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2 Percentages




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Introduction

Review the Year 7 syllabus on Percentages, specifically:

  1. Converting decimals to percentages
  2. Converting percentages to fractions

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

In addition:

  • 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

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