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Dhaval Bathia
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Dhaval Bathia
This is one of the fastest techniques of
multiplication
Helps you get the answer of anymultiplication problem in just one line !
We will begin with multiplication of two-
digit numbers
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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 2
6We get the answer as (3 x 2) equals 6.
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We follow step (C) as seen before:
A) * *
* *
2 3
X 1 2
6We get the answer as (2 x 1) equals 2.
72The 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 1
4We get the answer as (4 x 1) equals 4.
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We follow step (B) as seen before:
B) * *
* *
3 4
X 1 1
4We cross-multiply and add. (3 x 1) + (4 x 1)
is 7.
7
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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 16 : 3+4: 2 3 : 6+1: 2 2 : 8 + 1: 4
6 7 2 3 7 2 2 9 4
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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
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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
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3-digit Multiplication
We will use the 5 steps that are given below:
a) * * *
* * *
b) * * *
* * *
c) * * *
* * *
d) * * *
* * *
e) * * *
* * *
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Step (A) will be :
A) * * *
* * *
3 0 2
X1 2 1
2We get the answer as (2 x 1) equals 2.
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Step (B) will be :
A) * * *
* * *
3 0 2
X1 2 1
2We 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
X1 2 1
2We get the answer as (3 x 1) + (0 x 2) + (2 x 1)
equals 5.
45
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Step (E) will be :
A) * * *
* * *
3 0 2
X1 2 1
2We get the answer as (3 x 1) equals 3.
4563
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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
X1 6 1
2We get the answer as (2 x 1) equals 2.
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Step (B) will be :
A) * * *
* * *
5 0 2
X1 6 1
2We get the answer as (0 x 1) + (6 x 2)equals 12. We write 2 and carry-over 1.
2
1
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Step (C) will be :
A) * * *
* * *
5 0 2
X1 6 1
2We get the answer as (5 x 1) + (0 x 6) + (2 x 1)equals 7(plus 1carried over) equals 8
28
1
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Step (D) will be :
A) * * *
* * *
5 0 2
X1 6 1
2We get the answer as (6 x 5) + (1 x 0)equals 30. We write 0 and carry-over 3.
280
3
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Let us have a look at the steps used in
multiplication of four digit numbers
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4-digit Multiplication
We will use the 7 steps that are given below:
a) * * * *
* * * *
b) * * * *
* * * *
c) * * * *
* * * *
d) * * * *
* * * *
e) * * * *
* * * *
f) * * * *
* * * *
g) * * * *
* * * *
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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 suchnumbers.
By learning the formula, you will be able to do any
multiplication problem.
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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 21 = 3
When we multiply 3-digit numbers, the steps used are
2 x 31 =5
When we multiply 4-digit numbers, the steps used are2 x 41 =7
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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..