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Multiplication by 2 digit

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Do you know the process of multiplying by two digits? Here is a video which helps you with the procedure

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hi welcome to Math Antics in our last video we learned the basics of multi-digit multiplication we learn how to multiply a multi digit number by a one-digit number but in this video we're going to take it to the Next Level we're going to learn how to multiply a multi digit number by another multi digit number you remember the procedure for multiplying when we have a 1/2 bottom number right you break up the problem into a series of multiplication steps one for each of the top digits and in each step you just multiply the turn digit by a top digit starting with the ones place and working your way left until you've multiplied all of the digits well when the bottom number of your multiplication problem also has more than one digit you have to do that same procedure we learn for each bottom digit for example if you have a two digit bottom number multiply the first digit by each top digit and then you multiply the second digit by each toptygin  that means you're going to have twice as many steps to do and it means you're going to get two different answers  what how can we have two different answers for the same problem now don't panic the cancers are just what you get from doing the multiplication procedure for each digit of the bottom number separately in fact it's kind of like we're pretending we have to separate multiplication problems that each have a one digit bottom number which is nice cuz I kind of like pretending no Luke I am your unsurpassable I mean it's nice because we already know how to multiply when we have a one-digit bottom number but then what we do with the two different answers were going to get well it turns out that all we have to do is add them together once we're finished doing all of our multiplication steps are you ready to example it should make a lot more sense when you see the procedure in action so let's multiply 324 by 3 digit number by 46 is your number now remember we're going to do the same procedure that we did in the last video for each of the bottom digits and since our top number has three digits that means lb read multiplication steps for the first digit and three steps for the second digit fortunately we can start the same way we would if the bottom number only had one digit I just ignoring the second digit until we finish the first three steps alright so our first multiplication step is 6 times 4 which is 24 message 24 has two digits we can leave the Foreigner answer line but we need to carry the two and put it above the next top digit that were going to multiply so the next step is 6 * 2 which is 12 but we have to add in the two that we carried so 12 + 2 gives us 14 that's another two digit answer so we leave the Warner answer line and carry the one up above the next digit that were going to multiply and our third step is 6 * 3 which is 18 and then we add in the one that we can we get 19 this time we can leave both digits of the 19 and our answer line because there's no more multiplication steps to do well at least there's no more steps first digit remember we still have that other bottom digit that we've been ignoring now we have to multiply it by each of the top digits also which means we have three more steps it also means that we'll get a second answer and because we'll get a second answer we need to start a second answered line for the next set of steps we're going to put our new answer find just below the first one so this answer line comes from our first bottom digit and this answer line will come from our second bottom digit  at the very end are all the multiplying we're going to add the two answers together but for now let's continue with the second set of multiplication steps and I almost forgot to tell you there's something very important that you need to do when you start the second set of steps because the second digit of the bottom number is in the tens place that means that even though the did tell me a for its value was really 40 that's 10 times bigger so the answer we get should also be 10 times bigger so before we start multiplying we need to is 0 in the first spot of our answer line so it's 10 times bigger that means that all the other answer digits we put their or shift into the next bigger number place and just so you know if we happen to have a third bottom digit we would get a third answer line and we need to shift the third answer over by 2 zeros because it would be a hundred time and if we had a fourth digit there be a fourth answerline shift it over by three zeros and if we had a V bottom digit there be a 5th answer Line ship lower by 4 zeros see the pattern boy am I glad we've only got two bottom digits and now you see why we always put the number with the fewest digits on the bottom when multiple let's continue with our problem let's do the first step of our second bottom digit we multiply that digit four by the ones place digit top number which is also for 4 x 4 gives a 16 and that goes in our second answer one right next to the extra zero we put their battery because 16 is a two-digit answer we have to carry and we always put the digit we carry above the next top digit that will multiply but before we can carry it up to place we need to cross out all the digits that we carry from our first answering because we were to use them we don't want to accidentally add them to our second answering line now we can carry R12 the top of the tens place which means it will go on the column above this too because that's the next top digit that will multiply with our bottom digit now we can do the multiplication step four times to gives his 8 and then we'll add one that we carry and get 9 correct finally a one-digit answer so we don't have to carry we just write the Nyan in the next place of our answer line and move on to the next step the next and last multiplication step is 4 * 3 which is and since there's no more steps we can write both digits and our second answer lamp alright we're finally done with all our multiplication steps how to play Peach Bottom digit by each top digit just like we're supposed to but now what do we do we have to answer lines but this is just one multiplication problem well remember the reason we have to answer lines is that we're pretending that we're doing two separate multiplication problems we treated it like it was 6 x 300 4 and 4 * 324 but since the four was in the tens place we had to put an extra zero in our second answer since it would really be the answer 40 x 3 24 now as I mentioned earlier all we have to do to get the final answer is that those two answers together and the great news is that those answers are already stacked like an addition problem should be so we can just draw a line below them and stick a plus sign on the left side now we can add them call him by column starting from the ones place like we did in the multi digit addition video for plus 0 equals 44 plus 6 equals 10 so we carry the one one plus 9 + 9 equals 19 so we carry the one again one plus one plus two equals four and then our last answer digit is just one our final answer is a pretty big number 14900 for let's double-check with a calculator to make sure we got it right yep that's exactly what you get when you multiply 324 by 46 okay I know that procedure is kind of complicated so you're frustrated if you don't get it right away just take some time and practice to really get the hang of it and you can always re watch this video if you need to own if you romantic subscriber be sure to check out the extra problems I work through in the prob with Rob video example after that you can try some of the exercises on your own thanks for tuning in to Math Antics and I'll next time learn more at Math Antics

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Multiplication by 2 digit

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