Dhaval Bathia This is one of the fastest

This is one of the fastest techniques of multiplication… Helps you get the answer of any multiplication problem in just one line ! We will begin with multiplication of twodigit numbers © Dhaval Bathia

We will use the 3 steps that are given below: A) * B) * C) * * D)C) * * E) * * © Dhaval Bathia

Let us suppose we want to multiply: 2 3 x 1 2 © Dhaval Bathia

We follow step (A) as seen before: A) * B) * 2 3 * * X 1 2 6 We get the answer as (3 x 2) equals 6. © Dhaval Bathia

We follow step (B) as seen before: B) * * 2 3 X 1 2 7 6 We cross-multiply and add. (2 x 2) + (1 x 3) is 7. © Dhaval Bathia

We follow step (C) as seen before: A) * B) * * 2 3 * 1 2 2 7 6 X We get the answer as (2 x 1) equals 2. The final answer is 276 © Dhaval Bathia

Another example… Let us suppose we want to multiply: 3 4 x 1 1 © Dhaval Bathia

We follow step (A) as seen before: A) * B) * 3 4 * * X 1 1 4 We get the answer as (4 x 1) equals 4. © Dhaval Bathia

We follow step (B) as seen before: B) * * 3 4 X 1 1 7 4 We cross-multiply and add. (3 x 1) + (4 x 1) is 7. © Dhaval Bathia

We follow step (C) as seen before: A) * B) * * 3 4 * 1 1 3 7 4 X We get the answer as (3 x 1) equals 3. The final answer is 374 © Dhaval Bathia

More Examples: x 3 2 3 1 1 2 1 x 1 2 x 2 4 1 6 : 3+4 : 2 3 : 6+1 : 2 2: 8+1: 4 672 372 294 © Dhaval Bathia

Two-digit Multiplication With Carry-over Example: 4 4 x 2 2 © Dhaval Bathia

Step (A) will be : A) * B) * 4 4 * * X 2 2 8 We get the answer as (4 x 2) equals 8. © Dhaval Bathia

Step (B) will be: 1 B) * * 4 4 X 2 2 6 8 We cross-multiply and add. (4 x 2) + (4 x 2) is 16. We write 6 and carry-over 1. © Dhaval Bathia

Step (C) will be: A) * B) * * 4 4 * 2 2 9 6 8 X We multiply (4 x 2) and get 8. We add the 1 carried over and get the final answer as 9 © Dhaval Bathia

3 -digit Multiplication We will use the 5 steps that are given below: a) * * * d) * * * e) b) * * c) * d) * * * f) * e) * * f) * * * © Dhaval Bathia * *

Step (A) will be : 3 0 2 A) * * * B) * * * X 1 2 We get the answer as (2 x 1) equals 2. © Dhaval Bathia

Step (B) will be : 3 0 2 A) * * * B) * * * X 1 2 1 4 2 We get the answer as (0 x 1) + (2 x 2) equals 4. © Dhaval Bathia

Step (C) will be : 3 0 2 A) * * * B) * * * X 1 2 1 5 4 2 We get the answer as (3 x 1) + (0 x 2) + (2 x 1) equals 5. © Dhaval Bathia

Step (D) will be : 3 0 2 A) * * * B) * * * X 1 2 1 6 5 4 2 We get the answer as (3 x 2) + (1 x 0) equals 6. © Dhaval Bathia

Step (E) will be : 3 0 2 A) * * * B) * * * X 1 2 1 3 6 5 4 2 We get the answer as (3 x 1) equals 3. © Dhaval Bathia

Three-digit Multiplication With Carry-over Example: 5 0 x 1 6 © Dhaval Bathia 2 1

Step (B) will be : 1 5 0 2 A) * * * B) * * * X 1 6 1 2 2 We get the answer as (0 x 1) + (6 x 2) equals 12. We write 2 and carry-over 1. © Dhaval Bathia

Step (C) will be : 1 5 0 2 A) * * * B) * * * X 1 6 1 8 2 2 We get the answer as (5 x 1) + (0 x 6) + (2 x 1) equals 7…(plus 1 carried over) equals 8 © Dhaval Bathia

Step (D) will be : 3 5 0 2 A) * * * B) * * * X 1 6 1 0 8 2 2 We get the answer as (6 x 5) + (1 x 0) equals 30. We write 0 and carry-over 3. © Dhaval Bathia

Step (E) will be : 3 5 0 2 A) * * * B) * * * X 1 6 1 8 0 8 2 2 We get the answer as (5 x 1) equals 5. We add to it the 3 carried over. The final answer © Dhaval Bathia is 8.

More Examples: x 34 2 361 7 1 4 2 01 x 14 2

Let us have a look at the steps used in multiplication of four digit

4 -digit Multiplication We will use the 7 steps that are given below: a) * * d) * * g) * * * * e) b) * * c) * d) * * * f) f) * * * e) * * * * * * © Dhaval Bathia

In this way, we can go on and multiply 5 -digit, 6 -digit, 7 digit and bigger numbers But rather than doing examples of every type, I will give you a simple formula that you can use for all such numbers. By learning the formula, you will be able to do any multiplication problem. © Dhaval Bathia

FORMULA The number of steps to be used in any multiplication technique can be found out by using the formula ‘ 2 x (number of digits) – 1’ • Thus, when we multiplied 2 -digit numbers, the steps used are 2 x 2– 1=3 • When we multiply 3 -digit numbers, the steps used are 2 x 3– 1=5 • When we multiply 4 -digit numbers, the steps used are 2 x 4– 1=7 © Dhaval Bathia

Just go a few slides back and carefully observe the notation of steps used in 2 -digit, 3 -digit and 4 -digit numbers. They follow a particular trend. . You can expand the same trend to multiply higher order numbers. . © Dhaval Bathia