How to do Long Multiplication?

       
           

Multiplication means repeated addition. By multiplication, we mean that the number of times any particular number is added up. So we say 10 * 3 means that a number 3 is to be added 10 times. To get the result we proceed also as 3 * 10 = 30. For this we need to remember the tables of the numbers. Now we will discuss How To Do Long Multiplication. In order to perform long multiplication, we will use the method of Column Multiplication. So if we write the number 12456 * 3, in this situation, addition will not work as we can not get the accuracy of the result by adding the number 3 for 12456 number of times. Though in both the cases we get the same result, but applying column method of multiplication is a feasible solution for long multiplications. We proceed as follows:

First we will write the place values at the top of the number and the digits of the multiplicand are placed at their particular places in the first row. In second row, we will write the multiplier, i.e. the number by which we are going to multiply.
Now starting from the ones place value we start picking the digits one by one and multiply each digit by the multiplier. The product  is written in the next row, keeping in the mind that if the  product is of two digits, then the ones place digit is placed at the bottom row and the tens digit is  taken as the carry over to the next place, where we add it with the product . Now we proceed as follows
    T.Th     Th      H     T     O
      1         2        4      5      6
X                                         3
     3        6     12        15   18

So it is written as follows after carry over:
3       7        3          6       8, which is the result of multiplication. 

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