Algebraic Fractions

Chapter summary, hard words and model exam answers for Hindi.

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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

Replace the 3 in 3/4 with (x+1) and the 4 with (x−2): you get (x+1)/(x−2). Every fraction rule from primary school still applies.

You may only cancel factors (things multiplied), never terms (things added). So (x²+x)/(x+1) becomes x(x+1)/(x+1) = x.

Factorise and cancel before multiplying to keep the algebra small. For division use KFC: Keep, Flip, Change.

If the bottoms share no factor, the common denominator is their product. Take care with the minus sign when subtracting.

numerator	the expression on the top of a fraction
denominator	the expression on the bottom of a fraction
factor	an expression that is multiplied with others; only factors can be cancelled
term	a part of an expression separated by + or −; terms cannot be cancelled
factorise	to rewrite an expression as a product of factors, e.g. x²+x = x(x+1)
reciprocal	the fraction turned upside down; b/a is the reciprocal of a/b
common denominator	a single bottom that all the fractions can be rewritten over
restriction	a value of x that is not allowed because it makes a denominator zero

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