Brain Exercise Through Mental Maths - Special Combination 2

Now let us take a look at 63 x 43.  What is special about this?  The left hand digits add up to 10 and the right hand digits are the same.

The was to do it is multiply the left hand digits and at the left hand digit to the answer.  This will be the two left and digits to the answer.  The right hand digits? Simply multiply the digits together.  Remember to add a 0 if the answer is a single digit.

In the above example:  Right hand digits = (6 x 4) + 3 = 27. 
                                      Left hand digits = 3 x 3 = 09

Thus the answer to 63 x 43 = 2709.

QED  (Quite Easily Done).

Brain Exercise Through Mental Maths - Special Combination 1

Some combinations of numbers are extremely easy to do.  For example, if someone asks you what is 63 x 67, you can say 4221 immediately.  Or  you can solve 32 x 38 instantaneously, which is 1216.

If you look at the two examples above, you will notice that the special combination goes like this: 1) the left hand digits for the numbers to be multiplied are the same, and 2) the right hand digits add up to 10.

And the answer is simply obtained by multiplying the left hand digit with (itself + 1) which gives you the left hand digits of the answer, and multiplying the two right hand digits which gives you the right hand digits of the answer.

Try it with the examples above, or any of the 45 possible special combinations.

You will simply be amazed.

Brain Exercise Through Mental Maths - Using Multiplying by 11 Method

By mastering the "multiplying by 11" method described in the previous article, you would be able to do whole lot more.  Multiplications like  76 x 66 can be solved easily.  You would be surprised to know that combinations like 33 x 33 or 44 x 44 are alot easier to do.  It is just a matter of looking at the numbers slightly differently.

For 76 x 66, you need to look at it as 76 x 6 x 11.  If you are already fast in multiplying with a single digit number, you will quickly get 76 x 6 = 456.  Applying the technique of multipying by 11, you then get 456 x 11 = 5016.

You think of 44 x 44 as 4 x 4 x 11 x 11 which simplifies things tremendously.  4 x 4 = 16,   16 x 11 = 176,  176 x 11 = 1936.

Now you are beginning to discover that many problems can be solved a whole lot easier just by looking at them differently.  This is applicable not only to mathematical problems but to the our everyday life as well.

Brain Exercise Through Mental Maths - Multiplying by 11

Using pen and paper, this would not be too difficult.  However, trying to do it in the head, you may find it hard to align the numbers as you do it on paper.

For a two-digit number, the idea is simply to add the 2 digits and place the answer in the middle. Example:  32 x 11  >   3 + 2 = 5 >  place 5 in the middle  >  352.

It gets a little more tricky if there is a carry-over from the sum.  Example:  67 x 11  >  6 + 7 = 13.  In such cases, you have to add 1 to the digit on the left and place the unit digit of the sum in the middle like before.  In the example, you add 1 to 6 and you place 3 in the middle, to arrive at the answer 763.

This method can be extended to any number of digits, by repeating the process of adding two adjacent digits starting from the left and placing the result next to the left digit.  Example:  123 x 11 >  1+ 2 = 3, 2 +3 = 5 > result = 1355.  With carry-overs, you add 1 to the number on the left as before.  Example: 678 x 11  >  6 + 7 = 13 >  add 1 to 6 to give 7 as the first digit of the answer and 3 as the 'interim' second digit,  >  7 + 8 = 15  > add 1 to the interim second digit (3) and that gives you 4 for the second digit and 5 as the next digit >  final answer = 7458.

The description may sound complicated, but as you do it yourself for different numbers, you will find that you will be able to arrive at the answer almost instantaneously.  The fact that you have to look ahead for carry-overs will exercise your brain to be more alert.  This 'look ahead' exercise will also prepare your brain for more exercises to come.

Now, you can exercise on your own.  Do try longer numbers.  As you do, you will come across combinations of numbers that force you to look two steps ahead.  Examples are given below:

456 x 11
637 x 11
2729 x 11

Next, we will explore more combinations of numbers using 'multiplying by 11' approach....

Brain Exercise Through Mental Maths - Multiplying by 99

One approach to multiply a number by 99 is to first multiply it by 100 (adding two zeros at the back) and then subtracting the the number from the result. For example:  45 x 99 = 4500 - 45 = 4455.

There is even a faster way - you can almost instantaneously provide the answer as soon as the number to be multiplied by 99 is given to you.  That is the beauty of this brain exercise. You will keep discovering different and perhaps faster ways to solve the same mathematical question.

Now, the faster method is simply to minus 1 from the given number which will give you the first two digits of the answer.  The last two digits are the result of 100 minus the given number.

In our example above, you are given 45. Immediately you say 44 while your brain does the 100 - 45, which is 55.  You will be amazed, and others will too, that you are able say the answer (4455) in a flash.

I taught this to a group of Year 6 primary school students.  They caught on it without any problem and began to show off to others immediately after the class.  Their interest in mathematics also increased significantly as I taught them more 'tricks' and they discover some themselves.

Be reminded that in this brain exercise program, we will be using only 2-digit numbers for the multiplication.  Of course when we get too good at it, we will explore 3-digit numbers as well.  But that is still long ways to go.

For now, happy exercising your brain and have fun!

Next: multiplying by 11.

Brain Exercise Using Mental Maths - Minus From 100

This is a simple exercise in preparation for more to come.  Pick a 2-digit number and quickly get the answer if you minus that number from 100.  Example:  pick 28, think 72;  pick  76, think 24.  Flick a page from a novel and take the last two digits, then think of the answer right away. If you can write a simple Excel program to generate 2-digit random numbers, you could do this exercise very effectively.  In no time you will be able to get the answer as soon as you see the number.

Next will be multiplying by 99...

Brain Exercise Using Mental Maths - Introduction

This is my first attempt at writing a blog.  This blog will be about exercising our brain using mental maths.  It is going to be fun as well as good for your brain.  Just for a teaser, you will be able to multiply a two digit number by 99 instantaneously.  I taught the method to a group of 12 year old students and within less than 10 minutes they mastered the method.  Eventually this brain exercise will lead you to discover new methods yourselves.  Let's first see the response to this blog....