Simplifying Algebraic Fractions

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Simplifying Algebraic Fractions

• Goals
• 1. Simplify Algebraic Fractions
• 2. Simplify Expressions with Involving Negative
  and Zero Exponents

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Algebraic Fraction

• Fraction that contains a variable
• Example
• In Arithmetic In Algebra
• 3 Numerator a
• 5 Denominator b b ? 0

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Simplify

• Simplify an algebraic fraction by writing it in
  lowest terms.
• 1. Write the Prime Factorization of both the
  numerator and the denominator.
• 2. Divide by all the common factors.

4
Simplify
n5 n2

• a. b.

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Quotient of Powers Rule

• To divide powers having the same base but
  different exponents, subtract the exponents.
• Example
• am
• an

am-n , a ? 0
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Simplify
5x7 x3
d3 4d

• a. b.

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Product of Powers Rule

• To multiply powers having the same base, but
  different exponents, add the exponents
• Example
• am ? an amn

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Simplify

• a. 3a4 ? 4a6 b. 16m3 ? m9

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Zero Exponents

• Replace each ___ with the number that makes the
  statement true
• a. a2 a ? a
• a2 a ? a
• b. a2
• a2

_____
a2 2 a
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Negative Exponents

• Replace each ___ with the number that makes the
  statement true
• a. a3 a ? a ? a 1 1
• a5 a ? a ? a ? a ? a a ? a a
• b. a3
• a5

a3 5 a
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Simplify

• x-7 b. 3-3
• c. (-2)-2 d. (5.67)0

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Scientific Noatation

• Move the decimal point to get a number between 1
  and 10 ( 1 lt x lt 10)
• Example1 Write 0.065 in Scientific Notation
• 0.065
• Example 2 Write 4.7 x 10-4 in Decimal Notation
• 4.7 x 10-4

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Homework

• Worksheet