How fast would you able to calculate 105 X 104, without pen or paper or a calculator?

Let me demonstrate a method to compute the answer in your brain in less than 10 seconds!

If you are proficient with using a base number to calculate your squares or simple multiplications, this, then, is a breeze. First off, use 100 as your base number.

Simply add the deviations (either one) and .... multiply them (the deviations)!

105 X 104 = [104 + 5].[4 X5]

= [109].[20]

= 10920 #

Try it with other numbers nearer to 100 (either less or more). What do you think? With my own karat old brain, I can compute the answers in 5 seconds or less. Test yourself.

## Friday, February 29, 2008

## Thursday, February 28, 2008

### Donate Rice! Play and Feed the Hungry!

## Sunday, February 24, 2008

### Check with SPR.GOV quick, please people!

Please check the Election Commission's website for your polling stations and all the relevant channel and serial numbers. Write it down somewhere, if you can't print the data out. Check the location on a map and plan to be there early. I can't believe that this is my third time voting in this constituency!

I checked mine, which surprisingly, even came with a picture ;-)

I checked mine, which surprisingly, even came with a picture ;-)

## Monday, February 18, 2008

### Speed is the Key!

Lets look at the multiplications of 9 (that special number!) :

If you look closely, the product of the multiplication seem to follow a simple pattern. And if you are familiar with the concept of "Digital Sum", you will also notice something else. What?

First of all, if you look at the first result, (I have deliberately written it as 09 rather than just 9), you will notice that the Digital Sum of the the result is also 9. This is the same for all the multiplications of nine. So this is our first clue.

Secondly, when 9 is multiplied by a number (up to 10, in the first set), the result then starts with a number that is one less. Say for instance, 9 X 6, the result must start with a number one less than 6, which is 5. And since we know that the Digital Sum of the result must be also 9, so the second number must be....4, of course! So the answer is simply 54.

Simple isn't it?

Expanding if further, notice that any product of multiplications of 9 has a Digital Sum of 9: e.g.:

108 X 9 = 972

972 --> 9+7+2 --> 18 --> 1+8 --> 9!

9 X 1 = 09

9 X 2 = 18

9 X 3 = 27

9 X 4 = 36

9 X 5 = 45

9 X 6 = 54

9 X 7 = 63

9 X 8 = 72

9 X 9 = 81

9 X 10 = 90

9 X 2 = 18

9 X 3 = 27

9 X 4 = 36

9 X 5 = 45

9 X 6 = 54

9 X 7 = 63

9 X 8 = 72

9 X 9 = 81

9 X 10 = 90

If you look closely, the product of the multiplication seem to follow a simple pattern. And if you are familiar with the concept of "Digital Sum", you will also notice something else. What?

First of all, if you look at the first result, (I have deliberately written it as 09 rather than just 9), you will notice that the Digital Sum of the the result is also 9. This is the same for all the multiplications of nine. So this is our first clue.

Secondly, when 9 is multiplied by a number (up to 10, in the first set), the result then starts with a number that is one less. Say for instance, 9 X 6, the result must start with a number one less than 6, which is 5. And since we know that the Digital Sum of the result must be also 9, so the second number must be....4, of course! So the answer is simply 54.

Simple isn't it?

Expanding if further, notice that any product of multiplications of 9 has a Digital Sum of 9: e.g.:

108 X 9 = 972

972 --> 9+7+2 --> 18 --> 1+8 --> 9!

## Saturday, February 9, 2008

### Speed and Power: Multiplying Numbers with the Same Ending...

**Jagadguru Swami Sri Bhārati Kŗşņa Tīrthaji Mahāraja**showed through Nikhilam Navatascaram Dasatah that you can instantly multiply numbers using a base number. Lets say we are trying to multiply 18 X 13. Here if we use 10 as our base, and we find the deviation of the numbers from the base, the rest is so easy to calculate.

18 : deviation from base = 8

13 : deviation from base = 3

Now, we cross-add one of the deviations to the number, for instance, 18 + 3. Either way we get 21. That will be our left most number. Now we multiply the deviations, 8 X 3, to get 24. Now since we are using base 10, we leave 4 (from the 24) as the right most number and carry the 2 to the left most number, which is 21. So we get [21 + 2].[4] = 234!

This is explained quite thoroughly in other websites and posts, especially here.

But if that intrigued your interest, how about if we try something else? Lets say we have two numbers, both end with the same number, lets say 23 and 13.

If we want to quickly (and mentally) multiply the numbers, just do this 3 step process:

1. Square the ending number to get the the right-most number of the answer: in this case its 9

2. Add the two first numbers together, (2 + 1) and multiply it with the ending number (3): in this case its 3 X 3. This gives us the middle number, which is 9.

3. To get the left-most number, just multiply the first numbers together, in this case (2 X 1), to get 2.

So, the answer is 299.

Lets try that with a bigger number, lets say (212 X 312). In this case the common ending number is not 2 but 12! So to get the right-most number, we just square the ending number, which is 12 to get 144. But since the ending number is based on ten, we leave 44 as the right-most number of the answer and carry the 1 to add to the middle.

The middle number is simply (2+3) X 12, which is 60. Add the 1 from the carry we just did, and you get 61, which is the middle number.

The left most number is simply (2X3) = 6.

So the answer is: 66144.

Since the idea is to keep the multiplication as simple as possible, this technique can cut your calculation time considerably and even save on paper! I can do this similar calculations in less than 10 seconds, and I would think younger students can do it in less.

What do you think? Email me.

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