Year 10 Interactive Maths - Second Edition

Transpositions Involving Two or More Operations

In general:

To obtain the subject of the formula, we:

• Clear fractions by multiplying both sides by the lowest common denominator.
• Add (or subtract) the same number to (from) each side.
• Multiply (or divide) both sides by the same number.
• Take the square (or square root) of both sides.
• If necessary, rearrange the formula so that the subject of the formula appears on the LHS.

Example 42

Solution:

Note that we could have obtained t as follows:

We notice that there is no unique method to use. However, it is necessary to follow the laws of algebra carefully in isolating the subject.

Example 43

Solution:

First Method

Second Method

Note:

The two methods appear to lead to different results, but they are just different forms of the same result.

This is the same as the result obtained by the second method.