# CLASS-8INTRODUCTION OF ALGEBRAIC FRACTION

ALGEBRAIC FRACTION

Fraction in which the numerator or denominator or both are algebraic expressions are called algebraic fraction.

x           2               x - 6

Example.) -------, --------, and ----------- are algebraic fractions.

2        x² + 3         x² + 3x + 2

Algebraic fractions can be reduced, added, subtracted, multiplied and divided according to the same rules that govern arithmetic fractions.

Reduction To Lowest Terms

When the numerator and denominator of an algebraic fractions do not have any common factor except 1, the algebraic fraction is said to be expressed in the lowest terms.

To reduce an algebraic fraction to the lowest terms, take the following steps.

Step.1) Factorize the numerator and the denominator.

Step.2) Cancel the factors that are common to the numerator and the denominator.

15a⁴

Example.1) -----------

35a⁵

3 X 5 X a X a X a X a             3

= ------------------------- = ---------  =   3/7a

5 X 7 X a X a X a X a X a         7 X a

15a⁴           15           a⁴

Alternatively, --------- = -------- X --------

35a⁵           35           a⁵

3            1             3

= ------- X -------- = ---------          (Ans.)

7            a⁵⁻⁴          7a

9 aᶟb⁵c⁶

Example.2)  -------------

12 a⁶b⁴c²

3 X 3 X a X a X a X b X b X b X b X b X c X c X c X c X c X c

= -----------------------------------------------------------

3 X 4 X a X a X a X a X a X a X b X b X b X b X c X c

3bc⁴

= ----------     (Ans.)

4aᶟ

Alternatively,

9 aᶟb⁵c⁶

----------------

12 a⁶b⁴c²

9               aᶟ               b⁵              c⁶

=   ---------- X ---------- X ---------- X ----------

12              a⁶               b⁴              c²

3             1

=  -------- X --------- X  b⁵⁻⁴ X  c⁶⁻²

4             a⁶⁻ᶟ

3bc⁴

=    ----------     (Ans.)

4aᶟ

125a⁴b²c⁵

Example.3)  ----------------

175a⁴b⁵c⁴

5 X 5 X 5 X a X a X a X a X b X b X c X c X c X c X c

= ---------------------------------------------------------

5 X 5 X 7 X a X a X a X a X b X b X b X b X b X c X c X c X c

5c

= ----------         (Ans.)

7bᶟ

Alternatively,

125a⁴b²c⁵         125           a⁴            b²           c⁵

------------ = -------- X -------- X -------- X --------

175a⁴b⁵c⁴         175           a⁴             b⁵           c⁴

5 X a⁰ X c⁵⁻⁴

=   -----------------

7 X b⁵⁻²

5 X 1 X c¹               5c

=  ----------------  =  ---------          (Ans.)

7 X bᶟ                  7bᶟ