One hundred percent is the whole thing so if we have 100% of cake we have the whole cake.
This is far simpler to picture than a percentage being one hundredth of a whole or one of a hundred parts.
For people who struggle with mathematics and those who are learning about percentages it is simpler to have a visual picture, as Martin Bell explained in his article "How to Teach Fractions." Cake makes for a good mental image.
If 100% of cake is the whole thing and half of 100 is 50 it follows 50% of cake is half the cake. A quarter of the cake is, of course, 25% because 25 is a quarter of 100.
If a really big cake is cut into 100 pieces each piece is just 1% and 18 % would be 18 slices. Hence, 18% of $1.00 is $0.18, this is easy to understand because $1.00 is already divided into 100 parts. supposing you need to find 18% of $0.75c, before we do the maths lets think about cake.
How to Calculate a Percentage of a Fraction of Cake
It gets more complicated if the cake was not whole to start with. Imagine one quarter has been eaten and three quarters of the cake remain. In order to get a percentage we must divide the incomplete cake into 100 pieces each slice being 1% of the remaining cake. Obviously these slices are smaller than if the cake was whole.
To calculate 18% of $0.75c we first find 1% by dividing 75 by 100 = 0.75
Then 18 parts or 18% is 0.75 x 18 = 13.5
So 18% of 75c is between 13c and 14c
From simple fractions of cake we can go on to understand more difficult problems involving percentages, such as taxes, service charges and how course work and exams contribute to an overall final score in college.
How to Calculate Fees as a Percentage & Addition Tax such as VAT
Calculating the fees to the agent for selling a house could be a good way to practise using percentages.
In the UK agents' fees are often a percentage of the final sale price, perhaps 2.5%. Suppose the house sells for £135,999 and on top of the fee there is Value Added Tax (VAT) of 20%. How much does the seller owe to the agent?
One percent is 135,999 divided by 100 = 1,359.99
So 2.5% is 1,359.99 multiplied by 2.5 = 3399.975
So the fee to the agent is £3399.97
But there is the additional VAT for public funds which is 20% of this fee. The fee is now the whole cake and we need an extra bit.
One percent is 3399.97 divided by 100 = 33.9997
So 20% is 33.9997 multiplied by 20 = 679.995
Hence the VAT is £680.00
The full cost of selling the house at £135,999 was £3399.97 + £680.00 = £4,079.97
How to Calculate a Discount From a Given Percent
If there is a discount the figure is calculated in exactly the same way as working out the estate agent fee as shown above. The 2.5% could have been an amount discounted off the full price of the house.
What is The Price Without The Tax?
If you know the full inclusive price and the percentage which was allowed for tax how do you work out the pre-tax price?
The agent was paid £4,079.97 which was the fee + 20% tax. Imagine his fee was one whole cake which is 100% and then we added an extra slice of cake to pay the tax, this was an additional 20%. The fee was like 120 slices of cake!
So, to get one percent divide £4,079.97 by 120 = £33.9997
The agent fee was 100% which is 33.9997 x 100
The tax was 20% which is 33.9997 x 20
Working Out Percentages is as Easy as Cutting Cake
Calculations involving percentages can be far simpler when you understand the logic of what you are doing.
One easy way is to think about it is:
- 100% is a whole cake,
- more than 100% is more than one cake,
- smaller than 100 is just a piece of cake.
Deborah Percy - BSc. MA. Managing Director of a heating & plumbing business. Interest in maths, science & research. Mother of 3, including twins.
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