A gentle start..

Let me talk about two pretty basic things today.These things may not have a lot of direct applications but you will find them useful if you begin using them regularly.In my experience,they have helped me a lot in doing my calculations faster and hopefully they will help you guys too.Here it goes-

a)The average of two numbers-

This trick will help you calculate the average of two numbers in a different way from just adding them and dividing them by 2.I will show you the application after I highlight the funda.Lets say we have two numbers a and b.We can find their average by-

1-Subtract the smaller number from the larger one

2-Divide the difference by 2.

3-We get the average by either adding the answer obtained in 2 to the smaller number or subtracting the same from the larger number.

For example-I have two numbers 4 and 8.I subtract 4 from 8 to get 4.I divide 4 by 2 to get 2.And I add 2 to 4 or subtract 2 from 8 to get the average as 6.

Application-Now this seems pretty weird right?I mean its basically increase of a step from the general method.But the application comes in when you look to calculate the average of 2 numbers which are easier to subtract than add.

Case in point-999 and 1999.The difference is 1000.I get 500 when I divide it by 2.And when I add it to 999 or subtract it from 1999 I get the average which is 1499.

Believe me once you start using this frequently you will become so comfortable with it that you will use it subconsciously.

Note-This can only be used to find the average of 2 numbers.

b)Digital Sum

First of all let me explain what digital sum is.It is as the name specifies the sum of all the digits of a number until you have just a single number.

For example-The digital sum of 887 is 5(8+8+7=23;2+3=5)

Now that you know what digital sum is the point I want to make is-

Funda-The sum of the digital sum of 2 numbers is the digital sum of the sum of the same 2 numbers.

Confused?Read it again and understand it.

Example-What is the sum of the digital sums of 23 and 45?

Now either you can calculate the digital sums of 23 and 45 separately(5 and 9 respectively) and add the two.This gives the answer as 5(5+9=14;1+4=5)

Or you could add the two numbers which will give you 68.The digital sum of 68 is also 5(6+8=14;1+4=5)

Additional note-For any number with any number of 9s and a few other digits,the digital sum can be calculated by ignoring the 9s.

That is to calculate the digital sum of 9698 I just need to add 6 and 8 to get the digital sum as 5.You can add all the 4 numbers and you will get the same answer.Try it..9+6+9+8=32 which also gives the digital sum as 5.

That is all for today.I will be coming out with more advanced concepts in further posts.Hope you all enjoyed reading the 2 fundae for today and that you come back for more.