Year 10 Interactive Maths - Second Edition

## Transposition of Formulas

A formula is an algebraic relationship between two or more variable quantities.

For example, A = lw is a formula for the area, A, of a rectangle of length l and width w.  In the formula, A is expressed in terms of l and w.  We say that A is the subject of the formula.

If we know the values of l and w, the corresponding value of A is determined by substituting l and w into the formula.  However, if we know the values of A and l and are required to find the value of w, then it is convenient to rearrange the formula in order to express w in terms of A and l as follows:

Now w is the subject of the formula.

The process of expressing w in terms of A and l is called transposition or changing the subject of the formula.  The methods used to change the subject of the formula are the same as those used for solving equations.

### Literal Equations

The methods used to transpose literal equations are the same as those for solving equations.

## Transpositions Involving One Operation

To rearrange the terms in a formula, the same operations are performed to both sides of the formula, i.e. whatever is done to one side of the formula must be done to the other.

### Transpositions Involving Addition

###### Recall that:

The same number can be added to each side of a formula.

#### Example 34

##### Solution:

###### Key Terms

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