## Division by 9…

As we read earlier, 9 is a magic number.

And there must be something unique when we divide any number by 9. We are going to learn a method with which we can easily and quickly find the quotient and remainder in one line.

Let’s learn this with few examples. Example 1 and Example 2 covers simple examples and Example 3 covers special case where there are carries while finding the answers.

To find remainder:

Step 1: Find the digit sum of all digits of dividend. Digit Sum.

Remainder is this digit sum.

To find quotient : We move from left to right.

Step 1: The left most digit of quotient is the leftmost digit of dividend itself.

Step 2: The next right digit of quotient is the sum of above number in step 1 and 2nd next digit in dividend.

Repeat this pattern till you reach rightmost digit in dividend. The rightmost digit in dividend is not part of this pattern.

Example 1:

Example 2:

Example 3: Special Case – When there are carries:

This method can be extended to any length of number divided by 9.

Let us practice with more examples:

Divide the following by 9:

## Thought of the Day

Humanity is Not Physics!

Every Action has a Reaction, Equal and Opposite?

For me, it was never the case;

Experience showed many, diferent reactions!!

## Happy New Year 2021

Dear All,

Year 2020 was tough for all of human kind. We fought well with many new challenges and adversaries.

From today, new year has started. Some of the challenges remain same, some has become tougher than earlier and some are no more existent.

Let us pledge to do better than last year and bring more value to our life and people around us.

## Square Roots of Perfect Squares

Finding Square Roots in the traditional way, i.e. by long division method is quite time-consuming.

However, there is a much simpler and faster method of finding square roots of a perfect square. In Vedic Maths, we use Sutra “The First by the First and the Last by the Last“.

A perfect square is an integer that is the square of another integer. For example, 1024 is a perfect square of 32. Here, 1024 and 32 both are integers.

Square of 32 or 32 ^2 = 1024.

So, the square root of 1024 or √1024 is 32.

Let’s understand the method to find square root of any perfect square with this example.

√1024 = 32

Step 1: We have to mark the digits in the number in pairs starting from the right, i.e. 24 as one pair, 10 as another pair in 1024.

The leftmost pair gives the left-most digit of the answer.

The rightmost pair give the right-most digit of the answer.

Step 2: Find the leftmost part of the answer.

Consider the leftmost pair first, i.e. 10 in this case is the leftmost pair.

The largest number whose square is less than 10 is 3 (3^2 = 9).

So, the leftmost digit of the answer is 3.

Step 3: Find the rightmost part of the answer.

Consider the rightmost pair, i.e. 24 in this case is the rightmost pair.

Since the number 1024 ends in 4, so the last digit in the answer will be either 2 or 8 (as only square of 2 (= 4) or square of (8 = 64) ends in 4).

How to chose whether 2 or 8 is the last digit?

From Step 2, find the remainder of 10 – 9 (= 1). As 1 is less than 3 (obtained from step 2), the last digit will be 2.

Had the above remainder been greater than 3, then the last digit would have been 8.

Let’s understand this from below graphical representation: Take another example:

√2209 = 47 ## Multiplication with Special Numbers

I have added a new page to my website: Multiplication with Special Numbers

This is a special method of multiplication, that gives the answer in one line and mentally too.

Why not read this and surprise your friends with real fast calculations!!

## Using the Average to Multiply

I have added a new page to my website: Using the Average to Multiply

This is a special method of multiplication, that gives the answer in one line and mentally too.

Why not read this and surprise your friends with real fast calculations!!

## Multiply by 99, 999, etc.

I have added a new page to my website: Multiply by 99, 999, etc.

This is a special method of multiplication, that gives the answer in one line and mentally too.

Why not read this and surprise your friends with real fast calculations!!