Multiplying Decimals - Free Educational videos for Students in K-12 | Lumos Learning

Multiplying Decimals - Free Educational videos for Students in k-12


Multiplying Decimals - By Anywhere Math



Transcript
00:0-1 While in your room is 5.6 m by 3.2 m
00:04 . A small can of paint will cover about 20
00:08 m2 . Do you have enough paint to paint your
00:11 wall ? Welcome to anywhere . Math . I'm Jeff
00:31 , Jacobson . And today we're gonna talk about multiplying
00:34 decimals . All right , so let's talk about that
00:37 wall . Uh , it was 5.6 m by 3.2
00:41 m . So if you think drawing a picture ,
00:46 You know , this is gonna be about 5.6 m
00:49 by 3.2 m , we want to know if we're
00:53 gonna have enough paint . So what we need to
00:54 find is area . That's what we're covering with the
01:00 paint . So to do that , we're just gonna
01:02 multiply right ? Lake times with uh , so 5.6
01:05 times 3.2 5.6 times 3.2 . Now , if we
01:14 were going to estimate this , that would be about
01:16 six , that would be about three . six times
01:23 3 is about 18 . So hopefully If our estimation
01:28 is somewhere accurate , uh we should have enough .
01:31 So let's see , let's just multiply six times two
01:34 is 12 . 10 plus one is 11 0 .
01:40 Uh 18 . Another 1 , 15 plus one is
01:44 16 2971 . Now , if you're thinking well where
01:52 This is decimals , right , where's my decimal point
01:54 gonna go ? You think it should be close to
01:56 18 ? That's what point goes there , 17.92 .
02:01 Don't forget your units . It was meters times meters
02:04 . So that becomes meters squared , which makes sense
02:07 for area . So 17.92 m squared . The small
02:13 can of paint could cover 20 m squared or 20
02:16 m2 . So do we have enough ? And the
02:18 answer is yeah . Yes . Okay , so let's
02:23 try another example . All right . Here's example 1
02:26 , 6 times 3.91 . Now , when you're dealing
02:30 with decimals , it's always a good idea to estimate
02:34 . And the reason is because it can be very
02:36 easy to put the decimal point in the wrong spot
02:40 , which completely changes your answer . Uh So if
02:43 you estimate that will help kind of catch those heirs
02:46 . So if we're going to estimate this would be
02:53 six is okay 3.91 , we can just round up
02:57 to four . So we're thinking Our products should be
03:02 around 24 . So let's see now when you're multiplying
03:07 with decimals , the trick is to treat it like
03:11 the decimal isn't there set up the problem like you
03:14 would a normal multiplication problems . So what I'm saying
03:17 is Don't think of this as 3.91 . Imagine it's
03:21 just 391 Times six . Well if it was that
03:26 You would put the 391 mm on top , Multiply
03:32 it by six . That's how you would set it
03:35 up . Right . Um And we can do that
03:38 because order doesn't matter with multiplication because of the community
03:41 of property . So we can do that once you
03:43 set it up like that , then go ahead and
03:45 put the decimal point back in . Just don't forget
03:49 that . And now we just multiply like normal .
03:51 Um that's gonna be 66 times nine is 54 carry
03:57 the 56 times three is 18 plus five is 23
04:02 . Now this is the last step and it's really
04:07 important . Where does the decimal point go in ?
04:09 Our answer ? Can all you have to do ?
04:13 Yeah is look at how many places you have after
04:16 the decimal points in your problem . So here we've
04:21 got the nine and the one two places after the
04:25 decimal and 3.91 . So that's two six . Does't
04:29 have any right . The decimal point if we want
04:32 it would be here . There's nothing over there so
04:36 that's going to be zero . So in our answer
04:40 we need two decimal places . Yeah . Okay .
04:48 So yeah , 12 The decimal point goes there and
04:55 that is our product . That's our answer . 23.46
05:00 . And let's check , does that make sense with
05:03 our estimate ? Yeah , it's really , really close
05:05 so we know we're good . Okay , let's try
05:08 another one . Another example Here is example , #
05:13 two , times 100 . Um When you're multiplying by
05:17 powers of 10 , Uh like 100 is it's 10
05:22 times 10 or 10 squared ? There's a really nice
05:27 shortcut that you can make if you remember our whole
