Simple Algebraic Fractions/Rational ExpressionsSessions 1 - 2

ObjectivesDefine rational expressionsSimplify rational expressions

RECALL: Simplifying numerical fractions

Simplify these fractions:

1. 2.

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

Quotient of PowersExample 1:

3

5

4

4

444

44444

44

Write out as a product of factors.

16

Cancel out common factors

Quotient of PowersNotice what we could have done using the property.

3

5

4

4 24 16

Subtract exponents!

Quotient of PowersExample 2:

8

3

r

r

rrrrrrrr

rrrrrrrr

1

Write out as a product of factors.

5

1

rCancel out

common factors!

Quotient of PowersNotice what we could have done using the property.

8

3

r

r5

1

r

Subtract exponents!

Quotient of PowersExample 3:

3

42

8

88

3

6

8

8 38

Simplify top 1st.

512

Power of a Quotient Property

12

42

x

4

3

2

x 12

16

x

Example 4:Example 4:

6

35

h

3

2

5

h 6

125

h

Example: 5

Algebraic Fraction/Rational Expression

- A fraction whose numerator and denominator are polynomials

Examples:

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.

Simplifying Algebraic Fractions/Rational Expressions

1) Factor the numerator and denominator completely.2) Cancel common factors.

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

TRY THISExercise 4a, p. 119

numbers 6 – 10(Notebooks)

Simplify the expression

Simplify the expression

Simplify the expression

REMEMBER: Cancellation is done after both numerator

and denominator have been completely factorized.

SEATWORKAnswer Exercise 4b –

1-10 (Notebooks)

Exercise 4b

1)

Exercise 4b

2)

Exercise 4b 3)

Exercise 4b 4)

Exercise 4b 5)

Exercise 4b 6)

Exercise 4b 7)

Exercise 4b 8)

Exercise 4b 9)

Exercise 4b 10)

Exercise 4b 11)

Exercise 4b 12)

Exercise 4b13)

Exercise 4b14)

Exercise 4b 15)

Exercise 4b 16)

Exercise 4b 17)

Exercise 4b 18)

Exercise 4b 19)

Exercise 4b 20)

Exercise 4b 21)

Exercise 4b 22)

PRACTICE TEST # 11)

PRACTICE TEST2)

PRACTICE TEST3)

PRACTICE TEST4)

PRACTICE TEST5)

PRACTICE TEST6)

PRACTICE TEST7)

PRACTICE TEST8)