CORE_MATH • SHS 1Term 1WAEC / WASSCE SyllabusVIP Lesson
Linear Equations in One Variable (Fractional Equations)
Techniques for solving multi-step linear equations, clearing algebraic fractions using LCM, and solving word problems.
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Real-World Context & Relevance in Ghana
Susu collection managers and mobile money merchants calculate expected returns and commissions across multiple transactions using linear equation models.
Key Syllabus Learning Objectives
- 1Clear fractional coefficients by multiplying equations by the lowest common multiple
- 2Solve multi-bracket linear equations without algebraic sign errors
- 3Translate practical Ghanaian real-world word problems into linear equations
- 4Verify the validity of solutions by direct substitution
1
Clearing Denominators Using LCM
The most reliable method to solve fractional equations is to multiply every term—both fractions and whole numbers—by the LCM of all denominators. This instantly converts the problem into an integer linear equation.
- Identify all denominators.
- Calculate their LCM.
- Multiply every term on left and right sides by LCM.
- Simplify each term before expanding brackets.
Core Takeaway:
Every term must be multiplied by the LCM, not just the fractions.
WAEC / WASSCE Examiner Tips
- Do not forget to multiply solitary integer constants by the LCM (e.g. if the equation has + 2, multiply 2 by LCM as well).
- Place brackets around numerators when clearing fractions: e.g. 12 × (2x - 1)/3 = 4(2x - 1).
- Check your final answer by substituting back into the original equation.
Common Candidate Pitfalls & Errors to Avoid
- Multiplying only the fractions by the LCM while forgetting whole number terms.
- Sign errors when expanding negative brackets: -3(x - 2) is -3x + 6, not -3x - 6.
- In word problems, failing to state units in the final conclusion.
Topic Mastery Checklist
- Can I find the LCM of denominators 3, 4, and 6?
- Can I solve (x - 2)/3 - (x + 1)/4 = 1?
- Can I formulate and solve an age problem in algebra?
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