simple algebraic fractions/rationa l expressions sessions 1 - 2
TRANSCRIPT
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Simple Algebraic Fractions/Rational ExpressionsSessions 1 - 2
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ObjectivesDefine rational expressionsSimplify rational expressions
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RECALL: Simplifying numerical fractions
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Simplify these fractions:
1. 2.
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Division Property of Exponents To divide powers that have the same base, you subtract the exponents.
For any base b ≠ 0 and positive integers m and n
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Quotient of PowersExample 1:
3
5
4
4
444
44444
44
Write out as a product of factors.
16
Cancel out common factors
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Quotient of PowersNotice what we could have done using the property.
3
5
4
4 24 16
Subtract exponents!
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Quotient of PowersExample 2:
8
3
r
r
rrrrrrrr
rrrrrrrr
1
Write out as a product of factors.
5
1
rCancel out
common factors!
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Quotient of PowersNotice what we could have done using the property.
8
3
r
r5
1
r
Subtract exponents!
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Quotient of PowersExample 3:
3
42
8
88
3
6
8
8 38
Simplify top 1st.
512
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Power of a Quotient Property
12
42
x
4
3
2
x 12
16
x
Example 4:Example 4:
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6
35
h
3
2
5
h 6
125
h
Example: 5
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Algebraic Fraction/Rational Expression
- A fraction whose numerator and denominator are polynomials
Examples:
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An algebraic fraction/rational expression is in lowest terms or simplest form if the numerator and denominator have no common factors other
than 1 and -1.
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Simplifying Algebraic Fractions/Rational Expressions
1) Factor the numerator and denominator completely.2) Cancel common factors.
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Simplify:
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Simplify:
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Simplify:
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Simplify:
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Simplify:
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TRY THISExercise 4a, p. 119
numbers 6 – 10(Notebooks)
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Simplify the expression
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Simplify the expression
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Simplify the expression
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REMEMBER: Cancellation is done after both numerator
and denominator have been completely factorized.
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SEATWORKAnswer Exercise 4b –
1-10 (Notebooks)
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Exercise 4b
1)
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Exercise 4b
2)
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Exercise 4b 3)
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Exercise 4b 4)
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Exercise 4b 5)
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Exercise 4b 6)
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Exercise 4b 7)
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Exercise 4b 8)
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Exercise 4b 9)
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Exercise 4b 10)
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Exercise 4b 11)
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Exercise 4b 12)
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Exercise 4b13)
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Exercise 4b14)
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Exercise 4b 15)
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Exercise 4b 16)
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Exercise 4b 17)
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Exercise 4b 18)
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Exercise 4b 19)
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Exercise 4b 20)
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Exercise 4b 21)
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Exercise 4b 22)
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PRACTICE TEST # 11)
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PRACTICE TEST2)
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PRACTICE TEST3)
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PRACTICE TEST4)
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PRACTICE TEST5)
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PRACTICE TEST6)
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PRACTICE TEST7)
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PRACTICE TEST8)