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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 _____x 2 – 9___ (2x + 1)(3 + x)

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Example 3 2x 2 + x – 3 2 – x – x 2

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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 · y 2 y 3 · 15

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Examples x 2 – x - 12 · x 2 -25 x 2 – 5x x + 3

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Rule of Exponents for a Power of a Quotient For every positive integer m. (a/b) m = a m /b m

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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 ÷ y 2 y 3 15

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Examples 18 ÷ 24 x 2 – 25 x + 5

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Examples x 2 + 3x – 10 ÷ x 2 – 4 2x + 6 x 2 – x - 12

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6-4 Least Common Denominators

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Finding the Least Common Denominator 1. Factor each denominator completely. 2.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 x 2 – 8x + 16 x 2 – 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 1. 3c + 5c 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 8x 2 6. a - 3 - a – 4 a 2 – 2a a 2 - 4

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6-6 Mixed Expressions

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Simplify 1. 5 – x – 3 x + 2 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 x 2 - 3x 3 + 5x – 2 x + 1

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Divide 15x 2 + 34x - 16 5x - 2

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Divide 2a 3 + 5a a – 3 You must use 0 coefficients for the missing terms

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