Fractions

- Chapter 6

6-1 Simplifying Fractions

Restrictions

- Remember that you cannot divide by zero. You

must restrict the variable by excluding any

values that would make the denominator equal zero.

Example 1

- 3a 6
- 3a 3b

Example 2

- _____x2 9___
- (2x 1)(3 x)

Example 3

- 2x2 x 3
- 2 x x2

6-2 Multiplying Fractions

Multiplication Rule for Fractions

- To Multiply fractions, you multiply their

numerators and multiply their denominators. - a c ac
- b d bd

Examples

- 6x y2
- y3 15

Examples

- x 2 x - 12 x2 -25
- x2 5x x 3

Rule of Exponents for a Power of a Quotient

- For every positive integer m.
- (a/b)m am/bm

Examples

- 1. (x/3)3
- 2. (-c/2)2 4/3c

6-3 Dividing Fractions

Division Rule for Fractions

- To divide by a fraction, you multiply by its

reciprocal. - a c ad
- b d bc

Examples

- x xy
- 2y 4

Examples

- 6x y2
- y3 15

Examples

- 18 24
- x2 25 x 5

Examples

- x 2 3x 10 x2 4
- 2x 6 x2 x - 12

6-4 Least Common Denominators

Finding the Least Common Denominator

- Factor each denominator completely.
- Find the product of the greatest power of each

factor occurring in the denominator.

Example

- Find the LCD of the fractions
- ¾, 11/30, and 7/45

Example

- Find the LCD of the fractions
- 3 and 8
- 6x 30 9x 45

Example

- Find the LCD of the fractions
- 9 and 5
- x2 8x 16 x2 7x 12

6-5 Adding and Subtracting Fractions

Addition Rule for Fractions

- a b a b
- c c c

Subtraction Rule for Fractions

- a - b a - b
- c c c

Examples

- 3c 5c
- 16 16
- 2. 5x 4 - 3x - 8
- 10 10

Examples

- 3. __3__ __1__
- x 4 x 4
- 4. a - 5 12a
- 4 18

Examples

- 5. __3__ - __1__
- 2x 8x2
- 6. a - 3 - a 4
- a2 2a a2 - 4

6-6 Mixed Expressions

Simplify

- 5 x 3
- x 2
- x 5x 2 - __7_
- x 1 x - 1

Simplify

- 3. 4a 3
- a
- 4. 2x 5 - 3x
- x 2

6-7 Polynomial Long Division

Long Division

- Dividend
- Divisor
- Quotient Remainder
- Divisor
- .

Long Division

- Arrange the terms in each polynomial in order of

decreasing degree of the variable before dividing

Divide

- x2 - 3x3 5x 2
- x 1

Divide

- 15x2 34x - 16
- 5x - 2

Divide

- 2a3 5a
- a 3
- You must use 0 coefficients for the missing terms

- END