Hi, I am Dr. Shah. I was the National Lecture Competition in 1999. I am the Maths Master at Mathscool. Now, I would show you how to do a long multiplication. For example, multiply 4325 by 21. First thing I would do is to write 4325 and write 21 under it so that they are lines up in the right hand side. Then, I multiply each of the upper digits by the first of the lower 4325 digit. One times 5 is 5. One times two is 2, one times three is three and one times four is four. Then, I would multiply the upper digits by the next lower digit. For that, I would shift the digits by one space. Write zero under the first digit. And then, start multiplying by 2.2 times 5 would be 10. So will keep zero under 2 and carry one. Then multiply 2 by 2 and add the carry over one to it to get 5. Similarly, 2x3 would be 6 and finally 2x4 would be 8. It will be 86500. Then add up the two rows which comes to 90825. So that is my final answer. Now you could ask the same question in a slightly different way. You can have decimals, for example you multiply 43.25 X 2.1. 4325, 86500, 90.825. For this, I would shift the decimals out by two places in the first row and one place in the second. After that, multiply in the same manner. After that, to place the decimal, shift the decimal back to the left by three places and the answer of 43.25 times 2.1 would be would be 90.8251. So that is the long method of multiplication. .

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