Solving Equations Involving Fractions

How do we solve equations that involve fractions? Before we get started, I am assuming you already know how to solve equations by balancing: you must do the exact same thing to both sides. So lets have a look at how to solve equations involving fractions. EXAMPLE: (2f + 8) / 3 = 6. The whole of 2f plus 8 has been divided by 3. We need to move this ‘3’ first so that everything is on the same level. No denominators. So multiply both sides by 3. Multiplying by 3 and dividing by 3 on the left hand side means that the 3's cancel each other on the left hand side. This leaves a simple linear equation to solve. 2f + 8 = 6 X 3 which simplifies to 2f + 8 = 18. Solve it: 2f = 10, so answer f=5. Easy! As always, check your answer. Substitute f=5 into the original question. EXAMPLE 2: (20 + 7e) / 2 = 2e + 7. Start by multiplying both sides by 2 to remove the '2' from the denominator on the left hand side. This means the times by 2 and divide by 2 on the left hand side cancel each other out. We now have this equation: 20 + 7e = 2(2e + 7). Expand the bracket on the right hand side and solve. 20 + 7e = 4e + 14. Simplify and solve: 3e = -6. Answer: e = -2.