Maths for Diploma Studies

When we say fractions, we are not just talking about halves or quarters etc., we mean terms made of numerators and denominators. Let’s find out more.

The inverse operation of multiplying by a fraction is multiplying by the opposite fraction. The opposite fraction is called its reciprocal. You can check this works by following this calculation:

The same applies for dividing by fractions:

For example, in this equation from a heat transfer lesson:

We can isolate t by multiplying both sides by the reciprocal of  which is . This cancels out the  on the left to give us:

But what if the term we need to isolate is part of a fraction? Say we need to know what A is in this equation:

First, we can do an inverse operation to move the rest of the fraction, so multiply both sides by  cancelling out the  on the left and giving us:

Then to isolate A, we just need to divide both sides by t to give us:

Troublesome numerators

What if you need to isolate a term in a bracket in the numerator of a fraction? Let’s say we need to isolate  in the equation for Stoke’s law (shown below):

A numerator’s job is to be divided by a denominator. As the numerator is the subject of an action and not performing an action on another term, it isn’t actually doing anything, so we can’t undertake an inverse operation on it. We therefore need to undertake an inverse operation on all the other terms on the same side of the equation. See what we mean about troublesome numerators!

We can start by dividing both sides by g R²  to get:

We now have a fraction multiplying what we need to isolate so we can multiply both sides by its reciprocal  to move it across the equals sign and get:

And now we can multiply both sides by  to get:

 And finally add  to both sides to get:

To help reinforce what we have just learned, on the next page there are some practice questions. Answers and explanations can be revealed by clicking on show answer.