Multiplying 2-digit by 2-digit: 36x23

let's start with a warm-up problem to avoid getting any mental cramps as we learn new things so this is a problem that hopefully if you understood what we did in the last video you can kind of understand what we're about to do right now and I'm going to escalate it even more in the last video we finished with a I think we finished with a four digit number times a one digit number let's let's let's up the stakes to a five digit number so let's do 6400 let's do sixty-four thousand three hundred and twenty nine times now let me think of a nice number times four times four I'm going to show you right now that this is we're going to do the exact same process that we did in the last video we just have to do it a little bit longer than we did before so we just start off saying okay what's four times nine four times nine is equal to 36 right 18 times 2 we got 36 so we write the six down here carry the 3 up there just put the three up there then you got 4 times 2 4 times 2 4 times 2 and then you're going to have to add the 3 so let me just write that there plus 3 is equal to you do the multiplication first so you can even think of it as an order of operations but you know you just should know that you do the multiplication first so it's 8 plus so 4 times 2 is 8 plus 3 is equal to 11 put the this one down here and put the 1 10 and 11 up there then you got 4 times 3/4 times 3/4 times 3 you got that one up there so you have to add that plus 1 is equal to that's going to equal 12 plus 1 is equal to 13 so 13 then you have 4 times 4 4 times 4 you have this little one hanging out here from the previous multiplication so you have to add that and that's equal to 16 plus 1 it's equal to 17 take the 7 down here put the one up there we're almost done almost done we have four times six four times six plus one plus one what is that 4 times 6 is 24 plus 1 is 25 but the 5 down here there's nowhere to put the - there's no more multiplications to do so we just put the 2 down there so 64 thousand three hundred and twenty-nine times four is two hundred and fifty-seven thousand three hundred and sixteen and in case you're wondering these commas don't mean much they just help me read the number so I put it after every three digits so I know that for example that everything after this these are in the thousand thousand I've had another comma here then I know this is millions so it just helps me read the problem a bit so if you got that you're now ready to escalate to the to a slightly more complicated situation although the first way that we're going to do it it's actually not going to look any more complicated it's just going involve one more step so everything we've done so far are a bunch of digits times a one digit number now let's do a bunch of digits times a two digit number so let's say we want to multiply let's say we want to multiply 36 times instead of putting a one digit number here I'm gonna put a two digit number so times 23 aha so you start off doing this problem exactly the way you would have done it if there was just a three down here you can kind of ignore the two for a little bit so three times six three times six is equal to 18 so you put the eight here put the 10 there or the one there because it's 10 plus 8 3 times 3 is 9 3 times 3 is 9 plus 1 so 3 times 3 plus 1 is equal to this 9 plus 1 is equal to 10 so you put the 10 there there's nothing left you put the 0 there there's nothing left to put the ones you put the 10 there so you essentially have solved the problem that 36 let me do this in another color that 36 times 3 is equal to 108 that's what we've solved so far but we have this 20 sitting out here all right we have this 20 we have to figure out what 20 times 360 is or sorry what 20 times 36 is so what you do to multiply this is this 2 is really a 20 and to make it all work out like that what we do is we throw a 0 down here we throw a 0 right there and in a second I'm going to explain why exactly we did that so let's just do the same process as we did before with the 3 now we do it with the 2 but we start filling up here and move to the left so 2 times 6 2 times 6 that's easy that's 12 so 2 times 6 is 12 we put the one up here and we have to be very careful because we had this one from our previous problem which doesn't apply anymore so we could erase it or you know that one we could get rid of you have an eraser you get rid of it or you can just keep tracking your head that the one you're about to write is a different one so what were we doing we wrote 2 times 6 is 12 put the 2 here put the one up here and I got rid of the previous one because that will just mess me up now I have 2 times 3 2 times 3 is equal to 6 but then I have this plus 1 up here so I have to add plus 1 so I get 7 so that is equal to 7 2 times 3 plus 1 is equal to 7 so this 720 we just solved that's literally let me write that down what is that that is 36 times 20 36 times 20 is equal to 720 and hopefully that should explain why we had to throw this 0 here if we didn't throw that 0 here we would have just a 2 we would just have a 72 here instead of a 720 and 72 is 36 times 2 but this isn't the 2 this is a 2 in the tens place this is a 20 so we have to multiply 36 times 20 and that's where we got 720 there so 36 times 23 let's write it this way let me write it let me get some space up here so we could write 30 well actually let me just finish the problem then I'll explain to you why it worked so now to finish it up we just add 108 to 720 so 8 plus 0 is 8 0 plus 2 is 2 1 plus 7 is 8 so 36 times 23 is 828 now you're saying Sal why did that work how why were we able to figure out separately 36 times 3 is equal to 108 and then 36 times 20 is equal to 720 and then add them up like that because we could have rewritten the problem like this we could have rewritten the problem as 36 let me write the original problem was this we could have rewritten this as 36 times 20 plus 3 and this and I don't know if you've learned the distributive property yet but this is just the distributive property this is just the same thing as 36 times 20 plus 36 times 3 if that confuses you then you don't have to worry about it but if it doesn't then then this is good it's actually teaching you something 36 times 20 we saw was 720 we learned that 36 times 3 was 108 and when you added them together we got what 828 so what we got we got 828 and you could expand it even more like we did in the previous video you could write this out as 30 plus 6 times 20 plus 3 actually let me just do it that way because I think that could help you out a little bit if it confuses you ignore it if it doesn't that's good so we can do it 3 times 6 3 times 6 is 18 18 is just 10 plus 8 so it's 8 and we put a 10 up here and ignore all this up here 3 times 33 times 30 is 90 90 plus 10 is a hundred so 100 is 0 tens plus 100 I don't know if this confuses you or not if it does ignore it if it doesn't well you know I don't want to I don't want to complicate the issue and now we can multiply 20 we could ignore this thing that we had before we're ready 20 times is 120 so that's 20 plus 100 plus 100 so I'll put that hundred up here 20 times 30 you might not notice 2 times 3 and you have 2 zeroes there and I think I'm maybe jumping the gun a little bit assuming a little bit too much of what you may or may not know but 20 times 30 is going to be 600 and you add another 100 there that's 700 and then you add them all up you get 800 all right 100 plus 700 plus 20 plus 8 which is equal to 828 my point here is to show you why that system we did worked why we added a 0 here to begin with but if it confuses you don't worry about that right now learn how to do it and then maybe re-watch this video let's just do a bunch of more examples because I think the examples are what really hopefully explain the situation so let's do 77 let's do a fun one 77 times 77 7 times 7 is 49 put the one up here the one up there 7 times 7 well that's 49 plus 4 is 53 53 there's nowhere to put the 5 so we put it down here 7 times 7 is 49 plus 4 is 53 stick a 0 here now we're going to do this 7 so let's take a 0 here 7 times and we get let's get rid of this right there because that'll just mess us up 7 times 7 is 49 stick a 9 there put a 4 there 7 times 7 is 49 plus 4 which is 53 53 so notice when we multiplied 7 times 77 we got 539 when we multiplied 7d times 77 we got 5390 it makes sense they just differ by a 0 by a factor of 10 and now we can just add them up and what do we get 9 plus 0 is 9 3 plus 9 is 12 carry the 1 1 plus 5 is 6 6 plus 3 is nine nine and then we have this five so it's five thousand nine hundred and twenty nine