Time Calculation May Not Be Easy

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Counting from 1 to 100 is normal for anyone. Just increment by 1. It's that simple.

But counting time may be another story for young math students.

Why is this so?

There is the seconds, the mintes, and the hours to handle. They differ by the umber 60.

The "carry over" through addition is the number SIX!

1 min 30 sec added by 40 sec gives .......

1 min 70 sec?

Here the 70 sec includes 60 sec + 10 sec. You need to understand that for time, 60 sec means one whole minute.
Thus, 70 sec = 60 sec + 10 sec ===> 70 sec = 1 min + 10 sec.

Therefore, 1 min 30 sec add 40 sec gives ==> 2 min 10 sec.

Compare this to adding 30 by 40. Answer = 70. No more analysis.

Time base on 1 hour = 60 min, 1 min = 60 sec concept.

To test true understanding of addition (and subtraction), time is a good gauge and tool to assess learners.

Test it on young kids today to annoy them... *#^&@!
Cheers!

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Negative Value Equated to Exponential Expression

This is a very interesting maths question, that may trick many students.

2^x = -1

What is the value for x?

I got all sort of answers.
Some gave me x = 0 (knowing that 1 = anything to the power of 0).
Some treat the expression to be 2x = -1 ==> x = -1/2.
Some used the calculator, applying "logarithm" operation and getting an "Error" message!

Those who know the answer, congratulation. You can stop reading this post.

For those interested and wanting to know what's the answer, read on...

Knowing the answer, is fine here. But knowing with understanding is better.

Now, let's put some numerical values of x into the expression.

If we choose x = +3, y = 2³ = 8 ( a positive number).
If we choose x = -3, y = 2^-3 = 1/8 ( a positive number).
If we choose x = 0, y = 1 (again a positive number).

Conclusion: All the x values substituted will get us positive number instead of the desired negative number.

Then how do we get a NEGATIVE number from the exponential expression?

The answer is:
WE can NEVER get a valid numerical value for x for expression in the form a^x or equivalent when it is equated to a negative value.

Clear?
Do not fall into this mathematical trap. You will not look good, if you can solve it!

Have fun testing your classmate.

:-)

Logical Solution in Maths

Maths can be solved in many ways, as one learning it knows.

There are the conventional techniques or methods type of solving.
You follow all the rules and laws, applying them diligently to solve the problem.
It is OK, not wrong.

However, sometimes by looking at the problem, you can twist a bit and deviate to use the "logical" method to short-cut the solving.

What do I mean?

Let's look at an example.

(This method of logical thinking is applied, especailly, in solving Partial Fraction.)

5 = A(x - 1) + B (x + 2)

Find A and B.

Conventional method ==> maybe simultaneous way.
Logical mehtod.....

Let x = 1, to eliminate the unknown A, and keeping the other unknown B.
5 = A(1 -1) + B (1 + 2)
==> 5 = 0 + 3B
==> B = 5 / 3 Get it?

Now to figure out getting A.
Let x = -2, to get rid of B.
5 = A(-2-1) + B(-2 + 2)
==> 5 = (-3) A + 0
==> A = - 5/3.

Finish. Short and sharp, and easy.

This is when you apply the logical part to maths solving.

Simple trick, right? Maths is Interesting. Don't forget this.
:-)