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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