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At the end of the lesson students should be able to:
a. Define rational equation
b. Simplify rational expression
c. Apply the procedure on how to simplify rational expression
II. Subject Matter
Topic: Equations Involving Rational Expression
References: Oronce, O.A and Medoza, M.O
Materials: PowerPoint presentation, LCD, activity sheets, metacards, and cartolina
Time: one hour
Strategies: Guided-Discovery Learning, Exposition and Cooperative Learning
III. Lesson Proper
Teachers Activity Student’s Activity
May I request everyone to stand up and
start our day with a prayer. Everybody,
let’s recite our mathematical prayer.
Good morning, Class!
Before you take your seats please pick up
the pieces of paper under your chairs and
arrange your chairs as well.
You may now take your seat.
Chloe, may I know who are absent today?
Kindly give us your report.
Thank you, Chloe.
Last time, we discussed about what is a
complex fraction and we learned that there
are two methods used in simplifying
complex fraction. Let’s see if you really
understood the lesson by recalling some
concepts about our previous lesson. Let’s
do our review in the form of Music and
Learning is Fun.
Students will recite the prayer
Good afternoon, Miss Pagaduan!
Students will pick up the pieces of paper
and arrange their chairs
Students will take their seat
I’m glad to tell you nobody is absent today.
To play this game, When the music starts I
will give the ball in the class and it will be
passed around. Pass the ball to your
classmate next to you. When the music
stops, the students with the ball will
answer the question. Is my instruction
So let’s start. (Music plays then stop)
It is a fraction that has a rational
expression either in the numerator,
denominator or both.
How many methods were used in
simplifying complex fraction?
In method one, in simplifying complex
fraction you have to invert the denominator
to its what?
In method two I simplifying complex
fraction, we multiply the numerator and
denominator to its what?
What is the LCD of x+4 and x-6?
Before we proceed to our new lesson,
remember that during Grade 7 you
discussed about how to find x, right?
Let’s play a short game again. It is called
“Find your X”. I will choose 10
representatives from the class .Each
representative will be given a metacards.
The metacards consists of an equation to
find x and the answer. Everybody will be
scattered around the room and when the
music starts you must find your x by
greeting to each other and solving the
equation if it matches to yours. When the
music stops, you must already found your
partner and tell to the class how come you
arrive in that pairing. Is it clear?
We multiply it by the LCD
(The class will choose a representative)
So, let’s begin! (Music starts)
(Music stops) Since you already found
your pairing, will you tell now to the class
why you arrive with that pairing?
Very good! You may now take your seats.
Today, we’re going to discuss about
Equations Involving Rational Expression
and it involves how to find x.
Our activity before I discuss our topic is
that you’re going to complete the table
first. (Showing the cartolina with a table to
fill). The first and second column are the
values of a and b. The third and fourth
column, you have to multiply the values of
a and b and simplify it. You will be given 7
minutes to finish the task. Afterwards, I will
randomly call some of you to fill the
a b a˙b Simplified
Let me answer number one for you. What
is the value of a and b?
In the third column, we have to multiply the
value of a and b? What does it look like if
we multiply a and b?
If we multiply it the simplified form of
number one is what?
Students will mix around the room to find
(Students will explain why they come up
with such paring)
The representatives will take their seat
The value of a and b are 5 and x+
Do you understand what are you going to
Ok, you may now begin.
(After 7 minutes) Ok, time’s up. Let’s
answer the activity. (The teacher will
randomly call to fill the columns)
Very good! How about if we’re now going
to find x? (Showing another set of rational
Observe our denominators first. What do
you notice in our denominators?
Since they are dissimilar fractions, what
are you going to find?
In number 1, what is the LCD of our
Next thing, we’re going to multiply both
sides by 20 then simplify. What is now our
Students will start answering the activity
a b a˙b Simplified
) 12m – 1
They are dissimilar fractions
We’re going to find the LCD
The LCD of 5, 4 and 2 is 20.
That’s right! Our new equation is 4x+5=
10x. What are we going to do next to find
Very good! What is x?
Excellent! To see if x is
we will only
substitute the value of x to our equation to
see if our answer is correct. (Showing the
checking to the class) So we have the
In number two, what is our LCD?
Since our LCD is x+1, what are we going
to do next? Are we going to multiply first or
cancel out the common factors?
After we cancel out and multiply we can
now combine like terms. So what is our
So what is x?
Let’s see if our x is equal to -5. Let’s
substitute -5 to our x. (Showing the
checking) Therefore, the value of x is
What if our x didn’t match in our checking?
How are you going to write the solution if it
Very good! If our equation doesn’t have
any solution it is called extraneous
Will you try to solve the remaining items? I
will be giving you 7 minutes to complete
the task. Then after 7 minutes, we’re going
to check. Is that clear, Class?
(After 7 minutes)Okay, time’s up! Finish or
not finish, let’s check. (Checking of
Apply the subtraction property and divide
both by 6.
The LCD is x+1
We will cancel out the common term then
The new equation is 5x+11=3x+1
x is -5
The equation has no solution
Based on the two activities we have, can
you described to me rational equation? Or
what is a rational equation?
How do we simplify rational equation?
What is an extraneous solution again,
Do you have any question, class?
Do you understand now how to solve
Let’s have one last activity. I’ll be grouping
you into three groups. I will call the three
leaders of the group to come in front and
get the list of your members and the
activity sheet. I will be giving you another
10 minutes to complete the task then we
will check. Is it clear, class? (The teacher
will call the leaders and give the activity
(After 10 minutes) Ok, time’s up. Finish or
not finish, let’s check.(Randomly calling
students for the checking of activity) Are
you done checking, Class?
Please pass your paper to the center aisle
then to the front.
Rational equation is an equation that
contains one or more rational expressions.
Rational equation is an equation that
contains in which one or more terms is a
To simplify rational equation we must
eliminate the rational expressions in the
equation by multiplying both sides of the
equation by the LCD. Solve the equation
Extraneous solution is an apparent
solution that does not solve its equation.
Students will pass the papers to the center
aisle then to the front
For your assignment, answer page135
nos. 2, 3, 21, 27 and 28. Show your
solution. Put it in your notebook.
Eileen M. Pagaduan
Mr. Jeffrey S. San Juan
Ms. Nenita S. Juvida
Ms. Claribel S. Verdadero
SGD Felicidad O. Rodelas
Practice Teaching Supervisor