Adding Fraction & Mixed Numbers w/ Common Denominators - Part 1 - [23] - By Math and Science
Transcript
| 00:00 | Hello . Welcome back . The title of this lesson | |
| 00:02 | is called adding mixed numbers with like denominators part one | |
| 00:06 | . So we're going to be adding fractions here but | |
| 00:09 | we're going to introduce something slightly additional and it's called | |
| 00:12 | a mixed number . So you know when you have | |
| 00:14 | half of a pizza , right ? That represents less | |
| 00:17 | than one pizza , it's half of a pizza . | |
| 00:18 | We all know that If you have 1/4 or a | |
| 00:21 | quarter of a pizza , you cut the pizza into | |
| 00:23 | four pieces , you have 1/4 1 piece of four | |
| 00:26 | , that's called 1/4 . It's less than a whole | |
| 00:28 | pizza . All of these fractions like 3/4 and one | |
| 00:31 | half and so on , they're all less than one | |
| 00:34 | whole right here , we're going to introduce mixed numbers | |
| 00:37 | . What if I have not just half of a | |
| 00:39 | pizza but what if I have 1.5 piece pizzas ? | |
| 00:43 | What if I have 2.5 pizzas ? That would mean | |
| 00:46 | that I would have to whole pizzas plus an additional | |
| 00:49 | half . Or maybe it's one and three quarters of | |
| 00:53 | a pizza . It would mean I would have one | |
| 00:55 | whole pizza plus three quarters of another pizza . So | |
| 00:59 | a mixed number . Just means that I have some | |
| 01:01 | whole numbers of whatever it is I'm talking about . | |
| 01:03 | But then I also have a fractional part also . | |
| 01:06 | So we're gonna be learning about rick mixed numbers and | |
| 01:08 | we'll also learn how to add them . So let's | |
| 01:10 | talk about for our first problem . Let me write | |
| 01:13 | it down and then we will use the models and | |
| 01:16 | we'll talk about what it means . What if I | |
| 01:17 | have one and 1/4 ? This is a mixed number | |
| 01:21 | . I'll talk about it a little more in just | |
| 01:23 | a second And I'm going to add to that . | |
| 01:25 | Another mixed number . It's called two and 1/4 . | |
| 01:30 | All right . So each of these things , these | |
| 01:32 | are called mixed numbers . The reason they're called Mixed | |
| 01:35 | is because they have whole numbers , the one and | |
| 01:37 | the two these are whole pizzas , like one whole | |
| 01:40 | pizza and this is two whole pizzas . And then | |
| 01:43 | you have the fractional part which is additional or extra | |
| 01:46 | to that . So if I have one and 1/4 | |
| 01:49 | of a pizza , I have one whole entire pizza | |
| 01:52 | . But I also have 1/4 . And here I | |
| 01:54 | have two entire whole pizzas and I have another fourth | |
| 01:57 | . So I'm adding these all together . So just | |
| 02:00 | to see if we can understand this here , the | |
| 02:02 | one and 1/4 means I have one whole pizza that's | |
| 02:06 | represented by this entire whole pizza here . But then | |
| 02:09 | I also have 1 4th additional to that . So | |
| 02:13 | if I cut another pizza into four pieces , 1/4 | |
| 02:17 | 2 4th , 3/4 and 4/4 . But if I | |
| 02:21 | only have one of those four pieces , then that | |
| 02:24 | would be the amount that I would actually have one | |
| 02:26 | and 1/4 . So I'm going to be adding that | |
| 02:30 | to another number here . Another mixed number . This | |
| 02:34 | is called two and 1/4 . So that means I | |
| 02:36 | don't have one pizza entirely hole , I have actually | |
| 02:39 | two of them . So I'm kind of kind of | |
| 02:41 | put this down here just to make it kind of | |
| 02:44 | make it line up . So here I have two | |
| 02:46 | entire pizzas , but I also have 1/4 extra . | |
| 02:49 | So this is what we're adding up here and it's | |
| 02:52 | important in your mind in the beginning we're going to | |
| 02:54 | use the model . So you understand what you're doing | |
| 02:56 | when we start solving a lot of problems , you're | |
