Year 10: Linear equations involving fractions

This cheat sheet provides a quick reference for solving linear equations involving fractions.

Key Concepts

1. Finding a Common Denominator: The most important step! To add or subtract fractions within an equation, they must have the same denominator. Find the Least Common Multiple (LCM) of the denominators. Convert all fractions to have this LCM as their denominator.

2. Cross-Multiplication: This is a useful alternative method, particularly helpful when dealing with complicated fractions. It’s based on the principle of proportionality.

3. Solving for x: Once fractions are simplified with a common denominator, you can solve the equation for 'x' using standard algebraic rules (inverse operations).

Example

Solve: (x + 1)/3 = 5/6

1. Multiply both sides by 6: 6 * (x + 1)/3 = 6 * (5/6)
2. Simplify: 2 * (x + 1) = 5
3. Expand: 2x + 2 = 5
4. Subtract 2 from both sides: 2x = 3
5. Divide both sides by 2: x = 3/2

Tips

• Always check your answer by substituting it back into the original equation.
• Pay careful attention to signs (positive and negative) when multiplying and dividing fractions.
• Practice! The more you work through examples, the more comfortable you'll become.