© Dhaval Bathia

© Dhaval Bathia

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 two-digit numbers

© Dhaval Bathia

We will use the 3 steps that are given below:

A) * *

* *

B) * *

* *

C) * *

* *

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Let us suppose we want to multiply:

2 3

x 1 2

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We follow step (A) as seen before:

A) * *

* *

2 3

X 1 26

We get the answer as (3 x 2) equals 6.

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We follow step (B) as seen before:

B) * *

* *

2 3

X 1 26

We cross-multiply and add. (2 x 2) + (1 x 3) is 7.

7

© Dhaval Bathia

We follow step (C) as seen before:

A) * *

* *

2 3

X 1 26

We get the answer as (2 x 1) equals 2.

72

The final answer is 276

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Another example…

Let us suppose we want to multiply:

3 4

x 1 1

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We follow step (A) as seen before:

A) * *

* *

3 4

X 1 14

We get the answer as (4 x 1) equals 4.

© Dhaval Bathia

We follow step (B) as seen before:

B) * *

* *

3 4

X 1 14

We cross-multiply and add. (3 x 1) + (4 x 1) is 7.

7

© Dhaval Bathia

We follow step (C) as seen before:

A) * *

* *

3 4

X 1 14

We get the answer as (3 x 1) equals 3.

73

The final answer is 374

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More Examples:

3 2 3 1 1 4

x 2 1 x 1 2 x 2 1

6 : 3+4 : 2 3 : 6+1 : 2 2 : 8 + 1 : 4

6 7 2 3 7 2 2 9 4

© Dhaval Bathia

Two-digit Multiplication With Carry-over

Example:

4 4

x 2 2

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Step (A) will be :

A) * *

* *

4 4

X 2 28

We get the answer as (4 x 2) equals 8.

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Step (B) will be:

B) * *

* *

4 4

X 2 28

We cross-multiply and add. (4 x 2) + (4 x 2) is 16. We write 6 and carry-over 1.

6

1

© Dhaval Bathia

Step (C) will be:

A) * *

* *

4 4

X 2 28

We multiply (4 x 2) and get 8. We add the 1 carried over and get the final answer as 9

69

© Dhaval Bathia

3-digit MultiplicationWe will use the 5 steps that are given below:a) * * *

* * *

b) * * *

* * *

c) * * *

* * *

d) * * *

* * *

e) * * *

* * *

© Dhaval Bathia

Step (A) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (2 x 1) equals 2.

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Step (B) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (0 x 1) + (2 x 2) equals 4.

4

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Step (C) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (3 x 1) + (0 x 2) + (2 x 1) equals 5.

45

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Step (D) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (3 x 2) + (1 x 0) equals 6.

456

© Dhaval Bathia

Step (E) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (3 x 1) equals 3.

4563

© Dhaval Bathia

Three-digit Multiplication With Carry-over

5 0 2

x 1 6 1

Example:

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Step (A) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (2 x 1) equals 2.

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Step (B) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (0 x 1) + (6 x 2) equals 12. We write 2 and carry-over 1.

2

1

© Dhaval Bathia

Step (C) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (5 x 1) + (0 x 6) + (2 x 1) equals 7…(plus 1 carried over) equals 8

28

1

© Dhaval Bathia

Step (D) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (6 x 5) + (1 x 0) equals 30. We write 0 and carry-over 3.

280

3

© Dhaval Bathia

Step (E) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (5 x 1) equals 5. We add to it the 3 carried over. The final answer is 8.

2808

3

© Dhaval Bathia

More Examples:

3 4 2 3 6 1 7 1 4

x 2 0 1 x 1 4 2 x 9 3 5

68742 51262 667590

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

© Dhaval Bathia

4-digit MultiplicationWe will use the 7 steps that are given below:a) * * * *

* * * *

b) * * * *

* * * *

c) * * * *

* * * *

d) * * * *

* * * *

e) * * * *

* * * *

f) * * * *

* * * *

g) * * * *

* * * *

© 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..