Amazing Set of Fractions!

What if I tell you to form two fractions with sums equal to their products?

This is like think of two numbers: Add the two numbers and then multiply the two numbers.

The result should be the same!

Is there a way for you to find out how can this be?

Fortunately, there is a formula for this!

Let x be any whole number.

Then the two numbers (x) and (x/x-1) are the two numbers we are looking for!

Sample: Let x be 5.

Then the two numbers should be 5 and 5/4.

Both have a sum and product of 6.25!

Agree with me?

Multiplication Techniques: Part 2

Multiplying a two-digit number by itself starting with 5.

Sample: 54 x 54 = ?

First, multiply the last digit: 4 x 4 = 16. This will be the last two digits of the answer.

Second, multiply the other digit by itself: 5x5 = 25

Now add the last digit to the product in Step 2. This will give you ->

25 + 4 = 29. This will be the first two-digits of the answer!

Presto! The answer is 2916. Got it?

Another example: 59 x 59? Did you see how did you arrive at 3,481?

Tickle IQ Test

I visited one of the IQ tests over the internet last January 18, 2008.

I was surprised that I got an IQ of 120 with Intellectual Type of the mathematician Pythagoras.

Attached is the report of my answers vs. the correct answers to the questions. IQ Report.

Before you view the report, take a shot and know your IQ too.

Exercise your mind.

Hardest Logical IQ Problem

They say that logic problems is the best way to measure one's IQ because these kinds of problems do not take into consideration your background. Although, it certainly helps having a degree in analysis subjects such as mathematics, engineering, finance, accounting, etc.

This is so far the hardest logic IQ problem that I encountered. They say that when you solved this IQ Problem, you'll belong to the top 2% of the world's most intelligent people. It was called Einstein Quiz!

Modesty aside, I was able to solve this problem in around 1 hour of hard thinking.

Luckily, with just one try I got the answer correctly!

Try it for yourself too!

Here's the file!

Multiplication Techniques

Let me share to you multiplication techniques.

This involves a two-digit number!

1. How to multiply any two-digit number by 11?


Example: What is 23 x 11? 41 x 11? What about 97 x 11?

You want to know the technique?

Very Simple!

Just add the digits and insert the sum in the middle!

Very simple right?

Here's how it works...

23 x 11 => 2 + 3 = 5

Insert 5 in the middle of 2 and 3 so it will become -> 253!

What about 41 x 11?

41 x 11 => 4 + 1 = 5

Insert 5 in the middle of 4 and 5 so it will become -> 451!

Got it?

There's one problem....

How about if the sum exceeds 10? Just in the case of 97 x 11?

Simple... 9 + 7 = 16

So how can you insert 16 in the middle of 9 and 7?

Simple...

Insert 6 and 1 should be carried over to 9 just like addition...

So the last two digits of the answer is 67...

What happened to the 1 from the sum 16?

Add it to 9.

So then, 9+1 = 10

So there 10 is the first two digit of the answer!

And the last two digit is 67 as stated above...

So the answer is 1067!!!!

Isn't it amazing?


2. How to multiply any two-digit number ending in 5 by itself?

Sample: What is 25 x 25?

What about 95 x 95?

Simple...

Take the first digit of the number....

In the first example, that would be 2.

Add 1 to it. 2 + 1 = 3

And the multiply it to the original digit.

That would be 3 x 2 = 6

Lastly, affixed 25 as the last two-digits

Presto!

Answer is 625!!!


So can you now decipher how 95 x 95 became 9,025?

Isn't it amazing?

Simple Logic Problem

OOPPPSSS.... Don't scroll down too much!!!


What is:

(a-x) (b-x) (c-x) (d-x) ... (z-x) = ????

Please note that parentheses indicates multiplication.

Come on use your intuition!

Guess it first and before you view the answer below...



















KEPT THINKING????















ANSWER IS ZERO!!!!

WHY?





Beacause there will come a time for (x-x) which is of course ZERO.
And any number multiplied by zero is ZERO!!!


Isn't it amazing?

Magic Squares

One of the things that fascinated me was the so-called Magic Squares.

I did a self-study on this. Magic Squares are a set of numbers 1 to n squared, without repetition, that were placed in an n by n grid of square such that the sum of all the columns, rows, and diagonals were all the same and equivalent to a single number.

Please refer to this post to my other blog:

Fascinating Magic Squares

The Sum of 'N' Consecutive Numbers

How do you add:

1+ 2 + 3+ 4+ 5+ ... +100?

1+ 2+ 3+ 4+ 5+ ... + 1000?

You want a technique?

You might be smarter than a calculator!

Why not try this formula?

= n(n+1)/ 2

And so,

1+ 2 + 3+ 4+ 5+ ... +100 = 100(100+1)/2 = 5,050

1+ 2+ 3+ 4+ 5+ ... + 1000 = 1,000 (1,000+1)/2 = 500,500

1+ 2+ 3+ 4+ 5+ ... + 78 = 78 (78+1)/2 = 3,081

Isn't it math amazing?

Math Olympian

Math is always the hardest subject for a lot of persons.

But during my study of the different fields of Mathematics during my college years, I would say that Mathematics is the Queen of All Sciences.

You have Math in your everyday life. Be it in school, work and day to day living. Everyday, you have numbers.

I was one of the competitors of different math competitions during my active years in high school. This began during my second year high school.

I was included in the Saturday trainings of Mathematics Teachers Association of the Philippines or MTAP. We used to train at Stella Marris College in Cubao Quezon City from 9am to 12 noon.

We tackle math topics in advance. We have different modules. And in these modules, there are different questions. Classified as easy to challenging questions.

I used to compete in MTAP from 2nd year to 4th year high school. We were classified into division of schools according to locations. We were included in the PAMARISAN division. These are schools located at Pasig, Marikina, and San Juan. At the end of the traning, we have a 1 hour math questions of 50 items. It was during my 4th year high school when I achieved the highest rank which was top 4 in our school. Unfortunately, the top 3 ranks only have the chance to represent our school to compete in the regional finals.

Aside from MTAP, I was also chosen to compete in the Philippine Math Olympiad or PMO during my third year. Unfortunately, PMO is harder than MTAP and so no one from us entered into the regional finals.

Last competition that I joined was the SIPNAYAN during my 4th year high school. This was a math contest sponsored my the Ateneo Mathematical Society, an organization for math enthusiasts in Ateneo de Manila University.

There are a lot of schools that we consistently see during the competitions. These are Grace Christian High School, Chiang Kai Shek, UNO High School, Philippine Science High School, among others.

I miss those days. I miss the excitement and the thrill especially as we near the competition.