Rearranging is a very important topic. You will definitely need it for a lot of questions in Maths, Physics and Chemistry. Maybe even in Biology!

Rearranging basically means making a certain quantity the subject of the formula.

LHS means the left hand side of the equation.

RHS means the right hand side of the equation.

In the equation: y = mx + c,

‘y’ is the LHS (left side of the equal sign)

‘mx + c’ is the RHS (right side of the equal sign)

### Rules:

Make ‘a’ the subject of the formula in the following equations.

1) c = b – a

c – b = -a

-a = c – b

(Reverse signs on both sides)

a = -c + b

a = b + c

2) c = b + a

c – b = a

a = c – b

3) c = b ÷ a

a = b ÷ c

4) c = b x a

a = c ÷ b

5) c = a ÷ b

a = b x c

6) c = a x b

a = c ÷ b

7) c = (-a) x b

-a = c ÷ b

(Reverse signs on both sides)

a = -(c ÷ b)

8) 3) c = b ÷ (-a)

-a = b ÷ c

(Reverse signs on both sides)

a = -(b ÷ c)

You may also be asked to rearrange a quantity which is being square rooted.

c = b + √a

√a = c – b

(Square both sides)

(√a)² = (c – b)²

a = (c – b)² = c² -2bc + b²

**Complicated Questions**

You probably came across some really tough rearranging questions whilst doing past papers. They make look intimidating at first but it is important to do everything step by step.

Do what you can at first and then build up.

**Example:
**Rearrange the following formula to make ‘t’ the subject of the formula:

a = √(b + t)

cd

**Step 1**: Rearrange the denominator ‘cd’ from RHS to LHS

You get:

acd = √(b + t)

**Step 2**: Square both RHS to LHS

You get:

(acd)² = {√(b + t)}²

a²c²d² = (b + t)

**Step 3**: Rearrange ‘b’ from RHS to LHS

You get:

a²c²d² – b = t

t = a²c²d² – b