Math Antics - Multi-Digit Multiplication Pt 2 - Free Educational videos for Students in K-12

Math Antics - Multi-Digit Multiplication Pt 2 - By mathantics

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00:03	Uh huh . Hi , welcome to Math Antics .
00:08	In our last video we learned the basics of multi
00:11	digit multiplication . We learned how to multiply a multi
00:14	digit number by a one digit number . But in
00:17	this video we're going to take it to the next
00:19	level . We're going to learn how to multiply a
00:21	multi digit number by another multi digit number . You
00:26	remember the procedure for multiplying when we have a one
00:29	digit bottom number . Right ? You break up the
00:31	problem into a series of multiplication steps , one for
00:34	each of the top digits . And in each step
00:38	you just multiply the bottom digit by a top digit
00:41	, starting with the ones place and working your way
00:43	left until you've multiplied all of the digits . Well
00:47	when the bottom number of your multiplication problem also has
00:50	more than one digit . You have to do that
00:52	same procedure we learn for each bottom digit . For
00:56	example , if you have a two digit bottom number
00:59	, you multiply the first digit by each top digit
01:02	and then you multiply the second digit by each top
01:05	digit . That means you're gonna have twice as many
01:08	steps to do and it means you're going to get
01:11	two different answers . What ? How can we have
01:14	two different answers for the same problem ? Now ,
01:17	don't panic . The different answers are just what you
01:20	get from doing the multiplication procedure for each digit of
01:23	the bottom number separately . In fact , it's kind
01:26	of like we're pretending we have two separate multiplication problems
01:30	that each have a one digit bottom number . Which
01:32	is nice because I kind of like pretending no luke
01:37	. I am your father . No , that's impossible
01:44	. Uh No . No . Well , I mean
01:53	it's nice because we already know how to multiply when
01:56	we have a one digit bottom number . Wet .
01:58	But then what will we do with the two different
02:00	answers ? We're gonna get ? Well , it turns
02:02	out that all we have to do is add them
02:04	together . Once we're finished doing all of our multiplication
02:07	steps , are you ready to see an example ?
02:10	It should make a lot more sense when you see
02:12	the procedure in action . So let's multiply 324 A
02:16	three digit number by 46 a two digit number .
02:20	Now . Remember we're going to do the same procedure
02:22	that we did in the last video for each of
02:24	the bottom digits . And since our top number has
02:27	three digits , that means there'll be three multiplication steps
02:30	for the first digit and three steps for the second
02:33	digit . Fortunately we can start the same way we
02:36	would if the bottom number only had one digit by
02:39	just ignoring the second digit until we finish the first
02:42	three steps . All right . So our first multiplication
02:45	step is six times four which is 24 . And
02:49	since 24 has two digits , we can leave the
02:51	four in our answer line but we need to carry
02:53	the two and put it above the next top digit
02:56	that we're going to multiply . So the next step
02:59	is six times two which is 12 . But we
03:02	have to add in the two that we carried .
03:04	So 12 plus two gives us 14 . That's another
03:07	two digit answer . So we leave the foreigner answer
03:09	line and carry the one up above the next digit
03:12	that we're going to multiply . And our third step
03:15	is six times three which is 18 . And then
03:18	we add in the one that we carried when we
03:19	get 19 . This time we can leave both digits
03:22	of the 19 and our answer line because there's no
03:25	more multiplication steps to do well at least there's no
03:28	more steps for the first digit . Remember we still
03:31	have that other bottom digit that we've been ignoring now
03:34	we have to multiply it by each of the top
03:36	digits also which means we have three more steps to
03:39	do . It also means that we get a second
03:42	answer . And because we'll get a second answer we
03:44	need to start a second answer line for the next
03:46	set of steps . We're going to put our new
03:49	answer line just below the first one . So this
03:51	answer line comes from our first bottom digit and this
03:54	answer line will come from our second bottom digit at
03:58	the very end . After we're all done multiplying we're
04:00	going to add the two answers together . But for
04:02	now let's continue with the second set of multiplication steps
04:06	. Oh and I almost forgot to tell you there's
04:09	something very important that you need to do when you
04:12	start the second set of steps because the second digit
