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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:

A = lw can be transposed by dividing both sides by l and swapping the LHS and RHS to give w = A / l.

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

A literal equation contains only letters. For example, x + a = b is a literal equation.

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

Transpose the formula t = u - v to make u the subject.

Solution:

Add v to both sides and then rearrange to find u = t + v.


Key Terms

formula, subject of a formula, transposition, changing the subject, literal equation


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