# Fractions - PowerPoint PPT Presentation

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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.
• 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
25
• 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