Usage of Percentage

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In maths learning, every learners will come across the terms "percent" or "percentage".

Percentage is a ratio.
It is a ratio between two numbers.
The denominator is normally the total of an item.

The unit used is %.

The above may be common knowledge for anyone doing percent maths problems.

However, what is the presentation of the solution that is appropriate?

Let's us do an example.

Example:
Class A has 30 students. If 40% of them are girls, how many are boys?

Solution:
Number of boys in the class = 30 - 40%

Now, is this "30 - 40%" correct?

The idea may be there, but someting is amiss.

What is this "40%"?
Can we just write 40% as it is?

The answer is NO!

Percentage is a ratio of the total (the class size of 30).
We cannot simply write 40% if we want to know the actual number.

The correct way is to present the step or working as:  (40/100) x 30 = 12 students

We cannot simply write :   30 - 40%.
The correct way has to be  30 - (40/100) x 30 = 30 - 12 = 28 students.

2 mistakes, in concept, were made:

1) Number cannot subtract a percentage.  Their units are different.
    
2) Percentage is a ratio, an indication of the proportion of a piece to the total. It is a relative term, not an absolute number. Thus, an absolute number cannot operate with a relative term.

Understanding this concept of "percent" and "percentage" will be handy and avoid the unnecessary trouble and anxiety of doing maths.

Tips: 
Thinks of a slice of cake when doing "Percent". It has meaning only when compared to the whole cake.

Remember: Maths Is Interesting!  And it WILL be get more interesting. 


:D