# Finger multiplication on steroids

today I've got something lined up which is going to be really really useful for people who have trouble memorizing that times table well we've come very handy before for everybody was got little kids who who struggle with this a lot I start

With a clip from one of my favorite teaching movies Stand and Deliver we've already had another clip in this one is even better amazing now quite a few people are aware of this one here and quite a few teachers actually teach this

One and I mean I taught my kids the 9 times table like this and you know did still whenever they're on certain day they bring it out we construct things there it's really quite ingenious right so at the moment the eights finger is

Down and to the left of it there's seven left over and to the right of it there's two left over so at 72 pretty alright pretty and that works for the whole 9 times table so 1 times 9 2 times 9 all the way up to 10 times 9 why

Does it work well it's really not that hard I leave it for somebody to sort it out in the comments again so sort of odd me comments give you reasons why this works ok now a lot of people are aware of this most people wouldn't know that

By doing this you're also doing the 99 times table the 999 times table and so on at the story the 99 times table the 99 times table looks like this you know very similar to the 9 times table you just basically take the 9 times table

And insert nines in the middle of everything there and you get the 99 times table and with the 999 times table you insert two nines and so on again somebody figure out in the comments how this works I

Think on the door does everybody think okay okay they got a gold star very good star or a seal of approval all right now what I want to talk about today is something that not too many people are aware of has been around for hundreds of

Years and it's actually also something that I taught my kids and which works very well so what you do there is you associate the numbers from six to ten with the fingers of your left hand but also as

The fingers of your right hand like that and now I'm just going to go for it and show you how to multiply with this setup here so what's really nice about it is it kind of takes care of all the difficult products in the in the times

Tables so all the ones with large numbers the ones that nobody can remember like six times seven or seven times eight or these sorts of things run all right let's just go for it so we're going to do seven times eight seven

Times eight so we're looking on the left hand everything at the touching point and below there's two fingers there on the right side there are three fingers there two fingers but three fingers is five five fingers to put on the five

Above there's some fingers left over there's three there and there's two on the other side now those two numbers we have to multiply not add so three times two is six 56 7 times 8 is 56 that's right that's right that's right

But the multiplication is a easy one right so it's an easy one so it's just three times two and and people usually don't have any problem with that where's mr. big one you know people get uncertain you know that most of the

Trouble with times tables is with mr. large numbers huh okay let's do another example here we've got six times nine six times nine so here on that side we've got one finger on that side we've got four fingers one

Plus four is five yep and then on top we've got four and one four times one us so 54 600 works works okay let's do one more more kind of an extreme one okay we do six times ten okay now let's add

We've got one finger here we've got 5 1 plus 5 is 6 okay now on top gets kind of neat we've got 4 on the other side we've got 0 so 0 times 4 is 0 0 works 60 is 6 times 10 and it works for all of these things there's a slight complication

When you kind of go and multiply the smaller the number so let's go for that one so here we go four right 6 times 7 ok 6 times 7 so 1 plus 2 is 3 okay then on top 4 times 3 is 12

Mmm yeah but it's pretty obvious what we're gonna do right what you gonna do you just carry the 1 exactly and you get 42 and that works and so this is 2 another example here so the 6 times 6 has the same problem so 6 times 6 we've

Got one here put one there it gives 2 2 and then on top we've got 4 we've got another 4 let's give 16 that's right and I would carry the 1 but before we do this we actually kind of four what I want to talk about next is it kind of

Important to realize what we're really doing here well we're adding or we're just looking at the number of green fingers there and so that number we just attach a zero basically to it it's like a 20 and we add to it the product on top

That's what we're really doing right and that really works for all of them it's just you know okay so you could also look at it like this you know so it's 36 perfect perfect now the next thing I'm gonna do is something

That hasn't been done before in the history of this trick I think okay so let the Cisco I'm going to go for a countdown I'm going to do 7 times 8 and 6 is 7 times 7 and 7 times 6 okay let's just see what happens ok so again before

We head this one we've got five fingers down here so that's a 50 all right so it's a 50 and on top we've got 3 times 2 and I'm actually going to write down 3 times 2 4 4 what I have in mind I write down things like this okay so

Let's store this away okay now we're going to go to the next one which is seven times seven okay so we've got four here that means it's 40 40 and then we've got on top 3 times 3 so 3 times 3 okay just take it down there

Next one is sometimes 6 okay sometimes 6 now we've got 30 and we've got 3 times 4 that's right 2 times 4 so we also note this one down now the question is what comes next right so lift us done is we've taken

This finger here the 7th finger and touched it to the 8 to 7 the 6 what comes next that's the problem a 5/5 we come next but we ran out of fingers so I mean you know you know that's where people stop

Right but that's not necessarily where mathematicians stop like so acted like mathematics is full of these scenarios where you kind of know how something starts in any kind of hit a natural barrier and then you either stop or we

