The document discusses rational numbers and operations involving rational expressions such as addition, subtraction, multiplication, and division. It provides examples of simplifying rational expressions by factoring and canceling common factors. It also notes that dividing a rational expression by a fraction is equivalent to multiplying it by the reciprocal of that fraction. Exceptions to simplifying are mentioned as well.

1. Lsn 8­3.notebook January 12, 2010
What are these factor pairs equivalent to?
example:
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2. Lsn 8­3.notebook January 12, 2010
Equivalent Rational Numbers
a rational number is of the form where a,b are integers.
Since and , they are equal rational numbers.
One way to show that is to use factoring:
Reduce by factoring and canceling:
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3. Lsn 8­3.notebook January 12, 2010
Example 1: (monomials)
Reduce to lowest terms:
Example 2: (binomials)
Reduce to lowest terms:
(except when...
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4. Lsn 8­3.notebook January 12, 2010
A fraction is "simplified" or "reduced" by factoring and canceling common
factors (pairs that = 1): Exceptions:
Note: this would be like saying
Always completely factor before doing any canceling!
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5. Lsn 8­3.notebook January 12, 2010
Multiply or Divide Rational Expressions:
Recall:
for example,
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6. Lsn 8­3.notebook January 12, 2010
example:
now what?
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example:
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8. Lsn 8­3.notebook January 12, 2010
Division: quick calculator discovery...
Dividing by 1/2 is the same as _________________________.
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9. Lsn 8­3.notebook January 12, 2010
Recall Some Important Concepts:
Subtraction is the addition of the additive inverse to a number.
ex: 7 ­ (2) =
ex: 4 ­ (­3) =
Division is the multiplication of the multiplicative inverse and number.
ex:
ex:
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10. Lsn 8­3.notebook January 12, 2010
Division of Rational Expressions:
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