Sunday, 30 August 2009

Misconception of Percentage

Maths is interesting!

It catches you nicely when you are not aware of its full implication.

Many of its techniques and concepts has wide boundaries.

Any maths learners has to understand its fundamentals and basic concepts in order to "escape" being caught with wrong usage.

Percentage is one area I wish to mention in this post.

You may find that percentage or percent is a simple term in maths.

Besides being a ratio, it is a comparative element.

It tells how big the target is to the original, or how small it is.

Misconception of Percentage:

The numerator is always smaller than the denominator (which is the total).

Is it true?

A definite NO!


If a ratio has its numerator less than the denominator ==>  The numerator is relatively smaller in size than the total.

If the numerator is larger than the denominator ==> The numerator is bigger in size than the total.

An example can illustrate the concept.

If a costume is now priced at 90% of its original, $100, it means that the price is not only $90.
It is lesser than the original, since the ratio is 90 / 100 or 0.9.

If the costume is newly priced at 120% of its original, $100, it means that the price is now at $120!
A price value more than the original.
It is a practical real-life number.
  • Percentage can be more than 100%.
  • The numerator can be more than the denominator.
Understanding this concept will serve anyone good. Things in life goes up as well as down. Percentage reflects this sense through its number.

Interesting? You bet.

:)  Happy maths learning.

Wednesday, 26 August 2009

Usage of Percentage

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.

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

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.

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. 


Sunday, 23 August 2009

Average Explained

When you encounter the word "average", it means that all the items within the consideration has the same number.

When 3 tests has an average score of 80 marks. All the tests are 80, 80 and 80 marks each.

But nte that the three 80 marks each may not be true.
It is assumed to be to make the average correct.

The actual marks may differ from the 80 marks.

They may be 70, 80 and 90 actually, but their average is 80marks.

You may see the post on averaging if you need more information.


Friday, 21 August 2009

Sinc Function in Trigonometry

Trigonometrical graphs reveal many exciting properties of their functions.

One such function is the "Sinc" function.

This "Sinc" function is represented by the equation (sin x) / x.

NOTE: There is no typo error for the word "Sinc".

This special maths function is the trigonometric sine of an angle divided by that particular angle.

Looking at the graphs of various multiple of sinc functions, you will notice some unique properties in the cross-over angles (markings).

Looking closely at the multiples of radian pi, 2pi and 3pi, you will see that the amplitudes of the various sinc functions are zero.

This is a special characteristics of "Sinc" function.

If you sample these functions at interval of pi, you will get nothing or zero amplitude.

Interesting trigonometry, right?


Thursday, 6 August 2009

Character of A Person Revealed Through Maths

There are many ways to dig into the true character of a person.

One way is through maths.

By being in a classroom of maths learners, which I suppose everyone went through or is in one, you will notice many types of characters and behaviours.

Some are strong and stubborn, the never-say-die doer.
Some are the "can do, then do" type.
Some are the easy surrenders of maths.
Some cannot even be bordered to try!

Those who attempted the maths question, also revealed some weakness also.
The careless type and the long-winded type.

They made all sort of mistakes due poor handwriting or not reading the questions properly. They may miss a few variable or maths operators in an equation.
They may indirectly simplified the problems given through seeing or copying wrongly.

Those long-winded are the "better" lot with the will to stay on track.
They do and do, even when applying the wrong technique. They, however, do get the result through their hardworking attitude.

Some are the intelligent type who spot the trick just by reading the maths question.
They are the "flexible" ones.
They are the ones that seemed to enjoy most of the maths lessons.

Whatever, the type you are, maths is still an important life-long subject.
It is a practical module that serves us till we leave this world.

Love maths, and maths will love you, whatever your character and feeling towards maths.

Maths is interesting! You have a choice for that.



Sunday, 2 August 2009

Is Maths Really Interesting?

One question those who detest maths will ask is "Is maths really interesting?".

It is a very subjective question.

Everyone has likes and dislikes.

However, in the case of maths, it is the gain versus the lack.

Maths is a necessary life skill to have.

Knowing it makes a whole lot of different.

It will speed up your solving to some daily questions.

"What is the time needed if I drive at 60 km/h for a distance of 90km?"
"What is the area of the metal sheet needed to cover this pillar?"

We are weak in maths due to many reasons.
If you do not arrest these reasons, or reduces the obstacles to it, you will always fear maths.
This will create a mental block to your maths learning.

Practice and practice to reveal your weakness. Learn through mistakes.
You will feel the confidence of handling maths problems after that phase.

Like what Mark Twain said "Action speaks louder than words".

I would like to tweet it in the context of maths.

Instead of pure saying that you cannot do maths or you hate maths, practice (action) on it.
You will feel the difference.
You will get the hang of doing maths.
You will realise that maths is not that difficult.
You will find that it is your mindset that is the block, not maths!


Do it.

Practice speaks louder than words.

Maths is interesting.
That will be your final conclusion if you take action and do hands-on practice.

Cheers! :D