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Fractions

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Chapter 6 Fractions Long Division Dividend = Divisor Quotient + Remainder Divisor . Long Division Arrange the terms in each polynomial in order of ... – PowerPoint PPT presentation

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Title: Fractions


1
Fractions
  • Chapter 6

2
6-1 Simplifying Fractions
3
Restrictions
  • Remember that you cannot divide by zero. You
    must restrict the variable by excluding any
    values that would make the denominator equal zero.

4
Example 1
  • 3a 6
  • 3a 3b

5
Example 2
  • _____x2 9___
  • (2x 1)(3 x)

6
Example 3
  • 2x2 x 3
  • 2 x x2

7
6-2 Multiplying Fractions
8
Multiplication Rule for Fractions
  • To Multiply fractions, you multiply their
    numerators and multiply their denominators.
  • a c ac
  • b d bd

9
Examples
  • 6x y2
  • y3 15

10
Examples
  • x 2 x - 12 x2 -25
  • x2 5x x 3

11
Rule of Exponents for a Power of a Quotient
  • For every positive integer m.
  • (a/b)m am/bm

12
Examples
  • 1. (x/3)3
  • 2. (-c/2)2 4/3c

13
6-3 Dividing Fractions
14
Division Rule for Fractions
  • To divide by a fraction, you multiply by its
    reciprocal.
  • a c ad
  • b d bc

15
Examples
  • x xy
  • 2y 4

16
Examples
  • 6x y2
  • y3 15

17
Examples
  • 18 24
  • x2 25 x 5

18
Examples
  • x 2 3x 10 x2 4
  • 2x 6 x2 x - 12

19
6-4 Least Common Denominators
20
Finding the Least Common Denominator
  • Factor each denominator completely.
  • Find the product of the greatest power of each
    factor occurring in the denominator.

21
Example
  • Find the LCD of the fractions
  • ¾, 11/30, and 7/45

22
Example
  • Find the LCD of the fractions
  • 3 and 8
  • 6x 30 9x 45

23
Example
  • Find the LCD of the fractions
  • 9 and 5
  • x2 8x 16 x2 7x 12

24
6-5 Adding and Subtracting Fractions
25
Addition Rule for Fractions
  • a b a b
  • c c c

26
Subtraction Rule for Fractions
  • a - b a - b
  • c c c

27
Examples
  • 3c 5c
  • 16 16
  • 2. 5x 4 - 3x - 8
  • 10 10

28
Examples
  • 3. __3__ __1__
  • x 4 x 4
  • 4. a - 5 12a
  • 4 18

29
Examples
  • 5. __3__ - __1__
  • 2x 8x2
  • 6. a - 3 - a 4
  • a2 2a a2 - 4

30
6-6 Mixed Expressions
31
Simplify
  • 5 x 3
  • x 2
  • x 5x 2 - __7_
  • x 1 x - 1

32
Simplify
  • 3. 4a 3
  • a
  • 4. 2x 5 - 3x
  • x 2

33
6-7 Polynomial Long Division
34
Long Division
  • Dividend
  • Divisor
  • Quotient Remainder
  • Divisor
  • .

35
Long Division
  • Arrange the terms in each polynomial in order of
    decreasing degree of the variable before dividing

36
Divide
  • x2 - 3x3 5x 2
  • x 1

37
Divide
  • 15x2 34x - 16
  • 5x - 2

38
Divide
  • 2a3 5a
  • a 3
  • You must use 0 coefficients for the missing terms

39
  • END
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