Clothing Rearrangement

When numbers are "clothed" with symbols such as x, y, a, b etc. and put into equations, they can be rearranged using straightforward rules so that it is easier for you to solve problems.

First of all, you need to have a good basic understanding of how to solve a simple equation:

Equations are things that "balance" on each side. In just the same way as the old fashioned balances used to weigh gold, sugar, grain etc. mathematical equations must balance at each side all the time (otherwise we can't truthfully put an = sign in the middle).

Consider the equation: 5x + 6 = 21

We solve this by gradually stripping down the equation to leave the bare unknown (labelled as x).

Take away 6 from BOTH SIDES of the equation, giving:

Now divide BOTH SIDES of the equation by 5, giving:

When rearranging equations you will need to use exactly the same sort of technique as the one above.

The surface area A, of a sphere can be represented by the following equation. But what if we want to see the formula in terms of r (i.e. with r at one side of the = and all the other stuff at the other side of the =)?

A = 4r3 / 3

To rearrange this equation, we strip it down (look for the easiest ways to do this first always get rid of anything under the division bar at first).

To get rid of the "divide by 3" we do the OPPOSITE i.e. multiply BOTH SIDES of the equation by 3, this gives us:

3A = 4r3 (the 3 on the right hand side has disappeared because 3 / 3 = 1)

We leave tricky things like cubes and squares until last, hence the next easy thing to do is divide both sides by 4. Can you see we are now moving closer to getting r where we want it (one its own on one side of the =). This gives us:

3A / 4 = r3

All the remains now is for you to do the opposite of r3 on both sides (i.e. Cube Root) to get the equation in terms of r.