Fractions: Well, what can I say about fractions except that I consider this a very important topic. This is usually one of the first topics I tend to go over with new pupils.

**Basic Fractions**

The misconception below is common in KS3 and even at GCSE level.

Let us start with the basics:

A common misconception in adding or subtracting fractions is pupils treating the numerators and denominators as whole numbers so end up adding or subtracting the denominators as well (see above illustration 1 - misconception). Illustration 2 shows the right way to add fractions with different denominators. First find a common denominator before you can add the numerators. Copy the common denominator then simplify (see Right Way, illustration 2).

The same goes with subtracting fractions. Misconception is to subtract the denominators as you would the numerators as shown on illustration 3. Put this misconception right by finding a common denominator before subtracting the numerators then just copying the common denominator.

__Algebraic Fractions__

When my pupil and I got to the topic on Algebraic Fractions, a misconception was uncovered which remained uncorrected until we got into it.

There is a set of invisible brackets on both the numerator and denominator which means you cannot just cancel similar terms unless if they were factorised first.

It was this misconception that stopped my pupil from achieving that targeted grade! When this was sorted out and he was getting much better marks on the work set out by school, he regained his confidence back. Much to my surprise he decided to take on not just Cores 3 and 4 exams he was due to take but also to resit his Cores 1 and 2. He did it and to my amazement got A's on all of them! And all these were due mainly to a misconception sorted! (He did work so hard as well) After this, I made fractions one of the most important topics which I made sure all my pupils do well from the onset.