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**n shortcut techniques series (you can read remaining lessons from here). This method is called as "Eka Nyunena Purvena**". That means "

**By one less than the previous one**". This method works if one of the given numbers consists of all 9s. Lets try to understand this method with an example.

####
**Example 1 : 68 x 99 = ?**

**Method 1 :**

- Put four blanks in the result

**Step 1 :**

- The number preceding 99 = 68
- Complement of 68 = 32
- Put this complement in the two blanks on RHS of the result

Present Status :

**Step 2 :**

- The number preceding 99 = 68
- A number that is less by 1 than the given number = 68-1 = 67
- Put this 67 in the two blanks on LHS of the result

So 68 x 99 = 6732

**Method 2 :**99 x 68 = ?

- One of the given numbers is 99. It is having all 9s
- The second number can be anything.
- Put both the numbers as shown above.
- Put 4 blanks for the result.
- Reduce the second number by 1. It becomes 67 (68-1). Put this 67 exactly below the number 99 as shown below.
- Subtract the digit 6 from the 9 above. 9-6 = 3
- Put this 3 in the blank that belongs to 1.'s place of the result
- Present Status :
- Subtract the digit 7 from the 9 above. 9 - 7 = 2
- Put this 2 in the blank that belongs to units place of the result

**Result**= 99x68 = 6732

**Lets see another example.**

####
**Example 2 : 53 x 99 = ?**

We shall solve this using the method 1.

**Step 1 :**

- The number preceding 99 = 53
- Complement of 53 = 47
- Put this complement in the two blanks on RHS of the result

**Step 2 :**

- The number preceding 99 = 53
- A number that is less by 1 than the given number is = 53-1 = 52
- Put this 52 in the two blanks on LHS of the result

So, the answer is 53 x 99 = 5247

**Note**: There are two 9s' in the multiplier 99 in the given examples. Other number that is being multiplied is also of two digits. Hence the result may be of maximum of four digits. Hence we use four blanks for the result.

If the numbers are of three digits each, and one of them is 999, then we have to have 6 blanks for the result.

#### Example 3 : 123 x 999 = ?

**Step 1 :**

- The number preceding 999 = 123
- Complement of 123 = 877
- Put this complement in the three blanks on RHS of the result

**Step 2 :**

- The number preceding 999 = 123
- A number that is less by 1 than the given number = 123-1 = 122
- Put this 122 in the three blanks on LHS of the result

#### Example 4 : 15064 x 99999 = ?

**Step 1 :**

- The number preceding 99999 = 15064
- Complement of 15064 = 84936
- Put this complement in the five blanks on RHS of the result

**Step 2 :**

- The number preceding 99999 = 15064
- A number that is less by 1 thank the given number = 15064-1 = 15063
- Put this 15063 in the five blanks on LHS of the result.

So, 15064 x 99999 = 1506384936

**Method 2 :**99999 x 15064 = ?

- One of the given numbers is 99999. It is having all 9's
- The second number can be anything.
- Put both the numbers as shown above.
- Put ten blanks for the result
- Reduce the second number by 1. It becomes 15063 (15064-1). Put this 15063 exactly below the number 99999 as shown below.
- Subtract each digit of 15063 from 99999
- 9-1 = 8
- 9-5 = 4
- 9-0 = 9
- 9-6 = 3
- 9-3 = 6

Put these digits in the remaining blanks (RHS of the result) from left to right

Result : 99999 x 15064 = 1506384936

That's all for now friends. In our next post we shall discuss another useful method of Vedic Maths. Happy Reading :)

**About The Author***is a gold medalist from Osmania University (Hyderabad), one of the working members of*

**Rupali Shete (M.Sc., M.Phil., Ph.D)****Rananujan Mathematics Academy**and

**Institute of Scientific Research on Vedas (ISERVE)**, Currently working in

**University of Pune.**

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Welcome back Rulapali madam. I am your fan. Your posts are really very helpful. Please post regularly. Thank you.

ReplyDeletevalid only for same number of digits on both parts.....if the number of digits are not equal result will be different

ReplyDeleteOfcourse, I clearly mentioned that in the post itself. There are various techniques for multiplication if the numbers are completely different. you will get them soon..

DeleteThank you so much! You guys are great!!

ReplyDeleteHello Rupali Madam,

ReplyDeleteThis post is very useful for me

but how to calculate complement of number ?

can u explain with example

thank you in advance

Hello Madam

ReplyDeletehow to calculate complement of number

can u explain with example

I'll post a detailed procedure about Finding Complements by tomorrow Amol.

DeleteAwesome..good job sir.

ReplyDeleteI expect more from you .

Please continuously apply more short cut tricks...

Friends you need to subtract d given numbers n add 1 to that, u will get d complement no.

ReplyDeletethanks a lot...

ReplyDeleteThank u mam for ur wonderful effort

ReplyDeleteevery thing is gud.......... bt sir I cant understand the complement number.. can u explain that alone........

ReplyDeletethank you,very useful.explain about complement

ReplyDeletethank you.i need detailed notes of complement.

ReplyDeleteYe to sise ho jayega 99999 ko 100000 man lo aur ab 15064 she multiple yoga 1506400000-15064=1506384936

ReplyDeletemam what will do if 68 multiply 999

ReplyDeletehow many blank position we take