Year 9: Linear equations involving fractions

This cheat sheet helps you solve linear equations that involve fractions.

Key Concepts

• Cross-Multiplication: This is the most common method. Multiply the numerator of each fraction by the denominator of the other fraction.
• Example: 2/3 + 1/4 = ? -> (2 x 4)/(3 x 4) + (1 x 3)(4 x 3) = 8/12 + 3/12 = 11/12
• Finding a Common Denominator: If the denominators are different, you *must* find a common multiple to make them equal.
• Simplifying Fractions: Always simplify your fractions after cross-multiplication.

Steps to Solve

1. Identify the Denominators: Determine all the denominators in the equation.
2. Find a Common Denominator: Find the least common multiple (LCM) of the denominators.
3. Convert to Equivalent Fractions: Multiply *every* term in the equation by the denominator of the fraction you're working with, using the LCM as the new denominator.
4. Solve the Equation: Now you should have a standard linear equation (one with whole numbers).
5. Check Your Answer: Substitute your solution back into the original equation to verify it’s correct.