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Fractions

A fraction is a part of a whole. We write fractions with one number separated by a line above another. This merely means one number divided by another number. The top number is called the numerator which denotes the size of the portion or fraction and the bottom number the denominator which tells you the size of the fraction of the whole being referred to. 3⁄4 therefore means 3 lots of a whole when that whole has been divided into four.

Fractions can be manipulated. By this we mean that the numerator and the denominator can change but they can still represent the same fraction; 6⁄8 is the same fraction as 3⁄4. If someone offered me 12⁄16 of a million pounds or 3⁄4 of a million pounds I would not care because the value is exactly the same! The rule, therefore, is that if you want to express a fraction as a different value then multiply both the numerator and the denominator by the same number.

Equally, fractions can be expressed in values that can be 'simplified'. It might be easier to see the fraction 3⁄8 rather than 27⁄72! Dividing both the numerator and the denominator by the same number can help to simplify the fraction. When asked to simplify something you are being asked to express it in the shortest or lowest value possible. 3⁄8 cannot be expressed in any lower form whereas 6⁄8 can!

We can do all the four operations on a fraction but there are rules to remember.

Adding and Subtracting Fractions

When adding or subtracting two or more fractions with the same denominator, simply add or subtract the numerators. For example:

If adding or subtracting fractions with different denominators, you will have to express the fractions with a common denominator, i.e. make them all halves, eighths, quarters or whatever. If you want to turn 3⁄4 into eighths, simply multiply the numerator and the denominator by the same number - in this case to get to eighths, multiply each by 2. Once they all have the same denominator, you can go ahead and add or subtract the numerators and then do any simplification (cancelling down) necessary.

Multiplying Fractions

There are two basic approaches. The first approach is to simplify as many of the fractions as possible then multiply the numerators and then the denominators. The second is the other way round - multiply the numerators and the denominators and then do any simplification necessary! For example:

Dividing Fractions

Remember earlier we said that division was the inverse of multiplication? Well, this serves us well when dividing fractions. To divide, multiply by the inverse. For example, take the problem 2⁄3 ÷ 3⁄4. The inverse of 3⁄4 is 4⁄3, so the answer is then 8⁄9.

Where problems can arise is when numbers are replaced by letters representing some variable number. However, if you remember these basic rules then you should be in a position to tackle quite complex problems.

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