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# Multiplying multi-digit numbers

## Video transcript

we now have the general tools to really tackle any multiplication problems so in this video I'm just going to do a ton of examples so let's start off with and I'll start in yellow let's start off with 32 times 18 32 times 18 say 8 times 2 is 16 I'll still let me just well I'll do it in our head this time because you always don't have all the space to work with so 8 times 2 8 times 2 is 16 put the one up there 8 times 3 is 24 24 plus 1 is 25 25 so 8 times 32 was 256 now we're going to multiply this one which is really a 10 times 32 underline it with the orange one times 2 and we have to be very careful here 1 times 2 is 2 so you might say hey let's me take a 2 down there but remember this isn't 2 1 this is a 10 so we have to stick a 0 there to remember that so 1 10 times 2 is 20 right or you could say 1 times 2 is 2 but you're putting it in the twos place so you still get 20 so 10 times 2 is 20 works out then 1 times 3 and we have to be very careful let's get rid of what we had from before 1 times 3 is 3 there's nothing to add here so you just get a 3 and so you get 10 times 32 is 320 right this one right here that's a 10 10 plus 8 is 18 so now we just add up the two numbers you add them up 6 plus 0 is 6 5 plus 2 is 7 2 plus 3 is 5 let's keep going let's hit do 99 times 88 it's going to give us a big number 8 times 9 is 72 72 is to the 7 up there 8 times 9 and then you have 8 times 9 again 8 times 9 is 72 and I have the 7 up here so 72 plus 7 is 79 79 fair enough now we are done with this let's just delete it just so that we don't get confused in our next step and our next step we're going to multiply this 8 now times 99 but this 8 is an 80 so let's take a 0 down there 8 times 9 is 72 stick a 7 up there then 8 times 9 is 72 plus 7 is 79 79 2 plus 0 is 2 let me switch colors 9 plus 2 is 11 carry the 1 1 plus 7 is 8 8 plus 9 is 17 hairs 1 1 plus 7 is 8 8712 let's keep going can't do enough of these all right 53 times 78 I think you're getting the hang of it now let's multiply 8 times 53 first so 8 times 3 is 24 stick the 2 up there 8 times 5 is 40 40 plus 2 is 42 42 now we're going to deal with it seven that's seven right there which is really a 70 so let's go remember to put the zero there seven times three and let's get rid of this don't want to get confused 7 times 3 is 21 put the 1 there and put the 2 up here 7 times 5 is 35 plus 2 is 37 37 now we're ready to add ready to add 4 plus 0 is 4 2 plus 1 is 3 4 plus 7 is 11 carry the 1 1 plus 3 is 4 4134 let's up the stakes a little bit let's up the stakes so let's say I had 796 times times fifty Oh fifty-eight times 58 let's mix it up well alright let's so first we're going to just multiply eight times seven hundred ninety-six and notice I've thrown an extra digit up here so 8 times 6 is 48 put the 4 up there 8 times 9 is 72 plus 4 is 76 76 and then 8 times 7 is 56 56 plus 7 is 63 63 I'm sure I'll make a careless mistake at some point in this video and the goal for you is to identify if and when I do all right now we're ready so we can get rid of these guys up here now we can multiply this 5 which is in the tens place it's really a 50 times this up here because it's a 50 we stick a zero down there 5 times 6 is 30 put the zero there put the 3 up there 5 times 9 is 45 plus the 3 is 48 48 5 times 7 is 35 plus 4 is 39 39 now we're ready to add I'm ready to add 8 plus 0 is 8 6 plus 0 is 6 3 + 8 3 plus 8 is 11 1 plus 6 is 7 7 plus 9 is 16 and then one plus three is four so 796 times 58 is 46,000 168 and that sounds up about right because 796 it's almost 800 it's all you know which is almost 1,000 so it's you know if we multiplied a thousand times 58 we'd get 58 thousand but we're multiplying something a little bit smaller than a thousand times 58 so we're getting something a little bit smaller than 58,000 so the number is in though in the correct ballpark now let's just do one more here where I'm really going to step up the stakes let's do five hundred and twenty three times I'm going to do a three-digit number now times 798 that's a big three-digit number but it's the same exact process and you should once you kind of see the pattern you say hey this will apply to any time number of digits times any a number of digits it'll just start taking a long time and your chances of making a careless mistake are going to go up but it's the same idea so we start with eight times 523 8 times 3 is 24 stick the 2 up there let me now 8 times 2 is 16 16 plus 2 is 18 the one up there 8 times 5 is 40 plus one is 41 so eight times fifth 523 is 4184 we're not done we have to multiply it times the 90 and divide with a 700 so let's do the 90 right there so it's a 90 so we'll just stick a zero there it's not a 9 so 9 time and let's get rid of these guys right there 9 times 3 is 27 9 times 3 is 27 9 times 2 is 18 18 plus 2 is 20 and then we have 9 times 5 is 45 45 plus 2 is 47 40 I don't want to write that thick 47 let me make sure I did that one right and let's just review it a little bit 9 times 3 it was 27 we wrote the 7 down here and put the 2 up there 9 times 2 is 18 we added 2 to that so we wrote 20 wrote the 0 down there and the 2 up there the 9 times 5 was 45 plus 2 is 47 you really have to make sure you don't make careless mistakes with these then finally we have to multiply the 7 which is really a 700 times 523 and for a 91 was just an 8 we just started multiplying when it was a 90 when we were doing with a tens place we put a zero there now that we're doing something that's in the hundreds we're going to put two zeroes there two zeroes right there and so you have seven and let's get rid of this stuff that'll just mess us up seven times three seven times three is twenty-one put the one there stick the two up there 7 times 2 is 14 14 plus r2 is 16 16 put the one up there 7 times 5 is 35 plus one is 36 36 and now we're ready to add and hopefully we didn't make any careless mistakes so four plus zero plus zero that's easy that's 4 8 plus 7 plus zero that's 15 carry the 1 one plus one plus one is three four plus seven plus six that's what's four plus six is ten 17 17 and then we have one plus four is five 5 plus 6 is 11 carry the 1 one plus three is four so 523 times 798 is four hundred seventeen thousand three hundred and fifty four and we can even check to make sure and so this is the moment of truth let's see if if we add let's see 523 times seven hundred ninety-eight there you go moment of truth I don't have to re-record this video it's four hundred seventeen thousand three hundred fifty four but we did it without the calculator which is the important point