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

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


Math Antics - Adding Mixed Numbers - By



Transcript
00:03 Uh huh . Hi , I'm rob . Welcome to
00:07 Math Antics . In this lesson , we're going to
00:09 learn how to add mixed numbers . If you're not
00:11 quite sure what mixed numbers are then you should definitely
00:14 watch our video called Mixed numbers first . As you
00:17 remember , a mixed number is a combination or some
00:20 of a whole number and a proper fraction . And
00:23 for this lesson it's going to be important to remember
00:25 that even though the plus symbol isn't usually shown between
00:28 those two parts of a mixed number there being added
00:30 together . Three and 1/4 means three plus 1/4 two
00:35 and 5/8 means to plus 5/8 . And here's why
00:38 that's so important to remember . Let's say you're given
00:41 a problem where you need to add the whole number
00:43 two to the mixed number three and 1/4 . If
00:46 you know that three and 1/4 is the same as
00:48 three plus 1/4 then you can see that The problem
00:51 is really two plus three plus 1/4 . Well that's
00:55 easy . All you have to do is add the
00:56 two in the three to get five and you'll have
00:58 five plus 1/4 which is the mixed number five and
01:01 1/4 . So if you need to add a whole
01:04 number two , a mixed number , you can just
01:06 add the whole number of parts and you're done .
01:08 Okay . But what if you need to add a
01:10 mixed number to a fraction ? Like in the problem
01:12 one and 3/8 plus 1/8 . Again , if you
01:15 remember that one and 3/8 means one plus 3/8 then
01:19 you can see that this problem is really one plus
01:21 3/8 plus 1/8 . That looks pretty easy . Also
01:25 3/8 and 1/8 are what we call like fractions ,
01:28 they have the same denominator and can be added easily
01:31 . 3/8 plus 1/8 equals 4/8 . So our answer
01:35 is simply the mixed No . one and 4/8 .
01:38 Oh , but you might notice the fraction part can
01:41 be simplified . 4/8 simplifies to one half . So
01:45 we should write our answer as one and one half
01:47 instead . It's not mathematically wrong if you don't simplify
01:50 a fraction . But teachers and tests usually require you
01:53 to simplify whenever you can . So it's a good
01:55 habit to get into notice that in each of those
01:58 examples we just added whole numbers to whole numbers and
02:01 fractions two fractions . And it works the same way
02:04 when adding a mixed number to a mixed number ,
02:06 like two in 1/5 Plus four and 2/5 . Again
02:10 let's show our mixed numbers with the plus signs .
02:12 So we can see the real problem . Two plus
02:15 1/5 plus four plus 2/5 . Because all of these
02:19 parts are being added . In addition has the community
02:21 of property . It really doesn't matter what order we
02:24 do the addition that means we can rearrange this problem
02:27 to make it simpler . Now we have two plus
02:31 four plus 1/5 plus 2/5 adding the whole numbers is
02:35 easy to plus four equals six . And adding these
02:38 like fractions is easy to 1/5 plus 2/5 equals 3/5
02:43 . That leaves us with six plus 3/5 which is
02:46 the mixed number , six and 3/5 . So when
02:49 you add mixed numbers , you can just add the
02:51 whole number parts to get the whole number of the
02:53 answer and you add the fraction parts to get the
02:55 fraction part of the answer . That's why in a
02:58 lot of math books you'll see the addition of mixed
03:00 numbers written in a stacked form like this . This
03:03 is similar to the way you would stack multi digit
03:05 numbers up to add them . And it helps you
03:07 remember that you can add the fraction parts and the
03:09 whole number of parts in two separate columns and write
03:12 your answer below the answer line , just like a
03:14 multi digit edition . And do you remember how in
03:17 multi-digit edition if a column of digits added up to
03:20 10 or more you had to carry or regroup to
03:23 the next column ? Well something similar to that can
03:26 happen when adding mixed numbers . Sometimes adding the fraction
03:30 parts of two mixed numbers actually affects the whole number
03:33 part of the answer to see what I mean by
03:35 that let's say you hosted a massive pizza party for
03:38 all your friends . Hey man , this is a
03:40 great party . You've got some really cool friends .
03:43 Hey thanks . You should hang out with this more
03:45 often . I think you'd really fit in . Mhm
03:48 . After the party ended , you had one and
03:52 3/8 cheese pizzas left over and one and 5/8 .
03:55 Pepperoni pizzas left over . What's the total amount of
03:58 leftover pizza ? Well , we just need to add
04:01 those two mixed numbers together . Let's stack them .
04:04 Like I just showed you and add them calling my
04:05 column 3/8 plus 5/8 equals 8/8 and one plus one
04:10 equals two . So the answer is two and 8/8
04:14 . Ah But do you see what happened ? The
04:16 fraction parts of the two mixed numbers combined to form
04:19 what I call a whole fraction 8/8 . And we
04:22 know that 8/8 simplifies to one . So having two
04:26 plus 8/8 is the same as having two plus one