| 02:58 | not gonna be drawing all of these things . But | |
| 03:00 | in the beginning it's helpful for us to look that | |
| 03:02 | we have one and 1/4 additional pizza . And then | |
| 03:05 | to Plus 1 4th additional pizza . Now we're adding | |
| 03:09 | all of these together . Now without actually doing any | |
| 03:11 | math at all , how many whole pizzas are you | |
| 03:14 | gonna have if you add all this together ? Well | |
| 03:16 | I have one entire whole pizza here and I'm going | |
| 03:19 | to add it to all of this , which is | |
| 03:20 | two more . So I'm going to have three entire | |
| 03:23 | whole pizzas uh at the end . And then I'm | |
| 03:26 | also going to have to add the fractions together and | |
| 03:29 | that will be part of the answer to . So | |
| 03:31 | without doing anything , I know I'm gonna have at | |
| 03:33 | least three whole pizzas in the end because one plus | |
| 03:36 | two is three . So the way we're going to | |
| 03:38 | be adding mixed numbers is we're going to add the | |
| 03:41 | whole numbers , We're gonna get that new hole number | |
| 03:43 | down here and then we add the fractions and we | |
| 03:45 | get the fractional part . So adding mixed numbers is | |
| 03:47 | very simple . You just add the whole numbers , | |
| 03:49 | you add the fractional parts and then the answer you | |
| 03:52 | get is a new mixed number . Okay , so | |
| 03:55 | all we're going to do is we're going to say | |
| 03:57 | one plus two is let me scoot down here so | |
| 04:00 | that I can have enough room to kind of represent | |
| 04:02 | it all . Uh is going to be 31 plus | |
| 04:05 | two is three . Alright . And then what we're | |
| 04:08 | going to have is 1/4 +14 So let's add this | |
| 04:12 | . We have we have a four on the bottom | |
| 04:14 | and the four on the bottom . Remember to add | |
| 04:15 | any fractions . You need to have the same bottom | |
| 04:17 | number and the denominator in this case we have a | |
| 04:21 | four . So I'm gonna have a four on the | |
| 04:23 | bottom in the top , I have a one plus | |
| 04:25 | a one . So I'm just adding these fractions the | |
| 04:28 | same way as I've done in the past . So | |
| 04:30 | what am I going to have ? I'm going to | |
| 04:31 | have three and one plus one is two out of | |
| 04:34 | four pieces . Now this is the answer . I | |
| 04:36 | have three whole pizzas plus I have two out of | |
| 04:41 | two pieces out of four of another pizza . So | |
| 04:44 | we have a whole part and another fractional part . | |
| 04:46 | This is a new mixed number . But we always | |
| 04:48 | want to simplify our answers is this fractional part , | |
| 04:52 | fully simplified ? Two and four are both even numbers | |
| 04:55 | . So I know I can divide them both . | |
| 04:58 | So the way I'm gonna write this is the whole | |
| 05:00 | part is going to stick around and then the 2/4 | |
| 05:03 | I'm gonna divide both by two because I can divide | |
| 05:06 | top and bottom by any fraction that I want . | |
| 05:09 | You can think of this whole number in this fraction | |
| 05:12 | being kind of linked by an invisible plus side because | |
| 05:16 | when I have one and 1/4 it's one whole pizza | |
| 05:19 | plus 1/4 there's an invisible plus here , the two | |
| 05:21 | and 1/4 is two whole pizzas plus another fourth . | |
| 05:25 | So when I get an answer of three and 2/4 | |
| 05:27 | it's like three plus 2/4 of another pizza . So | |
| 05:31 | they're kind of linked together there . So what am | |
| 05:33 | I going to get from my final answer ? I'm | |
| 05:35 | going to have here three and then uh I'm going | |
| 05:39 | to have two divided by two is one and four | |
| 05:41 | divided by two is two because two times two is | |
| 05:45 | four . So the answer is that I'm thinking that | |
| 05:46 | I'm going to get is 3.5 . So let's see | |
| 05:49 | if this actually works . If I take the one | |
| 05:52 | and a quarter and add 22 and a quarter , | |
