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Numeracy
© copyright
M.J.Morris 2005

1.04 Rearranging Equations/Formulas (transposition).

The objective of transposing an equation, is to get one particular term on its own on one side of the equation, (and without it being the denominator of a fraction). This is called "making"" the chosen symbol "the subject of the equation". To do this we rearrange the equation following simple rules.

Equations involving only multiplication and division.

Note, when using symbols and letters in equations, we do not usually show the multiplication sign between any letters etc. that are being multiplied together.
i.e. AB means A x B, IR means I x R etc .
For equations which only involve the multiplication or division e.g.

• s = d/t ,
• V = IR ,

there is one simple rule for moving individual symbols.

• move the symbols diagonally from one side of the equation to the other.
• i.e. if a symbol appears on the bottom line of a fraction, then it will be on the top line if you move it to the other side of the equation, (and vice versa).

Examples.

• If s = d/t , then st = d .
• If V = IR , then V/I = R .
• if AB = C , then A = C/B .

Procedure for making a particular symbol the subject of the equation.

1. If the symbol is on the bottom line of a fraction, then move it (diagonally) to the other side.
2. If there are other symbols on the same side of the equation, then move them to the other side.

Examples.

a) If      I =V/R ,     make R the subject of the equation.
1 - IR = V .
2 - R = V/I .

b) If      at = v ,      make a the subject of the equation.
1 - ( a is not on the bottom line so doesn't require moving!)
2 - a = v/t .

Important!
In order to ensure that this simple rule remains mathematically correct, then if we remove all of the symbols from one side of the equation, or from the top line of a fraction, then we need to leave a "1" in their place.

Examples .

• If s = d/t , then s/d = 1/t .
• If V = IR , then 1 = (IR)/V .
• if AB = C , then 1 = C/(AB) .
• If x = y/z , then x/y = 1/z .

Finally, it is conventional to write the equation with the subject on the left hand side. Therefore rather than writing IR = V we would write V = IR etc.