## Fractions, Decimals and Percentages

Start off by referring to

and also take note of the Metric System

When you first meet division, it is often portrayed in a form like this

### \[ 7 \div 11\]

The more you get into mathematics this expression would tend be be replaced by

### \[ \frac{7}{11} \]

so a division can also be considered as a fraction, and vice versa

Consider an process like

\[ \frac{\frac{3}{4}}{\frac{7}{8}} = \frac{3\times 8}{4 \times 7} = \frac{6}{7} \]

Do this the 'old way' to convince yourself that this procedure is correct, i.e. use

### \[ \frac{3}{4} \div \frac{7}{8} \]

Compare the two methods to see how it works. In the 'top' method the numerator of the lower fraction goes into the denominator of the 'new' term' and the denominator of the lower fraction goes into the numerator of the 'new term'.

**Example** A man drives 40 km home in half an hour. What is his average speed?

Using the basic method

### \[ 40 \div \left(\frac{1}{2}\right) \]

### \[ = 40 \times \frac{2}{1} \]

### \[ = 80\ km/h \]

using the 'new' method \[ \frac{40}{\frac{1}{2}} \] \[ = \frac{40 \times 2}{1} \] \[ = \frac{80}{1} \] \[ = 80 \ km/h \]