4 9

?

4

242

30

k

k

3 ?

4 36

7 ?

5 65

k

k

7 7

5 5

6

6

k k k

k 7 ?

5 30

k

k

27

36

Slide 7.3-11

EXAMPLE 4 Writing Equivalent Rational Expressions


Rewrite each rational expression with the indicated denominator.

Solution:

9 ?

2 5 6 15a a

2

5 1 ?

2 2 1

k

k k k k k

9 ?

32 5 2 5a a

9 9

2 5 2

3

35a a

27

6 15a

1

5 1 ?

2 2

k

k k kk k

5 1 5 1 1

2 12

k k

k k k k

k

k

5 1 1

2 1

k k

k k k

Slide 7.3-12

EXAMPLE 5 Writing Equivalent Rational Expressions


HL # 7.3Book Beginning AlgebraPage 439 Exercises 38, 39, 40, 41, 42, 43, 44.Page 440 Exercises 55, 56, 57, 58, 64, 65, 67.

Chapter 7 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common...

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Transcript of Chapter 7 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common...