Math Antics - Subtracting Mixed Numbers - Free Educational videos for Students in K-12 | Lumos Learning

Math Antics - Subtracting Mixed Numbers - Free Educational videos for Students in k-12


Math Antics - Subtracting Mixed Numbers - By Mathantics



Transcript
00:03 Uh huh . Hi I'm rob . Welcome to Math
00:07 Antics . In our previous lesson we learned how to
00:10 add mixed numbers and in this lesson we're going to
00:12 learn how to subtract them . Subtraction is always a
00:15 little trickier than addition because subtraction does not have the
00:19 community of property . That means that the order of
00:21 the numbers you're subtracting matters and you can't switch it
00:24 like you can with addition subtraction is also tricky because
00:28 if you try subtracting a number from a smaller number
00:30 like 1 -5 you get a negative answer . Fortunately
00:34 we're not going to cover any problems that give negative
00:36 answers in this video . But as you'll see in
00:38 a few minutes there are cases where it seems like
00:41 you need to subtract a bigger number from a smaller
00:43 one at first all of this means that subtracting mixed
00:47 numbers can be quite a bit more complicated than adding
00:50 them . But don't worry we'll take it one step
00:52 at a time and it will help a lot if
00:54 you make sure that you have a good understanding of
00:56 topics like adding mixed numbers , subtracting fractions , order
01:00 of operations and multi digit subtraction . Because this lesson
01:03 built on all of those concepts . Okay to see
01:07 why subtracting mixed numbers is trickier than adding them .
01:10 Let's have a look at two problems side by side
01:12 . Five plus two and one third and five minus
01:15 two and one third . We learned how to do
01:17 problems like the first one in the previous video about
01:20 adding mixed numbers since two and one third just means
01:23 two plus one third . We learned that we could
01:25 rewrite the problem like this and simply add up the
01:28 whole number of parts to get the whole number part
01:30 of the answer . Five plus two is seven so
01:33 the answer is seven and one third . But if
01:36 we try to do the same thing with subtraction we're
01:38 going to get the wrong answer . If we rewrite
01:41 two and one third as two plus one third ,
01:43 it looks like we could just subtract the whole numbers
01:46 five minus two is three which leaves three plus one
01:48 third or three and one third as the answer .
01:51 But it turns out that's not correct . So what
01:54 did we do wrong ? Well when we subtract a
01:56 mixed number , we need to subtract the entire mixed
01:59 number . We need to subtract the whole number part
02:01 and we need to subtract the fraction part But we
02:04 didn't subtract the 1/3 , we added it . That's
02:07 because when we rewrote the mixed number as a sum
02:10 of a whole number and a fraction we forgot or
02:13 we didn't realize that they form a group , we
02:16 just put the two plus one third , right after
02:19 the minus sign . And it made it look like
02:21 we should subtract the two and add the one third
02:24 . But we actually should have subtracted both of them
02:26 . One way to avoid that mistake is to use
02:29 parentheses around the mixed number you're subtracting so you remember
02:32 that its parts form a group and you need to
02:34 apply the minus sign to the whole group and you
02:37 can only get rid of the parentheses after you apply
02:40 or distribute the subtraction to each member of the group
02:43 like this minus two minus one third . Now that
02:47 we have the problem written correctly , we'll get the
02:49 right answer . If we do these math operations going
02:52 from left to right , we have 5 -2 which
02:55 is three . But then for the last step we
02:57 need to subtract one third from three . That might
03:01 seem hard to do unless you remember what we learned
03:03 about whole fractions . In the last video when adding
03:06 mixed numbers , sometimes we'd get an answer like this
03:09 two and three thirds , but since three thirds is
03:12 what I call a whole fraction , its value is
03:14 just one . And we learned that we could simplify
03:17 an answer like that . Two and three thirds is
03:19 two plus one which is three . Well , how
03:22 about if we just do that same process in reverse
03:25 instead of simplifying let's unseen cliff . I we're trying
03:29 to take one third away from three . Right ?
03:31 So let's rewrite three as two plus one and then
03:34 let's rewrite two plus one is two plus 3/3 .
03:37 Does the problem look easier to do . Now we
03:40 converted part of the whole number into the whole fraction
03:43 3/3 . And we already know how to subtract fractions
03:46 3/3 minus 1/3 is to over three . So that
03:50 means our final answer is 2.2/3 . So as you
03:54 can see , subtracting mixed numbers can be a little
03:56 complicated . But not all problems are that hard .
03:59 Some are pretty easy like this . one , six
04:02 and 4/5 minus one and 3/5 . We still need
04:05 to remember that the mixed numbers form groups . So
04:08 we have to subtract both parts , but that's where
04:11 the stacked format that we learned about in the last
04:13 video can really help us out . Since the order
04:16 of a subtraction problem is important . We need to
04:18 be sure to put the mixed number that we're starting
04:20 with on top and the mixed number that we're taking
04:23 away on the bottom and doing that helps us remember
