Multiplication of any number with n digits of 9 in three seconds!!!

Multiplication with 9 is always fun. In Vedic Maths, we can solve Multiplication of any number with ‘n’ digits of 9 within few seconds with simple addition and subtraction.

When two numbers are multiplied, one is called Multiplicand and other one is called Multiplier.  For example, consider 11 x 99. In this 11 is Multiplicand and 99 is Multiplier. It can be in the other way also. Let us take it in a former way.

Based on the number of digits in Multiplicand and Multiplier, we have three cases.

Case 1: Number of digits in Multiplicand  = Number of digits in Multiplier (eg 44  x 99 or 234 x 999)

Steps to Follow:

1) Subtract 1 from the Multiplicand.

2) Write the Complement of Multiplicand. (All from 9 and the last from 10)

Example 1:

55 x 99 = ?

Step 1 – (55-1) = 54.

Step 2 – (Complement of 55) = 45.

Answer is 5445.

Example 2:

459 x 999 = ?

Step 1 – (459-1) = 458

Step 2 – (Complement of 459) = 541

Answer is 458541

Example 3:

what is 347868 x 999999?

Step 1 – (347868-1) = 347867

Step 2 – (Complement of 347868) = 652132

Answer is 347867652132

Exercises:

1. 33 x 99    2. 83 x 99    3. 424 x 999    4. 5251 x 9999    5. 213456 x 999999

Case 2 – Number of digits in Multiplicand is Less than the Number of digits in Multiplier (eg 43 x 999 0r 286 x 9999).

In case two, we follow the same steps as case one with a slight modification, which is adding ‘0’ or ‘0s’ before the Multiplicand and making sure that the number digits are same on Multiplicand and Multiplier.

Example 1 :

What is 88 x 999?

In this problem 88 is a two digit number. 999 is a three digit number.

Step 1 – To make the number of digits same, we change 88 to 088. So it becomes 088 x 999.

Now follow the same steps as case 1.

Step 2 – (088-1) = 087

Step 3 – (Complement of 088) = 912 (All from Nine and the last from Ten)

Answer is 87912.

Example 2:

What is 756 x 99999?

Step 1 – 00756 x 99999

Step 2 – (00756-1) = 00755

Step 3 – (Complement of 00756) = 99244

Answer is 75599244

Example 3:

What is 38637597 x 9999999999

Step 1 – 0038637597 x 9999999999

Step 2 – (0038637597-1) = 0038637596

Step 3 – (Complement of 0038637597) = 9961362403

Answer is 386375969961362403.

Exercises:

1. 34 x 999    2. 567 x 9999    3. 324 x 99999    4. 123 x 99999    5. 234852 x 99999999

Case 3 – Number of Digits in Multiplicand is Greater than the Number of digits in Multiplier (eg 892 x 99 or 2876 x 999)

In this case we follow 3 steps.

First step is dividing the Multiplicand into two parts (LHS and RHS) in such a way that the number of digits in RHS of Multiplicand should be equal to Number of digits in Multiplier.

For example, consider 597 x 99.

First step is dividing the Multiplicand into two parts. 5 / 97 x 99. LHS is 5 and RHS is 97. Now the number of digits of the RHS of the Multiplicand is equal to the Number of digits in Multiplier.

Second Step is Adding 1 to the LHS of the Multiplicand. And Subtracting the obtained number from the Multiplicand. LHS of the Multiplicand is 5. By adding 1 to it, we get 6. Now subtract 6 from 597. We will get 591.

Third Step is to write the complement of RHS of Multiplicand. Complement of 97 is 03.

The Answer is 59103.

Example 1: 

What is 353 x 99?

Step 1 – 3 / 53 x 99. (LHS is 3 and RHS is 53)

Step 2 – Adding 1 to LHS – (3 + 1) = 4. Subtracting the obtained number from Multiplicand – (353 – 4) = 349.

Step 3 – Complement of (53) = 47.

Answer is 34947.

Example 2:

What is 7349 x 99?

Step 1 – 73 / 49 x 99. (LHS is 73. RHS is 49) (Number of digits of RHS should be equal to Number of Nine’s in the Multiplier)

Step 2 – (73 + 1) = 74. Then (7349 – 74) = 7275.

Step 3 – Complement of 49 = 51.

Answer is 727551

Example 3:

What is 58036 x 999?

Step 1 – 58 / 036 x 999.

Step 2 – (58 + 1) = 59. (58036 – 59) = 57977.

Step 3 – (Complement of 036) = 964.

Answer is 57977964

Exercises: 

1. 333 x 99    2. 432 x 99    3. 19898 x 999    4. 3923 x 99    5. 43567 x 999