What Does "of" Means In Mathematics?

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Reading maths question is a critical skill to learn.

Without understanding the question, you will not be able to solve the challenge correctly.

A typical maths problem uses the word "of" to express ratio.

What really does this simple word means?

To an adult this is the understanding of English.
But to a kid, this is not English but a maths question!

What then is "of" in maths?

Answer:  It means MULTIPLY.

Examples:
half of the time ==>  0.5 x time

2/3 of the class ==> (2/3) x (class total)

If 40% of the apples are rotten, how many are left? ==> 0.4 x apples are rotten

Learn English well to handle maths.

This simple word "of" may make you happy or sad.
The choice is yours.

But remember, "Maths Is Interesting!".
So despair not, enjoy your maths.

Cheers  :-D

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Tricky Angles | Be Aware!

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Geometry in maths can means dealing with angles from a square or a rectangle.

Normally the question is to determine an unknown angle given some shape and angles.

However, mistakes can happen when basic knowledge of relationship between angles and  shapes are not proper understood.

Here, I will stress on the square and rectangular matters. This is basic but can pose a tricky problem to the unwarys. Poor thing.....

Let's look at the diagram below.

Here, if sides M and N are the same, that is, if the box is a square,  angle A will be 45 degree.

This is so since the corner where angle A lies is 90 degree divided EQUALLY by half due to the diagonal lines reaching to the opposite side. (symmetrical sides).

However, if the side M and N are not equal in length, then angle A WILL NOT be 45 degree. It will depends on the ratio of side M and N.

Note this message and unnecessary mistake can be avoided.

Sometime it is to test the logical thinkng through maths, by not telling you angle A is 45 degree but stating that the box is a square.

This type of maths problem will require you to calculate another angle but using angle A which is not given.

It is tricky but good to have. Your brain will be stretched to make it "flexible" for future use.

Maths is good in this sense as it twists our mind and makes our life interesting!

Work hard as well as smart.

For more examples on avoiding unnecessary mistakes, visit this time calculation post.

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Solving Maths Visually

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Maths is interesting!
There are many exciting concepts and techniques one can apply.
Read on ...

There are many ways to solve a maths question.
Normally it involves taking many steps with related sequence.

However, there are also simple ways to handle a maths problem.

One such solving method is simply through visual steps.
This has no working at all.

What do I mean?

Let's look at an example.

Example:
Determine the angle B from the diagram below. Angle A is 40 degree.

Solution:

Angle B is same as angle A = 40 degree.

There is no working at all. Just the visual determination.

Concept of this trigonometrical question in geometry:
When 2 straight lines cross and meet at an angle to each other, the angle opposite to any one is the same.

As such, angle C is also equal to angle D.

This is visual maths.

Interesting?

:-D

Math Challenge 18

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From the logarithm equation below, can you determine what is the expression for y?

 log y = x + log x

You may give your answer in the comment section and also help explain how you get it (for the sake of sharing).

Thanks ^^

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Time Mathematics | Tips On Avoiding Mistakes

Dealing with time and its calculation can be a bit tricky sometimes.

There are the hours, the minutes and the seconds to handle.

We can add or subtract them.
We do not operate in the hundreds, or ones, like any simple arithmetric.

We are calculating in terms of sixties.
1 hour = 60 minutes
1 minute = 60 seconds

Hence when given a maths question on subtracting two times, how do we go about to avoid mistakes?

Let's take an example to illustrate.

Question:
John start his journey to the market at 09:15am. If he arrived at the market at 10:05am, how long did he travelled?

Approach 1:
We can use the conventional method of carrying back 60 to the minutes, since the ending minute is smaller than the starting minute. And reducing the 10 to 9 (hour).
Next, we can then subtract with the new numbers.
That is 9:65 - 9:15 = 50 minutes.
This answer is fine.

Approach 2:
Change all the times to mintes.
10:05 ==> (10 x 60) + 5 = 605
09:15 ==> ( 9 x 60) + 15 = 555

Subtracting the two new numbers gives 50 minutes directly.
And that is the answer!

Remarks:
Comparing approach 1 with approach 2, you would notice that the latter seems to be simpler.

Why so?
This is because we have simplified the mixture of hours and minutes to only one dimension, that is, the minutes.
Thus, subtracting the newly created numbers involved only the minutes, avoiding the distraction of handling the hours.

To do maths, clear the mind of the unnecessary.

In the example above, we have removed the "hours" factor to focus purely on the "minutes".

Maths is interesting in that it is up to us to "play" with the techniques.
We can work with it or go against it.
The choice is up to us to select.

Hope you pick up some tips to make maths interesting.
Cheers!

:-D