Introduction

Review the Year 7 syllabus on Percentages, specifically:

The difference from Year 7 is that there may be decimals given in the percentage, or more complicated percentages to make it more challenging.

• You need to know how to convert a percentage with a fraction into a fraction. For example, $106\dfrac{1}{4}\%$. To do this, we first convert the 1/4 to a decimal, so the entire percentage becomes 106.25. Thus, this is $106.25/100=1.0625$
• You need to know how to convert a fraction into a percentage with rounding (for 2dp, where “dp” means “decimal places”) For example, $3/11=27.272727272727=27.27\%$

In Year 7, we talked about converting fractions to percentages. The idea of expressing a percentage composition as a percentage, by multiplying by 100% is based on the same principle.

For example, 10/50 as a percentage is $10/50*100/1=20\%$

More than 100%

When a percentage is expressed as a fraction, and that fraction’s numerator (top) is greater than its denominator (bottom), it is “more than 100%”.

For example, $30/20=30/20*100\%=150\%$, which is greater than 100%.

Percentages more than 100% are useful to know how many times greater something is than another thing.

For example, if Miley Cyrus is 165cm, and I am 182cm, if we calculate $182/165$, we get 1.103 (rounding off). Therefore, we know that I am 110% her height, or 10% taller than she is.

Application of Percentages

A large part of maths in year 8 relating to percentages will be about applying percentages, including in:

• Parts of a whole, which relates to a whole table of data given, for example the composition of carbon/nitrogen/oxygen/fluorine is given, and you need to find what percentage of that composition is oxygen.
• Profit, which relates to finding percentage profit (or loss), which is the profit/revenue. The other percentage is your expense
• Commission, which is the percent earned from a sale
• Discount, which is the percent decrease of the price of the item from its original price