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## Transposition

There are two general rules that must be followed when transposing.

(a) THE RULE OF OPPOSITES - Which indicates the appropriate operation to 'move' a symbol.

(b) THE RULE OF BALANCE - Which governs the way in which the operation is carried out.

To apply rule (a) you need to be familiar with opposite, or INVERSE, operations. Here is a list of those most commonly used:

 OPERATION INVERSE OPERATION Addition (+) Subtraction (-) Multiplication (x) Division (÷) Square (a²) Square Root (√)

For example in the formula: s = a + b the inverse of +b is -b

We can therefore, 'remove' the b by subtracting b from both sides of the formula.
So we get

Step 1: s - b = a + b - b
Step 2: s - b = a
Step 3: a = s - b

To apply rule (b) you should remember that a formula remains valid, or 'in balance', provided any operation is applied equally to both sides of the formula.

For example, if             P = VI

then      P + Q = VI + Q
or            √P = √VI

You'll notice that in each case, both sides of the formula were treated in the exactly the same manner.
Example
Make I the subject of the formula V = IR
To remove R, which is multiplying I, we must divide both sides by R:

V = IR
R    R

Hence:

V = I
R
(Note that 'R' cancels on the right hand side. In practice it is simply excluded).