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Introduction to Percentages
What are Percentages?
Percentages, like fractions, help people explain how much of something there is, even if it is smaller or larger in value than whole numbers.
Percentages are expressed in terms of a number out of 100, with 0 being none of the thing and 100 being the whole or full thing.
For instance, if you still had a full pizza to eat, you could say that you still had one hundred per cent, or 100% of your pizza, left. This could be shown as 100%.
If you started with 100% or all of one pizza and then gave 25%, (twenty-five per cent) or one quarter of the pizza, to someone and 25%,(twenty-five per cent) or another quarter of the pizza, to another person, you would have only 50 % (fifty per cent) or half of the pizza left over. As a maths calculation, that would look like this:
$$100\% – 25\% – 25\% = 50\%$$
If someone gave you another pizza, in addition to the pizza you already had, you would have had a one hundred per cent increase in pizzas in relation to what you had. This could be represented mathematically as follows,
$$100\% + 100\%= 200\%$$
How are Percentages Calculated?
Percentages are calculated as a fraction or multiple of one hundred, depending upon how much of the item there is, with 100% being one whole item.
There is more than one way to calculate percentages. The first is as follows, $$\%\;(percentage)\;=\;$$$$\frac{(the \;part)}{(the \;whole)}×\;100$$
The second is, $$\%\;(percentage)\;=\; $$$$(the \;part)\;÷\;(value\;of\;1\%)$$
An Example of Calculating a Percentage
For example, if you wish to know what percentage 480 is of 20000, with the first formula,$$\%\;(percentage)\;=\;$$$$\frac{(the \;part)}{(the \;whole)}×\;100$$$$\frac{480}{20000} = 0.024\;$$$$0.024\;×\;100\;= \;2.4\%$$And using the second formula, you get the same answer, $$\%\;(percentage)\;=\; $$$$(the \;part)\;÷\;(value\;of\;1\%)$$$$ 20000\;÷100\;=200\;(which\; is \;1\%) \;$$$$then\;480\;÷\;200=\;2.4\%$$
To Convert a Decimal to a Percentage
The simplest way to convert a decimal to a percentage is to multiply it by 100 on your calculator. For instance, to find the percentage which is equivalent to 0.175, put into your calculator the following,
$$0.175\;(decimal\;)\;×\;100\;= \;17.5\%$$
The other way to do this is to shift the decimal point of the decimal two places to the right. And do not forget to put the percentage sign.
To Convert a Fraction to a Percentage
The simplest way to convert a fraction to a percentage is to do the division of the fraction on your calculator and multiply it by 100. For instance, to find the percentage which is equivalent to 4/5, put into your calculator the following,
$$4\;÷\;5\;=\;\;0.8\;(decimal)$$$$\;0.8\;×\;100\;= \;80\%$$
Practice your skills with these ten percentage questions.
Different Percentage Sizes
50% means half of something because 50% is half of 100%. 25% is one quarter of something because 25% is one quarter of 100%. Likewise, since 200% is two times 100%, 200% describes two of the item or amount being described.
See if You Can Answer the Following Percentage Questions
$$a)\;70\% $$ $$b)\;100\%$$ $$c)\;200\%$$ $$d)\;120\% $$
Show Answer
$$c)\;200\%$$
$$a)\;45\% $$ $$b)\;25\%$$ $$c)\;5\%$$ $$d)\;75\% $$
Show Answer
$$b)\;25\%$$
$$a)\;65\% $$ $$b)\;25\%$$ $$c)\;28\%$$ $$d)\;75\% $$
Show Answer
$$d)\;75\% $$
Another Example
If your whole world stamp collection consisted of 50 stamps, you could say that those 50 stamps were 100% of your stamp collection. That would mean that one stamp in your collection was equal to 2% of your entire collection. If you gave 10 of your stamps to your younger brother or sister, you would have given away 20%of your stamp collection, and you would have 80 % of your stamp collection left over. As a maths calculation, that could look like this:
$$100\% – 20\% = 80\%$$
See if You Can Answer These Percentage Questions
$$a)\;80\% $$ $$b)\;16\%$$ $$c)\;12\%$$ $$d)\;15\% $$
Show Answer
$$a)\;80\% $$because every 1 of Edward’s cars is equal to 10 per cent of his collection. He sold 2 cars. 2 x 10 is 20. 100% – 20% = 80%
$$a)\;80\% $$ $$b)\;20\%$$ $$c)\;50\%$$ $$d)\;55\% $$
Show Answer
$$c)\;50\% $$ because 200 of Jen’s apples are 100%. Therefore 100 of Jen’s apples represent 50 per cent or half of all her apples. Jen sold 100 apples or 50% on market day, and has 100 apples or 50% left over. 100% – 50% = 50%
$$a)\;15\% $$ $$b)\;30\%$$ $$c)\;50\%$$ $$d)\;10\% $$
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$$d)\;10\% $$ because altogether there are 20 cars, which means each car represents 5% of the cars Tim counted. Since Tim counted 2 blue cars, and 2 times 5% is 10%, 10% of the cars which Tim counted were blue.
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(Practice your skills with Ten Percentage Questions)
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