| 05:54 | what's going to happen ? Well the whole numbers are | |
| 05:56 | going to be added together , so I'm going to | |
| 05:58 | have three entire whole pizzas here , that parts correct | |
| 06:02 | , and then I'm going to be taking these fractional | |
| 06:04 | parts and adding them as well and look what happens | |
| 06:07 | . The answer you get is 1/4 here's 2/4 2 | |
| 06:10 | 4th , 2 pieces out of four . If I | |
| 06:13 | cut the pizza into four pieces , two pieces out | |
| 06:15 | of four , so the three and 2/4 but then | |
| 06:18 | of course I can represent this uh 2/4 by one | |
| 06:23 | half here . So the answer really that I'm going | |
| 06:25 | to be getting is you can see this is the | |
| 06:28 | same thing as one half , so you can think | |
| 06:30 | of it as three and 2/4 or you can think | |
| 06:32 | of it and kind of move these upstairs and kind | |
| 06:34 | of get rid of them as 3.5 . Which is | |
| 06:37 | exactly the same thing . So , again , when | |
| 06:40 | you're solving these the first time , don't try to | |
| 06:43 | kind of get the answer without doing work . I | |
| 06:45 | mean drawing pictures is nice . I don't but I | |
| 06:47 | don't want you to try to guess the answer . | |
| 06:49 | I want you to solve the problem . We're adding | |
| 06:51 | the fractions and we're adding the whole number separately . | |
| 06:53 | That's all we're doing here . All right . So | |
| 06:56 | let's move on to the next problem . Let's say | |
| 06:58 | we have . Alright for our next problem . We | |
| 07:00 | need to pay extra care because I'm selecting this one | |
| 07:04 | on purpose . What about one and one third ? | |
| 07:07 | And we're going to add to that the number . | |
| 07:10 | One and two thirds . All right . So what | |
| 07:14 | do we do ? This is one whole pizza plus | |
| 07:16 | one third of another pizza . And this is one | |
| 07:18 | whole pizza plus two thirds of another pizza . So | |
| 07:21 | we add the whole numbers together first , then we | |
| 07:24 | add the fractions one plus one , you all know | |
| 07:26 | is two and then the one third and two thirds | |
| 07:30 | . We have the same denominator . So that goes | |
| 07:32 | in the answer and then one plus two . So | |
| 07:35 | we put one plus two here and then what do | |
| 07:37 | we have ? We have to And what does this | |
| 07:41 | come out to ? 3/3 . Now , this looks | |
| 07:44 | like a weird fraction . I want to talk about | |
| 07:46 | this a little bit because I want you to understand | |
| 07:48 | what's really happening here . So the one in one | |
| 07:50 | third , what does that look like ? This is | |
| 07:53 | one whole pizza and then we have a third of | |
| 07:56 | another pizza . Because think about it , This is | |
| 07:58 | one third , two thirds , three thirds . This | |
| 08:00 | is another pizza . Cut into thirds , So that's | |
| 08:02 | what this represents right here . Now this one is | |
| 08:05 | one and two thirds . So this one is going | |
| 08:08 | to be represented by this whole number of one plus | |
| 08:12 | two thirds . Here's one thirds . Here's two thirds | |
| 08:16 | . All right . What do you think is gonna | |
| 08:17 | happen when we add these guys together ? What we're | |
| 08:20 | saying is that we add these together ? What we're | |
| 08:22 | going to have is two whole pizzas and three thirds | |
| 08:26 | . So here's one third , two thirds . The | |
| 08:29 | other third comes in and slots in exactly like this | |
| 08:32 | . What happens here ? This forms a whole new | |
| 08:34 | pizza . So yeah , the answer , you can | |
| 08:37 | talk about it as two and three thirds , but | |
| 08:40 | by now we've been working with fractions enough that when | |
| 08:42 | you should know that when the top and the bottom | |
| 08:44 | number are the same thing , it's just a whole | |
| 08:47 | pizza . one third is one out of three pieces | |
| 08:50 | , two thirds is two out of three pieces , | |
