Fractions

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Fractions

• Chapter 6

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6-1 Simplifying Fractions
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Restrictions

• Remember that you cannot divide by zero. You
  must restrict the variable by excluding any
  values that would make the denominator equal zero.

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Example 1

• 3a 6
• 3a 3b

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Example 2

• _____x2 9___
• (2x 1)(3 x)

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Example 3

• 2x2 x 3
• 2 x x2

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6-2 Multiplying Fractions
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Multiplication Rule for Fractions

• To Multiply fractions, you multiply their
  numerators and multiply their denominators.
• a c ac
• b d bd

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Examples

• 6x y2
• y3 15

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Examples

• x 2 x - 12 x2 -25
• x2 5x x 3

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Rule of Exponents for a Power of a Quotient

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

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Examples

• 1. (x/3)3
• 2. (-c/2)2 4/3c

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6-3 Dividing Fractions
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Division Rule for Fractions

• To divide by a fraction, you multiply by its
  reciprocal.
• a c ad
• b d bc

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Examples

• x xy
• 2y 4

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Examples

• 6x y2
• y3 15

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Examples

• 18 24
• x2 25 x 5

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Examples

• x 2 3x 10 x2 4
• 2x 6 x2 x - 12

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6-4 Least Common Denominators
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Finding the Least Common Denominator

• Factor each denominator completely.
• Find the product of the greatest power of each
  factor occurring in the denominator.

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Example

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

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Example

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

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Example

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

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6-5 Adding and Subtracting Fractions
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Addition Rule for Fractions

• a b a b
• c c c

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Subtraction Rule for Fractions

• a - b a - b
• c c c

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Examples

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

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Examples

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

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Examples

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

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6-6 Mixed Expressions
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Simplify

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

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Simplify

• 3. 4a 3
• a
• 4. 2x 5 - 3x
• x 2

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6-7 Polynomial Long Division
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Long Division

• Dividend
• Divisor
• Quotient Remainder
• Divisor
• .

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Long Division

• Arrange the terms in each polynomial in order of
  decreasing degree of the variable before dividing

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Divide

• x2 - 3x3 5x 2
• x 1

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Divide

• 15x2 34x - 16
• 5x - 2

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Divide

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

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• END