Summary and Exam Tips for Algebraic Fractions
Algebraic Fractions is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. This topic focuses on simplifying algebraic fractions and understanding operations like addition, subtraction, multiplication, and division involving these fractions.
To simplify algebraic fractions, one must first factorize the numerator and denominator, then cancel out any common factors. When adding or subtracting algebraic fractions, it's crucial to find the lowest common multiple (LCM) of the denominators to derive a common denominator. For example, the LCM of and is . Once the denominators are the same, add or subtract the numerators.
In contrast, for multiplication and division, aligning denominators is unnecessary. Simply multiply the numerators and denominators directly, or for division, invert the second fraction and multiply. Always reduce the resulting fraction to its simplest form by dividing both the numerator and the denominator by their highest common factor (HCF). Remember, do not simplify through addition or subtraction terms directly.
Exam Tips
- Understand the Basics: Ensure you are comfortable with factorization and finding the LCM, as these are fundamental for simplifying algebraic fractions.
- Practice Multiplication and Division: Remember, no need to align denominators. Focus on multiplying numerators and denominators, and for division, invert the second fraction.
- Simplify Step-by-Step: Always factorize first and cancel common factors to simplify fractions. Avoid simplifying through addition or subtraction terms.
- Use Past Papers: Practice with past paper questions to familiarize yourself with the exam format and types of questions asked.
- Check Your Work: After solving, always recheck your steps to ensure all fractions are in their simplest form and calculations are correct.
