Column Method of Multiplication

We will discuss here about the column method of multiplication. We know how to multiply a 2-digit number by a 1-digit number and 2-digit number. We also know how to multiply a 3-digit number by a 1-digit number. Similarly, we can multiply a 2-digit number by a 2-digit number.


Example: Multiply 84 by 36.

Solution:

Here multiplicand is 84 and multiplier is 36

Step I: Multiply multiplicand by the ones digit of multiplier i.e.,

                2

                8              4

                ×             6 ones

                5              0              4 ones  partial product

Step II: Multiply multiplicand by the tens digit of multiplier i.e.,

                1

                8              4

                ×             3 tens                      

                2              5              2 tens partial product


Add the partial products

504 ones + 252 tens

504 × 1 + 252 × 10

504 + 2520 = 3024

It actually means.

                               8              4

                ×             3              3

                5              0              4                               84 × 6 = 504

2              5              2              0                        84 × 30 = 2520

3              0              2              4                        84 × 36 = 3024   


Now we shall apply the same method to multiply a 3-digit number by a 2-digit number.

                1              5              3

                ×             2              4

                6              1              2        153 × 4   = 612    partial product

3              0              6              0        153 × 20 = 3060  partial product

3              6              7              2        153 × 24 = 3672

Shortcut method (3-digit number by a 2-digit number) → Without Regrouping

Step I:

                1              2              3

                ×             1              2

                                               6

Step II:

                1              2              3

                ×             1              2

                                4              6

 

Step III:

                1              2              3

                ×             1              2

                2              4              6


Step IV:

                1              2              3

                ×             1              2

                2              4              6

                                3              ×

                                7              6


Step V:

                1              2              3

                ×             1              2

                2              4              6

                2              3              ×

                4              7              6

 

Step VI:

                1              2              3

                ×             1              2

                2              4              6

1              2              3              ×

1              4              7              6





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