Class 9 Math Chapter 6 Question Answer
Handwritten and composed notes Class 9 Math Chapter 6 Question Answer Algebraic Manipulation of Chapter No.6: Algebraic Manipulation notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Algebraic Manipulation for the students of Mathematics Science group of the (9 class) Matriculation and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Important notes of Class 9 Math Chapter 6 Question Answer for Matriculation part-I students.
- Complete chapter test according to the paper patterns of all Punjab boards of Chapter No.6: Algebraic Manipulation 9th class Mathematics Science group in English medium.
- Complete Multiple Choice Questions (MCQs) of Chapter No.6: Algebraic Manipulation 9th class Mathematics Science group in English medium.
- Complete Chapter exercise wise solved questions of Chapter No.6: Algebraic Manipulation 9th class Mathematics Science group in English medium.
- Complete chapter review exercise questions of Chapter No.6: Algebraic Manipulation 9th class Mathematics Science group in English medium.
- Important definitions asking in board question papers of Chapter No.6: Algebraic Manipulation 9th class Mathematics Science group in English medium.
- Here are the detailed 9th class math chapter 6 question answer pdf to help you prepare for your exams.
- Find Highest Common Factor and Least Common Multiple of
algebraic expressions.
- Use factor or division method to determine Highest Common
Factor and Least Common Multiple.
- Know the relationship between H.C.F. and L.C.M.
- Solve real life problems related to H.C.F. and L.C.M.
- Use Highest Common Factor and Least Common Multiple to reduce
fractional expressions involving, Addition (+) , Subtract (–) , Multiplication (x) , Dividing
- Find square root of algebraic expressions by factorization and
division.
- Introduction: In this unit we will first deal with finding H.C.F. and L.C.M of algebraic expressions by factorization and long division. Then by
using H.C.F. and L.C.M. we will simplify fractional expressions. Toward
the end of the unit finding square root of algebraic expression by
factorization and division will be discussed.
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- Highest Common Factor (H.C.F.) and
Least Common Multiple (L.C.M.) of Algebraic
Expressions:
- (a) Highest Common Factor (H.C.F.): If two or more algebraic expressions are given, then their common factor of highest power is called the H.C.F. of the expressions.
- (b) Least Common Multiple (L.C.M.): If an algebraic expression p(x) is exactly divisible by two or more expressions, then p(x) is called the Common Multiple of the
given expressions. The Least Common Multiple (L.C.M.) is the product
of common factors together with non-common factors of the given
expressions.
- (a) Finding H.C.F.:
- We can find H. C. F. of given expressions by the following two methods.
- (i) By Factorization (ii) By Division
- Sometimes it is difficult to find factors of given expression
that case, method of division can be used to find H. C. F. We consider
some examples to explain these two methods.
- (i) H.C.F. by Factorization:
- Example
Find the H. C. F. of the following polynomials.
x^2 – 4, x^2 + 4x + 4, 2x^2 + x – 6
- Solution: By factorization, x^2 – 4 = (x + 2) (x + 2)
- x^2 + 4x + 4 = (x + 2)^2
- 2x^2 + x – 6 = 2x^2 + 4x – 3x – 6 = 2x(x + 2) – 3(x + 2)
- 2x^2 + x – 6 = (x + 2) (2x - 3) Hence, H. C. F. = x + 2
- (b) L.C.M. by Factorization:
- Working Rule to find L.C.M. of given Algebraic Expressions
- (i) Factorize the given expressions completely i.e., to simplest form.
- (ii) Then the L.C.M. is obtained by taking the product of each factor appearing in any of the given expressions, raised to the highest power with which that factor appears.
- Square Root of Algebraic Expression:
- Square Root: As with numbers define the square root of given expression p(x) as another expression q(x) such that q(x). q(x) = p(x).As 5 # 5 = 25, so square root of 25 is 5. It means we can find square root of the expression p(x) If it can be expressed as a perfect square.
- In this section we shall find square root of an algebraic expression.
- (i) by factorization (ii) by division