04:15	of the bottom number is in the tens place .
04:17	That means that even though the digits only a four
04:20	, its value is really 40 That's 10 times bigger
04:23	. So the answer we get should also be 10
04:25	times bigger . So before we start multiplying we need
04:29	to put a zero in the first spot of our
04:31	answer line . So it's 10 times bigger . That
04:34	means that all the other answer digits we put there
04:36	are shifted to the next bigger number place . And
04:40	just so you know if we happen to have a
04:42	third bottom digit , we would get a third answer
04:44	line and we need to shift the third answer over
04:46	by two zeros because it would be 100 times bigger
04:50	. And if we had 1/4 digit there'd be 1/4
04:52	answer line shifted over by three zeros . And if
04:56	we had 1/5 bottom digit there would be 1/5 answer
04:58	line shifted over by four zeros . See the pattern
05:02	boy , am I glad we've only got two bottom
05:04	digits . And now you see why we always put
05:06	the number with the fewest digits on the bottom when
05:09	we're multiplying . But let's continue with our problem .
05:12	Let's do the first step of our second bottom digit
05:15	. We multiply that digit for by the once placed
05:18	digit of the top number , which is also a
05:21	four . Four times four gives us 16 . And
05:24	that goes in our second answer line right next to
05:26	the extra zero we put there Now remember because 16
05:30	is a two digit answer we have to carry .
05:33	And we always put the digit we carry above the
05:35	next top digit that will multiply . But before we
05:38	can carry it up to that place we need to
05:40	cross out all the digits that we carried from our
05:42	first answer line because we've already used them . We
05:45	don't want to accidentally add them to our second answer
05:47	line There . So now we can carry our one
05:50	to the top of the 10s place . Which means
05:52	it will go on the column above this too because
05:54	that's the next top digit that will multiply with our
05:57	bottom digit . Now we can do the next multiplication
06:00	step four times two gives us eight and then we'll
06:02	add the one that we carried and we get nine
06:05	. Great . Finally a one digit answer . So
06:08	we don't have to carry this time . We just
06:10	write the nine and the next place of our answer
06:12	line and move on to the next step . The
06:14	next and last multiplication step is four times three which
06:19	is 12 . And since there's no more steps we
06:21	can write both digits and our second answer line .
06:24	All right . We're finally done with all our multiplication
06:28	steps . We multiply each bottom digit by each top
06:31	digit , just like we're supposed to . But now
06:34	what do we do ? We have to answer lines
06:37	? But this is just one multiplication problem . Well
06:40	, remember the reason we have to answer lines is
06:42	that we're pretending that we're doing two separate multiplication problems
06:46	. We treated it like it was six times 324
06:49	and four times 324 . But since the four was
06:52	in the 10s place , we had to put an
06:54	extra zero in our second answer since it would really
06:57	be the answer from 40 times 324 . Now ,
07:00	as I mentioned earlier , all we have to do
07:02	to get the final answer is that those two answers
07:05	together and the great news is that those answers are
07:08	already stacked up . Like an addition problem should be
07:11	so we can just draw a line below them and
07:13	stick a plus sign on the left side . Now
07:15	we can add them column by column . Starting from
07:18	the ones place just like we did in the multi
07:20	digit edition video , four plus zero equals four ,
07:24	four plus six equals 10 . So we carry the
07:27	11 plus nine plus nine equals 19 . So we
07:32	carry the one again . One plus one plus two
07:35	equals four . And then our last answer digit is
07:38	just one . There are final answer is a pretty
07:41	big number . 14,904 . Let's double check with a
07:45	calculator to make sure we got it right , Yep
07:50	, that's exactly what you get when you multiply 324
07:54	x 46 . Okay . I know that procedure is
07:57	kind of complicated , so don't get frustrated . If
08:00	you don't get it right away , just take some
08:02	time and practice to really get the hang of it
08:04	, and you can always re watch this video if
08:06	you need to . And if you're a math antics
08:08	subscriber , be sure to check out the extra problems
08:11	I work through in the problem with rob video .
08:12	Examples after that . You can try some of the
08:15	exercises on your own . Thanks for tuning into Math
08:18	antics , and I'll see you next time learn more
08:21	at Math Antics dot com .

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