Multiplication of numbers near 100, 1000, 10000 and so on.

We always find difficulty in multiplying big numbers… Here is a trick to cover few of them, mainly the ones which are near to 100, 1000, 10000 and so on…

When we need to calculate 98 X 97, we rush to find calculator while after reading and practicing this, you will be able to answer immediately (within 10 seconds only)… Looks like I’m kidding… Try it once…


Methodology to multiply numbers

Step 1: Choose the base (100, 1000, 10000), nearest to both the numbers.

Step 2:
Case I: Subtract both the numbers from the base individually (with negative sign), if these are less than base

Case II: Subtract the base from the numbers (with positive sign), if these are more than base.

Step 3: To find first two digits:
Case I: Subtract the sum of numbers (found in Step 2) from the base.
Case II: Add the sum of numbers (found in Step 2) in the base.

Step 4: To find first last two digits, multiply the numbers (found in Step 2).



Let’s try it for 98 X 97.

Step 1: We know that in this particular case, both the numbers are near to 100, so we can take 100 as base.

Step 2: This is the example of case I. Now, subtract both the numbers from 100

9 8       - 2
9 7       - 3
-----------------

Step 3: To find first two digits, add 2 & 3 and subtract from the base (100) and result will be 9 5

1 0 0 – ( 2 + 3 ) = 9 5

Step 4: To find last two digits, multiply 2 by 3 i.e., ‘06’

9 8       - 2
9 7       - 3
-----------------
9 5       0 6
-----------------
Hence, 9 8 X 9 7 = 9 5 0 6


Another example:

999 X 995

Base – 1000

9 9 9    - 1
9 9 5    - 5
-----------------
9 9 4    0 0 5
-----------------

That’s the trick!!! One more example, this time example of Case II

1012 X 1008

Base – 1000

1 0 1 2             + 1 2
1 0 0 8             + 0 8
---------------------------
1 0 2 0              0 9 6
---------------------------

Here is an example of mixture of both the cases

1013 X 997

Base – 1000

1 0 1 3             + 1 3
0 9 9 7             -  0 3
-----------------------------
1 0 1 0             - 0 3 9
-----------------------------
1 0 0 9              9 6 1
-----------------------------

Square of numbers ending 5

Here is an example of square of two / three digit numbers ending 5.

We know,

(15)² = 15 X 15 = 225  

(25)² = 25 X 25 = 625

(35)² = 35 X 35 = 1225

and so on…

We might calculate it without calculator for the first two (15 & 25) but what about when number at ten’s place increases. Difficulty starts increasing… Right…

No Worries… Very basic rule, you need to remember…

Rule:

Take first digits (excluding 5) as ‘n’ and multiply it with ‘n+1’ and suffix ‘25’ to the result.



That’s it!!! Is it so simple??? Yeah… Wanna try… Go ahead…

(1 5)² = 1 X (1+1) / ‘25’ = 225

(2 5)² = 2 X (2+1) / ‘25’ = 625

(3 5)² = 3 X (3+1) / ‘25’ = 1225

……………………………………


(7 5)² = 7 X (7+1) / ‘25’ = 5625

(9 5)² = 9 X (9+1) / ‘25’ = 9025

(10 5)² = 10 X (10+1) / ‘25’ = 11025

(12 5)² = 12 X (12+1) / ‘25’ = 15625

(19 5)² = 19 X (19+1) / ‘25’ = 38025

Try it with your calculator… You will find it correct every time…