LESSON NOTES ON ALGEBRAIC FRACTIONS

LESSON NOTES ON SIMPLIFYING LINEAR ALGEBRAIC FRACTIONS

SUBJECT: Algebra

TOPIC    :  Algebraic Expressions

LESSON: Simplifying Algebraic Fractions

PREVIOUS KNOWLEDGE: Students are familiar with numerical fractions and can express them.

OBJECTIVES: By the end of the lesson, students should be able to express the sum or difference of two or more algebraic fraction into a single fraction.    

TEACHING METHODS: Demonstration, Questioning, and Assignment methods.

GRADE LEVEL: 7 ( Form 2)

DURATION: 40 minutes

DATE: 10/22/2018

INTRODUCTION: -What name is given to this number 2?

                                                                                        3

                               -Express i) 1+3 =?

                                                2  5 

                                               ii) 2-  4=?

                                                   3   5

                                               iii 4+1=?

                                                   7  3

                                                   

PRESENTATION:

An algebraic fraction is any fraction of the form, x + 5   where x and 5 are called the
                                                                        3.   x+2
  numerators; 3 and x+2 the denominators.                                      

  a) SIMPLIFYING ALGEBRAIC FRACTIONS.

To simplify an algebraic fraction, do the following:

-find the common denominator. This is usually the product of the denominators in the fractions present.

-adjust both fractions so that they are equivalent, using common denominator

-complete the simplification.

EXAMPLE( 1): Express i)x +  5

                                        3  (x+2) 

                                         ii) 2 +  1

                                             x.  (x+1)

                                SOLUTION

       x+      5

       3      x+2

 x(x+2)+3(5) =x²+2x+15

   3(x+2)            3(x+2)

Therefore, x +5         = x² +2x+1
                3  (x+2)          3(x+2)        Answer.

EXAMPLE (2) Express each of the following as a single fraction simplifying your result as far as possible.                                 i)      2 + 3 

                                                      3    7

ii)    2x +1 + x-2    

           3          4

iii)  1 + x-2   

         2      3

  iv)    3  +   2    

          x-4  x+3

  v)  y+2  + 3-y

        y-5      y+3

v) 2m+1 – 3m-2

     m+5       m-4

vi) 6  -  3               

 x-4     x

                                                            SOLUTION

  i)2    + 3 

    3       7

  14 +9  = 23

   (3)(7)     21 answer.

ii)   2x+1  +  x-2

        3            4

4(2x+1) +   3(x-2)  =8x+4+3x-6

      (3)(4)                        (3)(4)

     2x+1 + x-2         =11x -2

        3           4              12      answer.

iii) 1 + x-2

      2     3

    3(1)+2(x-2) =3 +2x-4

        (2)(3)              6

  1 + x-2         = -1+2x

  2       4                  6          answer.

iv)       3    +   2

          (x-4)   (x+3)

      3(x+3) + 2(x-4) =3x+9+2x-8

           (x-4)(x+3)        (x-4)(x+3)

         

           3  +    2         =  5x+1

        (x-4)  (x+3)        (x-4)(x+3)

                                = 5x +1

                                   X²+ 3x-4x-12

                               = 5x+1

                                  X²-x-12 answer.

                      EVALUATION.

Express each of the following as single fraction:

i)                    2x+1 + 3x-2

  3         2

     ii)         x-4  +  3

                  x-5     x-1

   iii          3x-2 -  x-4

                x-2      x+3  

                  SUMMARY.

 -Find the lowest common multiple of the denominators ; which is the product of the denominators.

-To express algebraic fractions, multiply numerator by denominators just as in numerical fractions.

-Factorize the numerator or denominator of one or both fractions to ease simplification.

              CONCLUSION.

ASSIGNMENT: Express as far as possible each of the following fractions.

i)                    x + 3x+2

3      5

ii)                  n-4  +  3n-1

            n+5     n-1

iii)                2y+1 – 5                                                                                                                                  4         y+3