Just try to keep going anyway and see where it takes you so for example I could say you know square of 2 I know what that is I know what square of 1 is I know what square root of 0 is and then I asked what is squared of minus 1 and

You know it doesn't make sense so most people just say what we have to stop here doesn't make sense but you know if you're if you're a true mathematician you just keep on going and you see what happens and chances are

You'll actually find something that's amazing ok and so the context for this finger multiplication is actually a society where you know they didn't think about you know anything like this it's really

Just kind of basic arithmetic that they were doing there okay so let's just go for it so how do we go next well I just add a 5 down there ok I have a friend paint me some fives and so now we will try to do it I will try to do it so

We've established enough context here so the green numbers we've got 50 40 30 what comes next 20 so let's just put it down let's see how that works out right so we've got two here that already accounts for a full 20 on the other side

We've got no finger perfect so nothing right then here we've got 3 times 2 3 times 3 3 times 4 then 3 times 5 let's roll up on the left side we've got 3 fingers on the right side we've got five fingers works out right

Also 20 plus 3 times 5 is 35 which is work sorry so we've just done something which probably nobody's done before amazing one but do we stop there no no not we are true mathematicians we're true

Mathematicians we keep on going I've got this friend you just painted me a and negative finger indent it I just put put put a negative figure so let's see how this works out okay 40 30 20 10 all right so let's just see how things work

Out and we've got 20 here we've got a negative finger on the other side which is in minus 10 so 20 minus 10 is 10 worked out okay then up on top what comes here 3 times 3 3 times 4 3 times 5 3 times 6 that see where this works so

Here on the left side we've got the usual 3 on the right side what we usually count is everything above the touching point numbers above the touching point okay and this is 1 2 3 4 5 6

Yeah not as extra finger just as the numbers that are kind of above or exception or whatever alright whatever comes above the touching point you know blue the count yeah so that works out and when you've got here 3 times 6 is 18

Plus 10 is 28 perfect but do we stop there obviously not we just keep on going good okay so so what we've got now is we've got these things extend it all the way down to minus 1 ok but of course you could keep on going come to the

Whole body and go out here forever but let's do 3 3 is our next guy right so we've got 30 20 10 zero okay let's have a look we've got 20 here and now on the other side where we've got two of those negative guys so that's minus 20 so 20

Minus 20 0 works out right then we've got 3 times 7 as the next one that comes up here could be usual here above the touching point we got seven works out right also three times seven is three times seven so

We're kind of losing a pointy early in terms of saving saving selling we're not saving anything anymore but we just keep on going anywhere okay so it comes next well obviously times two times one but

Let's just skip forward two times zero it's got interesting right so we do 7 times zero all right now now we should actually be able to figure out like without actually you know looking at anything that came

Before how this is going to work right so we've got two on that side okay 200 side now how many negative fingers do we have here that's right minus 5 so it's 2 minus 5 is minus 3 minus 30 and now we have to

Add up anything above the touching point right so that's really on that side as usual and on that side we've got 1 2 3 4 5 6 7 8 9 10 so 10 right so it's 3 times 10 right in a 30 plus 3 times 10 is is 0 it really works it's just amazing you

Know okay now what comes next well now I bring in both hands right and now I'm actually going to do something amazing I'm going to multiply minus 1 times minus 1 okay so the touching point is here at minus 1 all right and

Actually this is a this is a point where it kind of gets really interesting or it gets really interesting because at this point you can discover what minus 1 times minus 1 is or predict but what it should be worth and you know for the

People who've been using this over the ages they never thought about you know that that was something that they weren't interested in anyway let's do it okay so we're touching there so what I have to figure out first to figure out

Is how many negative fingers we have on the left well we've got 6 on the other side another 6 obviously right there's a total of 12 that corresponds to what number hundred 20 miles on 120 okay now

We need to figure out everything above the touching point so there's 1 2 3 4 5 6 7 8 9 10 11 and another 11 on the other side so that's 11 times 11 is a hundred in 21 and so we have to add 121 and what does

That give how did – and 20 plus 121 is it's 1 minus 1 times minus 1 is 1 how beautiful is that all right and so basically at this point in time we've made our big discovery right and it's a fingerprint there is a finger proof and

Where do we stop there well obviously we can kind of keep on going here right forever but we can also do this ok so now we've got a different sort of you know basically extended things all the way around so we've got

Like all the numbers here we've got into the minus here so we're gonna round it the corner here and then we going to the 11 12 13 that goes on forever – and I mean I kind of leave it to you now to figure out how you actually do a

Multiplication beyond here so for example you know what is 7 times 11 and so you have to figure that one out obviously there's lots of things that you can explore here now you know so algebraically how this works and you

Know if somebody's really keen and I haven't done this myself yet can you extend this to a complex number multiplication thrown out but you know okay