04:26 that both parts of a mixed numbers are being subtracted
04:29 . Even if we don't put parentheses around them .
04:31 To remind us that's because we'll subtract the parts column
04:34 by column , just like we would and multi digit
04:37 subtraction , we'll subtract the fraction on the bottom from
04:40 the fraction on the top and then we'll subtract the
04:42 whole number on the bottom from the whole number on
04:44 the top . 4/5 minus 3/5 is 1/5 And 6
04:49 -1 is five . So the answer is just five
04:53 and 1/5 . See that really was easy and that's
04:56 why I recommend using stack form whenever you can for
04:59 subtracting mixed numbers . It will help you remember that
05:01 both parts of a mixed numbers are being subtracted without
05:04 having to worry about groups or parentheses . But even
05:08 though the stack form is a great way to keep
05:10 from getting confused about groups , it doesn't make every
05:12 problem quite that simple . For example . Let's try
05:15 the problem . Five and 1/7 minus two and 3/7
05:19 . Unless you stack form again , we're starting out
05:22 with five and 1/7 . So it goes on top
05:24 and two and 3/7 goes on the bottom . But
05:27 when we try to subtract the fractions column you'll see
05:29 that we have a little problem . 1/7 is less
05:32 than 3/7 so we can't subtract it without getting a
05:35 negative number which we'd really like to avoid . So
05:38 what do we do now ? Well do you remember
05:41 what you do in multi digit subtraction ? When you
05:43 have to subtract a bigger digit from a smaller one
05:45 , yep you borrow or regroup from the column to
05:49 the left . And we can do something really similar
05:51 to that with mixed numbers . We can make the
05:54 fraction part of a mixed number bigger by borrowing from
05:57 the whole number part . In the video about adding
06:00 mixed numbers . We learned that a mixed number with
06:03 a fraction part . That's improper is bad form because
06:06 you can simplify out a whole fraction and then add
06:08 it to the whole number part . Well we can
06:11 do that process in reverse also . We can subtract
06:14 out one as a whole fraction from the whole number
06:17 part and add it to the fraction part to get
06:19 an improper fraction . And even though that's considered bad
06:22 form , it's ok because it's not our final answer
06:25 and it helps us subtract the fraction column without getting
06:28 a negative fraction . In this example we do that
06:31 by changing the whole number part five into four plus
06:34 one and then changing four plus one into four plus
06:37 7/7 . And finally we can combine that 7/7 with
06:42 the 1/7 to get 8/7 . now the fraction on
06:45 top is big enough to subtract 3/7 from 8/7 minus
06:50 3/7 is 5/7 . And then we just need to
06:53 subtract the whole number of parts . The top hole
06:56 number used to be five but we borrowed from it
06:59 . So now it's 44 minus two equals two .
07:02 So our answer is two and 5/7 . Let's try
07:05 another example to make sure you've got it . And
07:07 let's make it a story problem this time . Suppose
07:10 there's this guy who's a builder named rob and suppose
07:13 he needs to fix something by subtracting the mixed number
07:16 one and 5/8 from six and 1/8 . Can you
07:18 fix it ? Yes , I can . Well ,
07:22 at least with the help of my trusty cat ,
07:23 Richard , where did that rascal runoff to Richard ?
07:27 Richard ? Oh well the first thing we need to
07:30 do is put these in stacked form with the number
07:33 I'm taken away on the bottom . Then I need
07:36 to subtract the fractions . But I notice that the
07:38 fraction on top is less than the fraction on the
07:41 bottom . So I need to make the fraction on
07:43 top bigger by borrowing from the whole number part .
07:46 I can replace the six with five plus one and
07:49 I can replace five plus one with five plus 8/8
07:53 . To get the whole fraction I need to add
07:55 to the top fraction 8/8 plus 1/8 is 9/8 .
08:00 So now I can subtract the fraction column because the
08:02 fraction on top is bigger . 9/8 minus 5/8 is
08:07 4/8 . And then I can subtract the whole numbers
08:10 five minus one is four . So the answer is
08:13 four and 4/8 . Does that look right to you
08:15 ? Richard ? You're right . Four eights can simplify
08:19 to one half . So my final answer is four
08:22 and one half . Thanks for your help . Richard
08:25 . Good job rob the builder . So now you
08:27 know how to subtract mixed numbers . Some problems will
08:30 be easy . Like our second example where you can
08:32 just subtract the fraction parts and the whole number parts
08:35 . But in other problems you may need to borrow
08:37 or regroup using that unseen cliff eyeing procedure . And
08:41 remember that the stacked form is a great way to
08:44 keep everything straight . Of course you may also need
08:47 to solve problems where the mixed numbers have unlike fractions
08:50 and you'll need to change them into like fractions before
08:52 you can subtract . But that works the same way
08:55 as you saw in the last video so you already
08:57 know how to handle that . I know I'm always
08:59 saying it , but that's because it's true . The
09:01 way to really learn math is to practice by doing
09:04 some problems on your own . As always . Thanks
09:06 for watching Math Antics and I'll see you next time
09:09 , learn more at Math antics dot com
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