 Hello friends welcome again to another session on speed mathematics Today we are going to learn another very effective tool to multiply two numbers, but these numbers are of special type So yes, it doesn't You know Is like is very useful in terms of any two given numbers But if there is a special pair of number which I'll illustrate what these are then this technique can be very very handy So let's say I have a two-digit number say 43 Okay, so the number is 43 and it is getting multiplied by another two-digit number 47 Okay, 43 and 47 now What is the specialty about these numbers so if you see the Numbers the 10th place numbers if you see are same So the 10th place number. This is 10th place. Isn't it? 10th place number place numbers are same Numbers are same and if that is so And the second condition is unit units place units place number if you see Units place numbers Units place numbers add up to 10 Add up to 10 Right, so if you get such kind of numbers then multiplication becomes easier for example another set is 51 and 59 another example could be 63 and 67 another could be 81 and 89 another could be 72 and 78 all of these numbers if they have if you get such numbers and you want to multiply them It's very easy to multiply them how So what you need to do is you just multiply the Units place number that means in this case seven and three and write 21 like that no problem and in this case you take four and Multiply this with the next number to four right? What is next number to four five? So four into five that is 20 So this will be the solution or this will be the calculation right easy enough, right? So you don't need to do the long process of multiplication and all the same we were here Now here if you see nine into one is nine But then we we are supposed to write two digit numbers, right? So if you multiply nine into one Nine into one how much you will get nine but while writing if you get only single digit then write Zero and then nine okay because we have to have two slots there zero and nine and rest There's nothing but five and multiply this by Five plus one that is six so five into six you have to do five into six Is equal to 30 and this 30 will sit over here. So the now answer is three zero zero nine or the product is Three zero zero nine. Okay, let's do this one again So three into seven so first step is three into seven Is equal to 21 and the next is six into six plus one Right six sevens are 42 right and hence the product will be four two two one Easy now in this case again, let's say Here 81 and 89 so again nine times one is zero nine so nine into one We'll write zero nine and not Only nine okay and eight into nine so eight into eight plus one That is 72. So the product will be seven two zero nine Right very easy. So you can do multiple number of times and you can see take multiple examples and test for yourself So in this case now, I will not be I will not be writing anything I'll just simply write the product so two eight just 16 and seven it's a 56 isn't it so five six one sixty You can multiply so quickly another example thirty two into thirty eight. So eight two just sixteen Eight two just sixteen and three into four twelve. So twelve sixteen is the product. Okay another example 71 into 79. Let's say okay now here one into nine is zero nine and Seven into eight seven plus one right seven to seven plus one seven in the 56 so hence five six zero nine So how quickly you can simply multiply such numbers now? It is true not only for two digit number You can also do for three digit numbers Three digit digit numbers, but again the criteria will be same the units place must add up to ten and The other set of other digits, whatever is left over Have to be same for example if I have one one two Into one one eight So you know what to do. So these two plus eight units place digit add up to ten, right? So two ages sixteen simply right two ages sixteen now what is left eleven and they here also eleven So eleven into twelve is one thirty two isn't it so hence right one three two one six Okay, you can check the product is one three two one six Okay, now let's take another example to you know thirteen one thirty three into one thirty seven Okay, one thirty three into one thirty seven. So you now know what to do So seven into three is twenty one clearly and now you have to thirteen into thirteen plus one That is thirteen into fourteen that will come out to be one eighty two and like that You can go on doing like this