 Hello friends. So in this session, we are going to learn a technique of Multiplying any number by five So any number when multiplied by five can be equivalently Calculated as multiplying by ten and then dividing the result by two. How does it work? So let us say we have a number x and then if I multiply this by five It is equivalent to multiplying the number x by ten and then divide by two right because ten by two is five Let us see a few examples So here twenty four into five is given so first step is I'll go a little slow in while calculating this so that you Can understand it But then with a little bit of practice you'll be able to do it in your mind itself So you don't require even pen and paper to do it. So twenty four into five is nothing but twenty four into ten by Two now multiplying twenty four by ten is much easier. It will be simply 240 So in your mind itself two forty by two is nothing but one twenty Right similarly here. It is five seventy by two now I'm writing it but usually while calculating it you need not write it You can do it in your mind itself now five seventy by two is easier to calculate because it is two eight and then five Right, it has to be done in mind mind you it is not needed to use pen and pencil But initially for practicing you'll be requiring the help of pen and pencil But after that in the flow you will be able to calculate in your mind itself now two two four into five is simply two two four Zero by two. This is what the mind is calculating and here the number will be one one two zero This is how multiplication by five is done Now let us understand the process of multiplication by 25 Let us say we have to multiply a number x by 25 So if you see this is nothing but x into hundred by four because 25 is hundred upon four. So this technique we will be applying to multiply two numbers using by 25 now first step is to multiply it by hundred and then Divide it by four. So let us take 24 into 25 first example. So it is nothing but 2400 by four. So clearly this is not a big deal. This is 600 because 24 by 4 is 6 Now second is 57 into 25. So what do you need to do? 5700 by 4 so if you calculate it it is one then four and then two and five Okay, now this has to be done mentally guys because you know, this is a training module So we'll have to go a little bit slow. Let us take the third example. So in this example, what is this? This is 224 into 25. So it is nothing but 22400 by four, which is nothing but five six 00 correct. So this is the answer So likewise, you can have any two digit three digit five digit number and you when you have to multiply by 25 Simply multiply by hundred and divide it by four Now, let us understand the process of multiplying it any number by 125 again It is simple. So if you see multiplying any number X by 125 requires that you multiply that with 1000 first and then divide the entire result by eight because if you see thousand upon eight this number is Nothing but 125. Let us take examples now. So if you see first example is again 24 into Sorry, this is 125 24 into 125 so 24 into 125. How do you do 24,000 and divided by 8 now clearly 24 by 8 is 3. So answer is 3000 Okay. Now second one is 57,000 Divide by it, right? So now you'll see what is this eight seven times 56 and is there? So one 20 is there. So two and forty so seven one two five Right, so instead of multiplying otherwise, what you would have done you would have taken 125 and then 57 and then you have Multiplied 125 by seven first. So like this 7535 carry three. So seven twos are 14 17 carry one and seven on the seven eight 75 and then five five is a 25 carry two Five twos are 10 12 carry one five and a five and then six. So hence then you'll add Right. So this will take this much time to solve like this, right? Otherwise alternatively you can just multiply by thousand and divide by eight. You'll get the same result now Let us see what is 224 into 125. I'll go slow again. So two two four triple zero, right? And then this divide by eight. Okay. So now Multiplying by 125 is you know a little bit or relatively more tedious than dividing that number by eight So let us say what is this? This will be eight two times sixteen, right? So carry the six is remainder so 64 and now 64 is Eight times right done 28,000. So this is how it can be done so quickly