Fractions

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Fractions Fractions are a convenient method for representing numbers that are not whole numbers. We use fractions in our everyday lives, for example “half”, “third” or “quarter”. In this document we consider the meaning of fractions and how we can do arithmetic with fractions. Examples The following diagram shows a circle divided into two halves.

The following diagram shows a circle divided into a quarter and the remaining three quarters.

Numerator and Denominator The top part of the fraction is called the numerator and the bottom part is called the denominator. For example for the fraction , the numerator is 3 and the denominator is 4.

www.mathematics.me.uk Simplifying Fractions In order to write fractions in their simplest form, any common factors in the denominator and numerator are eliminated. To be written in their simplest form, the denominator and the numerator are relatively prime. For example

Addition and Subtraction From the diagrams above we can see that fractional arithmetic in general? For example, how do we compute

and

, but how do we do

?

The first step is to find the lowest common denominator, that is the lowest common multiple of the two denominators. For the example the lowest common denominator of multiple of 5 and 3 and is 30.

is the lowest common

We now write

The next step is to find the numerator of the result. In the example since we multiply the by to obtain the first contribution to the numerator of the result. Also, since we multiply 10 to get the second contribution to the numerator of the result. For the example, we obtain

As a second example (subtraction):

by

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Multiplication In order to multiply two fractions, the numerators are multiplied together to give the numerator of the result and the denominators are multiplied together to give the denominator of the result. For example:

Division In order to divide two fractions, the second fraction is turned upside down and the division is changed to a multiplication and we then proceed as above. For example:

Spreadsheet The accompanying spreadsheet adds, subtracts, multiplies and divides fractions.