Name: _______________________________________ Section: ______________________ Date: ________________
Learning Competency : Performs operations on rational algebraic expressions. (MULTIPLICATION OPERATION)
Activity Title
: Amplify Me!
Learning Target
: Multiplication operation on rational algebraic expressions
Concept Note
: demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions,
linear equations and inequalities in two variables, systems of linear equations and inequalities in two
variables and linear functions.
MULTIPLICATION OF RATIONAL ALGEBRAIC EXPRESSIONS
Steps
1. Multiply the numerators
2. Multiply the denominators
3. Factor out both numerator and denominator
4. Divide the common factor on both numerator and denominator.
5. Simplify to its simplest form/ lowest term
Examples in multiplying rational algebraic expression.
1. _2t_ ● 15_
5
8t2
→ numerators (2t and 15)
→ denominators (5 and 8t2)
= _2t_ ● 15_
5
8t2
→ multiply the numerators (2t and 15)
→ multiply the denominators (5 and 8t2)
= _30t_
40t2
→ product of the numerators
→ product of the denominators
= 1●2●3●5●t_ → prime factors of the numerators
1●2●4●5●t●t → prime factors of the denominator
= _1●2●3●5●t → 1●2●5●t is the common prime factor bet.
1●2●4●5●t●t the numerator and the denominator
= 1●2●3●5●t_ → divide both numerator and denominator
1●2●4●5●t●t by its greatest common factor which is 10t
= _3 _
4t
→ product in simplest form
Examples in multiplying rational algebraic expression.
Given
Product of Numerator
Product of Denominator
1.
2t_ ● 15_
30t_
5
8t2
40t2
2.
__3x__ ● _4x
___12x2___
2
x + 2x
2
2x2 + 4x
Exercises in multiplying rational algebraic.
Given
Product of Numerator
Product of Denominator
1. _x – 2_ ● _x + 2_
3
2
2. _4𝑎 + 8_ ● _𝑎 + 5_
𝑎2 – 25
5𝑎 + 10
2.. __3x__ ● _4x → numerators (3x and 4x)
x2 + 2x
2 → denominators (x2 + 2x and 2)
= __3x__ ● _4x_ → multiply numerators (3x and 4x)
x2 + 2x
2 → multiply denominators (x2 + 2 and 2)
= ___12x2___
2x2 + 4x
→ product of the numerator
→ product of the denominator
= 1●2●2●3●x●x → prime factors of the product
2x (x + 2)
→ factors of the product of the using CMF
= 1●2●2●3●x●x → 2●x common factors between
2x (x + 2)
numerator and denominator
= 1●2●2●3●x●x → divide both numerator and denominator
2x (x + 2)
by its greatest common factor which is 2x
= _ _6x__
(x + 2)
→ product in simplest form
GCF
Simplest Form
10t
_3 _
4t
_6x__
(x + 2)
2x
GCF
Simplest Form