Class 8 Maths - ODISHA

Fractions in Disguise

In the Chapter 'Fractions in Disguise' from the Class 8 Mathematics curriculum for Odisha (BSE), students explore rational numbers and algebraic expressions that look like complex fractions but can be simplified. This chapter builds upon basic fraction operations by introducing variables, algebraic identities, and rational expressions. Mastering these concepts is crucial for board exam success as it lays the foundation for solving advanced algebraic equations, factorisation, and word problems efficiently. Students will learn how to uncover the true, simpler form of disguised fractions through factorization and cancellation.

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Key Concepts

Rational Expressions

An algebraic fraction where both the numerator and the denominator are polynomials.

Simplification of Algebraic Fractions

Reducing a fraction to its lowest terms by cancelling common factors from the numerator and denominator.

Factorisation in Fractions

Splitting numerators and denominators into their product of factors to easily spot hidden common terms.

Domain Restrictions

Identifying values of the variable that make the denominator zero, which are excluded from the solution set.

Operations on Disguised Fractions

Performing addition, subtraction, multiplication, and division on complex algebraic fractions using LCM and reciprocal rules.

Important Formulas

(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
a^2 - b^2 = (a - b)(a + b)
Fraction Simplification: (a * c) / (b * c) = a / b (where c != 0)

Board Exam Info

In the Odisha (BSE) Class 8 Mathematics exams, this chapter typically carries around 6 to 8 marks. Questions usually include 1-mark objective questions, 2-mark short answer questions involving direct simplification, and 3-mark word or factorisation problems.

Frequently Asked Questions

Why are these fractions called 'in disguise'?

They look complicated or unfamiliar at first glance because they contain algebraic variables and polynomials, but they can be simplified into basic fractions using factorisation.

Can I cancel variables directly from the numerator and denominator?

No, you can only cancel common 'factors' (multiplied parts), not individual terms that are added or subtracted.

What happens if the denominator becomes zero after simplification?

Any value of the variable that makes the denominator zero is undefined, so those values must be explicitly excluded from the final answer.

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