Class 8: Chapter 21: Simplification of
Algebraic Fractions (Lecture Notes)
H.C.F. of Algebraic Expression: The H.C.F. of two or more algebraic expressions is an
expression of the highest degree which divides each of them without leaving any remainder.
L.C.M. of Algebraic Expression: The L.C.M of two or more algebraic expressions is an
expression of the lowest degree which is divisible by each of the given expressions without
leaving any remainder.
H.C.F. of Monomials: The H.C.F. of two or more monomials is the product of the H.C.F. of their
numerical coefficient, and the H.C.F. of the Literals (which is the lowest power of each of the
literals).
Method of Finding the H.C.F. of Monomials
H.C.F. of given monomials = H.C.F. of numerical coefficients x H.C.F. of literals
L.C.M of Monomials: The L.C.M. of two or more monomials is the product of the L.C.M. of
their numerical coefficient, and the L.C.M of the Literals (which is the highest power of each of
the literals).
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Method of finding L.C.M of Monomials
L.C.M of given monomials = L.C.M. of numerical coefficients x L.C.M of literals
HCF and LCM of Polynomials: For finding the H.C.F. and L.C.M. of given polynomials, we
factorize each of them and evaluate:
(i)
H.C.F. = (H.C.F. of Numerical Coefficients) x (Each common factor raised to lowest
power)
(ii)
L.C.M = (L.C.M. of Numerical Coefficients) x (Each factor raised to highest power)
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Reducing and algebraic fraction into its lowest form: An algebraic fraction is said to be in its
simplest form (or in lowest terms) if the numerator and denominator have no common factor
(except 1), i.e., if the H.C.F. of the numerator and denominator is 1.
To reduce the algebraic fraction, it is easy. Factorize the numerator and the denominator and then
cancel whatever is common. Let’s do one example to demonstrate that.
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Simplification of Expressions Involving Algebraic Fractions
When you have a polynomial as numerator and a polynomial as its denominator is called an
algebraic fraction.
Expressions involving algebraic fractions may be simplified in the same way as we simplify
arithmetical expressions as demonstrated above.
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