SIMPLIFYING RATIONALL EXPRESSION MATH 88

CLASS RULES
Decide what needs to be done to complete
your task.
Everyone should do the same amount of
work.
Do not disturb other group and avoid
unnecessary noise.
Stay on task, whatever is asked just answer
it.

OBJECTIVES
1.Define rational algebraic expressions;
2.Illustrate and Simplify rational
algebraic expressions; and
3.Demonstrate appreciation of
illustrating/ simplifying rational
algebraic expressions.

C
There are verbal phrases below. Look for mathematical
expressions in the figures that correspond to each verbal phrase.
a. a increased by twice b.
b. x added to thrice y.
c. The sum of a and b.

C
d. m decreased by n.
e. The product of twice a and thrice b.
f. The quotient of twice x and thrice y

C
1. The quotient of 2c and 3n
2. The fraction whose
denominator is 7 more than
the numerator n.

C
3. The ratio of a number n and four
added to 2.
4. The product of c and n divided by 3.
5. One-third of the square of c

4/5 OF SEVEN
IS WHAT 2, 4,
6, 8 AND 100
ARE CALLED..

4/5 OF LEAST
IS WHERE
THE SUN
SHINE.

3/8 OF
LEARNING IS
A PART OF
BODY.

½ OF TIME
IS OPPOSITE
OF YOU.

¾ OF SHOP IS
HOW THE
KANGAROO
MOVE.

2/3 OF PLANES
IS WHAT YOU
MUST STAY IN
ON THE
HALLWAY

7/9 OF
FRACTIONS
SPEAK LOUDER
THAN WORDS.

2/3 OF A
NUMBER IS
WITHOUT
FEELING.

4/9 OF
CHALLENGE IS
A LARGE
ROOM..

1/3 OF
MANUFACTURER IS
SOMETHING
YOU CAN TRUST
WITH..

½ OF FAREWELL
IS WHAT WE
GIVE TO A
TAXI DRIVER.

3/5 OF CHAIR
IS PRESENT
IN THE
ATMOSPHERE.

RATIONAL EXPRESSION
A rational expression is a
fractional expression in
which both the numerator
and denominator are
polynomials.

Here are some examples:
 
   
3
2 2
2 2
1 4 5 6
x y x x
x y x x

C
Simplifying Rational
Expressions
A “rational expression” is the
quotient of two polynomials..
2
2

n
n
2
3
10
3
2



x
x
x

C
Simplifying Rational
Expressions
To simplify rational expressions, we factor both
numerator and denominator and use following
property of fractions:
This allows us to cancel common factors
from the numerator and denominator.

AC A
BC B

Simplifying a rational expression is similar in reducing
fractions to lowest term.
To simplify:
a. Factor the numerator and denominator
completely.
b. Divide out (or cancel) any common
factors.
c. Rewrite the remaining factors in the
numerator and denominator.

Rational equations can be used to
solve a variety of problems that
involve rates, time and work.
( Distance to be run, time taken
to run the distance, number of
heart beats we take every minute
etc.)

A rational expression is in simplest
form when the numerator and
denominator have no common
factors (other than 1)
15
9
Simplify
5
3
3
3



5
3


SIMPLIFYING RATIONALL EXPRESSION MATH 88

C
x
x
5
10
5
:
Simplify

 
x
x
5
2
5 

Factor
 
x
x 2



C
Simplify:

 
2
2
1
2
x
x x
  
  

 








2
2
)
(Factor
(Cancel common factors)
1
1
2
1
2
2
1
1
x
x x
x
x
x
x
x
x

C
1
2
3
:
Simplify 2
2



y
y
y
  
  
1
1
2
1




y
y
y
y
1
2



y
y

C
y
y
48
24
12
:
Simplify

  
  
y
y
4
12
2
12 
y
y
4
2



C
2
2
9
Simplify:
2 15
a
a a

 
  
  
3 3
5 3
a a
a a
 
 
a + 3
a + 5

C
How to get a rational expression in
simplest form.
 Factor the numerator and
denominator completely.
 Cancel out any common
factors (not addends).
 Rewrite the remaining factors.

x
My Role as
a Member
Notetaker
Validator
Materials
Specialist
Secretary
Presenter

x
Mech
anics:
1.Solve the given equation.
2.Show the solutions
completely.
3.Box the final answer.

Accuracy 10
Presentation 10
Neatness 5
Speed 5

Question
s:
What did we do to arrive at the final answer?
When can we say that the given rational
expression is in the lowest term?
What is a rational algebraic expresssion?

SIMPLIFYING RATIONALL EXPRESSION MATH 88

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