Division is an important tool for solving linear equations, especially for students preparing for their GCSE exams. It helps us “undo” multiplication, which is often how we first see variables in equations.

Basic Concept

Let's look at a simple equation:

$$3x = 12$$

Here, we want to find out what $x$ is. Since $x$ is multiplied by $3$, we can isolate it. We do this by dividing both sides by $3$.

So, we have:

$$x = \frac{12}{3} = 4$$

This method is really important in algebra because it keeps the equation balanced. Whatever we do to one side, we must do to the other.

Importance of Division

1. Makes Things Simpler: Division helps simplify equations, so it's easier to find the value of the variable.
2. Keeps Equations Balanced: It makes sure the equation stays balanced, which is very important in algebra.

Examples

Let’s try another example:

$$5y + 10 = 30$$

First, we subtract $10$:

$$5y = 20$$

Now, we divide by $5$:

$$y = \frac{20}{5} = 4$$

By getting good at division, GCSE students can easily solve different linear equations. This skill sets the stage for tackling more advanced math topics later on.