05:30 number system is Base 10 . It's based on powers
05:34 of 10 . So if you think well yeah ,
05:39 Take it simpler . Well what's two times 10 ?
05:42 Well that's just 20 two times 100 adds 200 .
05:48 two times 1000 . That's 2000 . Okay , um
05:54 That's very simple because it's just a whole number .
05:56 All you do is add zeros at the end ,
05:58 right ? You do the one times the two and
06:00 then add however many zeros you have . Uh But
06:03 you can also think of it , well if there
06:05 was a decimal here , where would it be ?
06:09 Well with whole numbers we can put a decimal right
06:11 after . Okay . And now from here to here
06:18 , what happened to the decimal ? It went from
06:20 here over one And you just filled in a zero
06:25 Here . It was times 100 . So we're moving
06:28 it twice . Right , filled in those zeros here
06:32 times 1000 . You're moving the desperate 10000.3 times When
06:37 you're multiplying by powers of 10 , you're moving the
06:40 decimal point to the right And you just got to
06:43 think well how many powers of 10 , 10 ?
06:45 You're moving at once ? 10 is the same as
06:49 10 to the first power . 100 is 10 square
06:54 to your moving it twice . 1000 is 10 cubed
06:58 . You're moving it three times . You can also
07:00 think how many zeros are there , That's how many
07:02 times you're moving it . So with that in mind
07:07 this problem becomes much , much easier . I'm multiplying
07:11 by a power of 10 . I'm gonna move it
07:14 to the right because I'm multiplying And there's two zeros
07:18 or I can think of that as 10 squared to
07:21 the power of two . So I'm going to move
07:23 it once twice . So that becomes 135 . Right
07:31 ? Very simple . Here's something to try on your
07:33 own . All right . Here's our last example 3.1
07:41 times 0.05 . Now , if you remember at the
07:45 beginning of the video I said when you're multiplying with
07:48 death was pretend the decimal points aren't there ? And
07:52 set up the problem like that . So I'm not
07:55 going to think of this as three point when I'm
07:56 going to think of it as 31 times 005 .
08:01 Um Now there's a couple ways I could put the
08:05 31 on top or I could put the 005 on
08:09 top . Me personally I like to do whichever ones
08:13 have the most digits . I like to put that
08:15 on top But it doesn't matter . You can do
08:17 it either way you want . So I'm gonna set
08:19 this up at 005 times 31 . Okay , pretend
08:28 the decimal points aren't there ? And set it up
08:29 that way . Now that I've set it up ,
08:32 I'm going to put them back so I don't forget
08:34 . That's what point is there ? That's my point
08:36 is there . Now you'll notice these decimal points aren't
08:42 lined up . And that is the main difference between
08:46 adding subtracting decimals . Where the decimal points have to
08:49 be lined up and multiplying with decimals where they don't
08:54 . Okay , that's the main thing to remember .
08:56 So you should write that down when you're multiplying with
08:59 decimals . The decimal points do not have to be
09:02 lined up . Okay , so that's how we're setting
09:05 it up and now I just multiply One times five
09:08 is 5 . That's going to be 00 at zero
09:13 . Three times five is 15 carry the one that
09:16 zero plus one is 10 Add them up . I
09:21 get 5510 . Now the last step Is to count
09:30 my decimal places . This here , 0.05 has to
09:35 that has won Adam together . My answer should have
09:39 three decimal places . So 123 My aunt , my
09:45 decimal point goes right there And that is my answer
09:50 . Now . If I want to check if I
09:52 want to estimate , well if I'm going to estimate
09:55 that would be round of three times that's very close
09:59 to zero . So three times zero is zero .
10:01 Is my answer pretty close to zero . Yeah it
10:05 is . So that's the last example Again , remember
10:09 when you're multiplying decimals do not line them up ?
10:12 Sometimes they will line up just you know because they
10:15 have the same decimal places but they don't need to
10:18 be okay so that's the main difference . Here's some
10:21 more to try and europe . Thank you for watching
10:28 . And as always if you like this video please
10:30 subscribe .
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