How could you multiply nine with eight? Some of you have probably memorised the multiples of nine and know the answer. We know that it is 72, but in this session, we will understand multiplication in a very different way, Will this different way help us? Well, let me put it this way. Understanding this technique will help us solve problems like ‘nine hundred ninety eight’ times ‘nine hundred ninety seven’ in about five seconds. Yes, without a calculator. You don’t believe me do you ? Give me around two minutes to change your opinion! We use the concept of base to solve multiplication problems quickly! and bases are generally powers of Ten, like 10, 100,1000 and so on. When we are given the multiplication problem, the first thing we should ask ourselves is ‘which base is close to both the numbers?’ Here, both numbers are close to ten. So we can say that the base is ten. Once the base is decided, life becomes really easy. First, we subtract the base from each of these numbers! Subtracting the base from the first number, we get ‘9 minus 10’ that equals minus one. We write it next to that number. Next would be ‘8 minus 10’, that equals minus 2. These two numbers tell us how far these two numbers are from the base. 9 is ‘minus one units’ away from the base. and 8 is ‘minus two units’ away from the base. So the initial two steps: choose the base, and subtract it from the numbers. Once this is done, just make a partition like this. On the left, we write the sum. What sum? The sum of these two numbers or these two numbers! Both will result in the same answer! Either 8 plus ‘minus 1’, or 9 plus ‘minus 2’. Both equals 7. So we write a 7 on the left. On the right, we have the product of these two numbers! ‘minus 1 multiplied by minus 2’. And that equals 2. Yes, we should also consider the sign when multiplied these two numbers. There you go. We have the answer ‘9 times 8′ is 72. The steps are simple: we find the base, then subtract it from each number, write the sum on the left and the product on the right. Is there anything we need to be careful about here? Yes, on the right, the number of digits, should be equal to the number of zeros in the base! Here, the base has one zero, so we write just one digit on the right. Don’t worry… everybody thinks this is difficult at first. So let’s quickly solve a couple of problems and you will see how simple this technique actually is! Say we want to multiply ’98 with 97’. Both these numbers as we can see are close to 100. So the base is 100 here. 98 minus 100 is ‘minus 2’ and 97 minus 100 is ‘minus 3’. Then we make a partition. On the left we write the sum and on the right, we write the product. 98 plus ‘minus 3’ is 95. Even 97 plus ‘minus 2’ will give us 95. And ‘minus 2 times minus 3′ is 6. So should we write a 6 here? Don’t forget, the number of digits on the right will be equal to the number of zeros in the base! As there are 2 zeros and 100 ,there will be 2 digits here. 6 will be written as ’06’. There’s your answer! ’98 times 97′ is 9506. Find the base, find the deviation, find the sum and find the product and we get the answer in a few seconds! Okay, let’s try solving a problem with slightly bigger numbers. 9996 times 9997. Why don’t you try this? Remember the four simple steps. Find the base, find the deviation , find the sum and find the product. I give you ‘ten seconds’. Both numbers as we can see are close to ‘10,000’, so the base will be 10,000. This number is ‘minus 4’ units away, and this is ‘minus 3’ units away. Then we make the partition. Sum on the left and the product on the right! This plus this is 9993. The sum of these two will also give us 9993. The product will be ‘minus 4 times minus 3′ which equals twelve. The number of zeros in the base is four, which means we will have four digits on the right. 12 will be written as’ zero zero one two’. That’s our answer. The product of these two numbers will equal ‘Nine Nine Nine three zero zero one two’. Wasn’t this quick? Faster than a calculator you think? Notice that in all the examples we saw, both numbers were below the base. 98 and 97 were below 100. 9996 and 9997 were below 10,000. We will look at a couple of more examples in the next part of the session. Don’t forget the steps: Find the base, find the deviation, find the sum and find the product. And we get the answer!