Urdhva Tiryagbhyam

Feeling lengthy to use the multiplication technique taught at school....??

Now  we will discuss a method which is very powerful technique that can be use to multiply any n-digit number with any other n-digit number..

First let us understand this technique with the below figure.

From the above figure we can understand how the multiplication is performed using Urdhva Technique.

Step 1:    Initially the number in the unit’s digit is multiplied i.e. vertical multiplication.

Step 2:   The number in the unit’s digit of one number is multiplied with the tens digit of other  number in the criss crosses way.

Step 3:   The number in the unit’s digit is multiplied with the number in the hundreds digit in a  criss crosses way and the number in the tens digits are multiplied in a vertical way.

Step 4:   The number in the tens digit of a number is multiplied with hundreds digit of other    number in a criss cross way.

Step 5:   The number in the hundreds digit are multiplied i.e. vertical multiplication is carried      out.

Now let us take two three digit decimal numbers and understand the Urdhva technique in a better way. Let the first number be 123 and the second number be 456.

           Explaining of Urdhava Thiryagbhyam sutra with an example showing of  3-bit  numbers

Step 1:   Initially the unit’s digit numbers are multiplied and the unit’s digit of the                     

              product i.e. 8 is kept as the unit’s digit of the result, the carry 1 is kept aside.

Step 2:  The unit’s digit of the first number is multiplied with the tens digit of the second number and vice versa and both the products i.e. 12, 15 are added with the carry i.e. 1 which we attained in the step1. Now the units digit of the total sum i.e.8 is kept as the tens digit of the result and the carry i.e. 2 is kept aside.

Step 3:  The number in the unit’s digit of first number is multiplied with the number in the hundreds digit of second number and vice versa, the number in the tens digit are also multiplied. Now the sums of all the products i.e. 6, 12, 10 are added with the carry i.e. 2 which we attained in the step2. Now the units digit of the total sum i.e. 0 is kept as the hundreds digit of the result and the carry i.e. 3 is kept aside.

Step 4:  The number in the tens digit of first number is multiplied with the number in the hundreds digit of second number and vice versa and the products i.e. 5, 8 are added with the carry i.e. 3 which we attained in the step3. Now the unit’s digit of the total sum i.e. 6 is kept as the thousands digit and the carry i.e. 1 is kept aside.

Step 5:   The number in the hundreds digit of both the numbers are multiplied and the product i.e. 4 is added with the carry i.e. 1 attained in the step4. Now the result of the sum i.e. 5 is kept in the ten thousands digit.

Thus the product of the two numbers 123 and 456 is 56088.

This technique can be generalized even for N*N multiplication.

Multiplication of numbers under 10

Hard to remember the tables or multiplying numbers???

The methods we teach are not only fun to use, they are easy to learn. How happy would you feel if tell you that you can master tables under 10 within 15 minutes? Well here is a simple technique of doing that.

Lets take an example of multiplying 7 and 8

Step 1:

First write down the numbers to multiply and draw a circle under each of them.

 

Step 2:

First write down the numbers to multiply and draw a circle under each of them. Now go to the first number and see how much more is to be added so as the sum becomes 10 i.e 3 should be added to 7 to make 10. Therefore, write down 3 in the circle below 7. Similarly write down 2 in the circle below 8 so that the sum is equal to 10.

Step 3:

We now take away either one of the circled numbers (3 or 2) away from the number, not directly above, but diagonally above. Here, you either take 3 from 8 or 2 from 7. Either way, the resultant is the same, 5. This is the first digit in your answer.

*Tip: As you do this only once, choose the subtraction that is easy

Now you multiply the numbers in the circles. 3 times 2 is 6. This is the last digit of your answer. Therefore, the answer is 56. This is how the completed sum looks.

This method can be used for multiplying any numbers under 10.

What if the numbers I choose are greater than 10. What do I do? Does this method work?

It certainly does. But with a little modification. My next post will be on that !

Squaring the number ending with 5

Hard to remember the squares of the numbers????

A simple technique which helps you to need not remember the square of the number ending with 5 will be explained here...

Let me explain this technique with a simple example..

let us find the square of a number 35

1. First the square of the 5 is written in the units digit and tens digit viz. 25
2. Now multiply the number 3 with (3+1) i.e we need to find 3*(3+1) and write the result before 25 and we get the result as 1225

Now let us generalize this 
     If the number is of the form 'a5' and we need to find the square of that number then the result will be a(a+1)25

This method can also be extended to multiply two numbers whose sum of the unit's digit will be 10 and the remaining digit are same.
If the two numbers are 'ab' and 'ac' where b+c=10 then
Units and tens digit will be the units and tens digit of the product b*c and the remaining digits will be the product of a(a+1)

Let us understand this with an example..

Product of 13 and 17

As stated from the above technique

• The units and tens digit will be the product of 7 and 3 i.e 7*3=21
• The remaining digits will be the product of  1(1+1)=02
• Thus the product of 13 and 17 is 0221

Finger Multiplication

Want to remember 9 table very easily?

If yes then here is the method which will make you remember 9 table very easily... :)

Free your mind and pay attention to this simple method.

1. Open all the fingers of  both of your hands and number it from left to right.
2. Now the number on the finger acts as the number to be multiplied with 9. 
3. Suppose if you want to know the product of 9 with 4
4. Firstly you have to close your fourth finger.
5. Now see the number of fingers open to the right of the closed finger which will be the units digit of the product and the number of fingers open to the left of the closed finger will be the tens digit of the product.
6. According to this method we get the units digit as 6 and the tens digit as 3 and thus the product is 36.

By knowing this method 9 table will be at your finger tips...

NOTE:  The multiplication of 9 is possible only up to 10.