04:29 , which is three we added to mixed numbers together
04:32 and ended up with the whole number three . And
04:34 our leftover pizza shows us that we got the answer
04:37 right ? Here's another example that shows how the fraction
04:40 parts can affect the whole number part of the answer
04:43 when adding mixed numbers one and 3/7 plus two and
04:46 5/7 . This time we use the community of property
04:49 to rearrange the addition and then we had the whole
04:52 number of parts one plus two equals three and then
04:55 we'll add the fraction parts 3/7 plus 5/7 equals 8/7
05:00 . So the answer we get is three and 8/7
05:03 . But do you notice something funny about the fraction
05:05 part of that answer ? It's an improper fraction which
05:08 means that its value is greater than one . And
05:11 it's really bad form to leave an improper fraction in
05:13 a mixed number like this because as we saw in
05:16 the last video , the improper fraction itself can be
05:19 converted into a mixed number . 8/7 contains a whole
05:23 fraction that we can simplify out of it . It's
05:25 the same as 7/7 plus 1/7 . And since 7/7
05:30 equals one that gives us the mixed number one and
05:33 1/7 . So just like in the last example we
05:37 can add that extra one to the whole number part
05:39 of our answer which gives us four and 17 That's
05:42 a much less confusing answer than three and 8/7 .
05:45 Which almost sounds like it's less than four but it's
05:48 actually more than four . Are you getting it so
05:51 far adding mixed numbers is pretty easy when you realize
05:54 that you can just add the whole number of parts
05:56 and the fraction parts separately . And then just watch
05:59 for cases where the fraction parts add up to more
06:01 than one . But there are cases where adding mixed
06:04 numbers can get a little bit tougher . All of
06:07 the examples we've seen so far had fraction parts that
06:10 were like fractions . But what if you had to
06:12 add two mixed numbers with unlike fractions like this problem
06:16 ? One and one half plus two and 1/4 .
06:19 If we rearrange the problem as usual , we see
06:21 that the whole numbers are still easy to add one
06:24 plus two equals three , but the fractions have different
06:27 denominators , we can't add them until we change them
06:30 so that the bottom numbers are the same . We
06:32 cover how to change fractions so that they have the
06:35 same bottom number or a common denominator and other videos
06:38 that you may want to watch if the steps I'm
06:40 about to do seem new to you . four is
06:42 a multiple of two , so four is going to
06:44 be a good choice for a common denominator to change
06:47 one half into fourths will multiply it by the whole
06:50 fraction , 2/2 . On the top we have one
06:53 times two which is two . And on the bottom
06:56 we have two times two which is four just like
06:58 we want . So now we have 2/4 plus 1/4
07:02 which equals 3/4 . That means the answer to this
07:05 problem is three and 3/4 . That wasn't so bad
07:08 after all . Let's try one more example where we
07:11 need to change unlike fractions into like fractions in order
07:13 to add the mixed numbers three and two thirds plus
07:16 four and 3/4 . After rearranging the parts , we
07:20 see that we need to add three and four which
07:22 is seven and we also need to add two thirds
07:24 and 3/4 . Since these are unlike fractions , we
07:27 need to change them three and four are not multiples
07:30 of each other . So it looks like using the
07:32 easiest common denominator will be our best option here Three
07:35 times four equals 12 . So that will be our
07:37 new denominator . To convert two thirds . We multiply
07:41 it by 4/4 which gives us the new equivalent fraction
07:44 8/12 . And to convert 3/4 we need to multiply
07:48 it by 3/3 , which gives us the new equivalent
07:51 fraction 9/12 . Now that we have like fractions ,
07:55 we can add them easily . 8/12 plus 9/12 equals
07:59 17/12 . And that gives us seven and 17 12th
08:03 as our answer . But once again , the fraction
08:06 part is improper . So we have to simplify it
08:08 because its value is greater than one , 17/12 is
08:12 the same as 12/12 plus 5/12 which is the mixed
08:16 number . One and 5/12 . We need to add
08:19 that one to our whole number . Part seven plus
08:22 one equals eight , which means our final answer is
08:25 eight and 5/12 . All right . That should give
08:28 you a pretty good idea of how to add mixed
08:30 numbers . You can add the whole number of parts
08:32 and the fraction part separately , but the fraction part
08:35 of the answer may affect the whole number part .
08:37 If its value is one or greater . And remember
08:40 if the fraction parts have different denominators , you'll need
08:43 to change them to have a common denominator before you
08:45 can add them with complicated arithmetic like this . It's
08:49 important to practice what you've learned . So it'll really
08:51 make sense . So be sure to try some exercise
08:54 problems on your own . As always . Thanks for
08:56 watching Math Antics and I'll see you next time learn
09:00 more at Math Antics dot com .
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