Multiplying Algebraic Fractions Flashcards

GCSE Mathematics (Edexcel) 1MA1

Algebraic fraction

A fraction where the numerator, denominator, or both contain algebraic expressions.

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Terms in this set (10)

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Algebraic fraction

A fraction where the numerator, denominator, or both contain algebraic expressions.

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Step 1: Multiplying algebraic fractions

Multiply the numerators together to form the new numerator.

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Step 2: Multiplying algebraic fractions

Multiply the denominators together to form the new denominator.

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Simplifying algebraic fractions

Factorise both the numerator and denominator, then cancel any common factors.

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Example: Simplify (x/3) × (2/x)

Multiply numerators: x × 2 = 2x. Multiply denominators: 3 × x = 3x. Simplify: 2x/3x = 2/3.

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Common factors in algebraic fractions

A factor that appears in both the numerator and denominator, which can be cancelled to simplify the fraction.

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Example: Simplify (x^2/4) × (8/x)

Multiply numerators: x^2 × 8 = 8x^2. Multiply denominators: 4 × x = 4x. Simplify: 8x^2/4x = 2x.

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Multiplying fractions with brackets

Expand any brackets first if necessary, then multiply numerators and denominators.

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Key rule for cancelling terms

Only cancel terms that are factors of both the numerator and denominator, not terms that are added or subtracted.

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Example: Simplify ((x+2)/x) × (x/(x+2))

Multiply numerators: (x+2) × x = x(x+2). Multiply denominators: x × (x+2) = x(x+2). Simplify: x(x+2)/x(x+2) = 1.

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