multiplication of large numbers

We know how to multiply single-digit numbers. Let's learn how to multiply large numbers using an example. What is the product of 24 × 21?

Step 1: Put 24 over 21 with places lined up, 4 over 1 (ones place) and 2 over 2(tens place)    

Step 2:  Start multiplying the top number by the rightmost or last digit of the bottom number. Multiply 24 by 1

Step 3: Multiply the top number by the next digit to the left of the bottom number. Because 2 is at tens place and not in ones place write zero in the ones place in the next row so that we begin writing product from the tens place. Multiply 24 by 2 and write the product with 0 at the end.

       
Step 4: Add the two products so obtained, 24+480 to get the answer.

Now as we know how to multiply large numbers let's try one more multiplication problem.

What is 12 × 425? Write the smaller number at the bottom and the larger number at the top:

Multiply 425 by 2 = 850 (here carryover is used, as 5 times 2 is 10, so 1 is carried over to the tens place)

Now Multiply 425 by 1 = 425, write 0 in ones place and product before the zero. Lastly add both the products to get the answer. 
       
               
Points to remember:

• Multiply bigger number by smaller number.
• When multiplying whole numbers by multiples of 10, 100, 1000, and so on, simply “tag” as many zeros on the product as there are in factors 10, 100, 1000, etc. For example:

         300 × 20  = 6000 (multiply 300 by 2 and add one zero to the right)
         300 × 200 = 60000(multiply 300 by 2 and add two zeros to the right)