Multiplying Fractions

January 20, 2012

Multiplying Fractions

Objective To multiply algebraic fractions.

Multiplication Rule for Fractions

𝑎

𝑏∙𝑐

𝑑=𝑎𝑐

𝑏𝑑

To multiply fractions, you multiply their numerators and multiply their denominators.

3

8∙5

2=3 ∙ 5

8 ∙ 2=15

16

Example 1

Multiply: 8

9∙3

10

Solution 1 Multiply, then simplify.

8

9∙3

10 =

8 ∙ 3

9 ∙ 10 =

24

90 =

6 ∙ 4

6 ∙ 15 =

4

15

Example 1

Multiply: 8

9∙3

10

Solution 2 Simplify, then multiply.

8

9∙3

10 =

2 ∙ 4 ∙ 3

3 ∙ 3 ∙ 2 ∙ 5 =

4

3 ∙ 5 =

4

15

Example 2a

Multiply: 6𝑥

𝑦3∙𝑦2

15

Solution

6𝑥

𝑦3∙𝑦2

15 =

3 ∙ 2𝑥

𝑦2 ∙ 𝑦∙𝑦2 ∙ 1

3 ∙ 5 =2𝑥

5𝑦

𝑦 ≠ 0

Example 2b

Multiply: 𝑥2;𝑥;12

𝑥2;5𝑥∙𝑥2;25

𝑥:3

Solution 𝑥2 − 𝑥 − 12

𝑥2 − 5𝑥∙𝑥2 − 25

𝑥 + 3 =

𝑥 − 4 𝑥 + 3

𝑥 𝑥 − 5∙𝑥 + 5 𝑥 − 5

𝑥 + 3

=𝑥 − 4 𝑥 + 5

𝑥

𝑥 ≠ 0, 𝑥 ≠ 5, 𝑥 ≠ −3

Let’s take a break.

Then work the following Oral Exercises:

P 252: 1-12

Rule of Exponents for a Power of a Quotient

For every positive integer m,

𝑎

𝑏

𝑚=

𝑎𝑚

𝑏𝑚 .

Example 3

Simplify, 𝑥

3

3

Solution

𝑥

3

3

=𝑥3

33 =

𝑥3

27

Example 4

Simplify, −𝑐

2

2∙4

3𝑐

Solution

−𝑐

2

2

∙4

3𝑐 =

𝑐 ∙ 𝑐

4∙4

3𝑐 =

𝑐

3 =

𝑐2

4∙4

3𝑐

Class work: Oral Exercises: p 252: 1-16

Homework: p 253: 3-54 mult of 3, 55, p 254: MR