| 08:53 | three thirds is three out of three pieces , which | |
| 08:55 | is just another entire whole pizza . So what's going | |
| 08:58 | on here is this is an entire 3rd pizza right | |
| 09:00 | here , and so what we get for our actual | |
| 09:03 | answer , because we see we have the same number | |
| 09:05 | on the top and the same number on the bottom | |
| 09:07 | , This basically becomes like two plus one more entire | |
| 09:11 | whole pizza . This is a whole pizza here which | |
| 09:14 | is three . Because remember I told you in between | |
| 09:16 | the whole number and the fraction there's like an invisible | |
| 09:19 | plus sign , this is one plus one third of | |
| 09:22 | a pizza , one plus two thirds of a pizza | |
| 09:24 | , this is two plus three thirds of a pizza | |
| 09:27 | , which is two plus one more hole pizza , | |
| 09:29 | which is three . So the answer here is three | |
| 09:32 | . So any time you get an answer where the | |
| 09:35 | top and the bottom number are the same , it's | |
| 09:37 | just another hole and you add it to all the | |
| 09:40 | whole numbers you have and that is what is going | |
| 09:42 | to be the final answer . So as we move | |
| 09:46 | through a lot of these problems , sometimes we are | |
| 09:48 | going to have that situation happened where we have another | |
| 09:52 | whole pop up like that and if that happens , | |
| 09:55 | we'll just handle it as we usually do . All | |
| 09:58 | right now , we're gonna take the training wheels off | |
| 10:00 | just a little bit and start adding these mixed numbers | |
| 10:02 | without using the models . Let's say we have two | |
| 10:05 | and 3/9 and we're going to add to that seven | |
| 10:08 | and four nights . What do we do ? We | |
| 10:12 | add the whole numbers together . Seven plus two is | |
| 10:15 | what ? Seven plus two is nine . So the | |
| 10:18 | whole number part of our answer is 99 whole pizzas | |
| 10:22 | . But here we have the fractional part , we | |
| 10:23 | have the same denominator of nine and we have a | |
| 10:26 | three plus four so we put three plus four . | |
| 10:29 | And so what we get is a whole number of | |
| 10:32 | nine and 799 and seven nights . Okay . So | |
| 10:38 | can we simplify this answer ? Nine and seven nights | |
| 10:41 | ? Can we simplify the fractional part ? Can we | |
| 10:43 | divide the fractional part top and bottom by something to | |
| 10:46 | make that simpler and we can't so the answer is | |
| 10:48 | just nine and seven nights . Remember before when we | |
| 10:50 | added this guy we got three and to force we | |
| 10:53 | treated this fraction like any other fraction , we divided | |
| 10:56 | it to try to simplify it and we got to | |
| 10:58 | a simpler answer in this case , all that we | |
| 11:01 | did was we got down to the answer , we | |
| 11:02 | couldn't simplify it any further . So these problems are | |
| 11:05 | literally going to look like every other fraction problem we | |
| 11:08 | have done , it's just that we have these whole | |
| 11:10 | numbers sitting out in the front that we also need | |
| 11:12 | to add . That's really the only only difference here | |
| 11:15 | , let's say we have five and 1/6 and we're | |
| 11:18 | going to add to that three and 36 What do | |
| 11:22 | we do ? We look at the whole numbers , | |
| 11:24 | we have a five plus three and we know that | |
| 11:27 | five plus three is eight . So that goes in | |
| 11:29 | our answer , we have a common denominator of six | |
| 11:32 | that goes in our answer and then we have one | |
| 11:34 | plus three which is equal to eight and 46 And | |
| 11:40 | we say can we simplify the fractional part of that | |
| 11:43 | ? These are both even numbers . So I can | |
| 11:45 | say eight and 46 I can divide top and bottom | |
| 11:48 | by whatever I want . So I'm gonna divide by | |
| 11:50 | two , divide by two . What am I going | |
| 11:53 | to get ? Eight ? Four divided by two is | |
| 11:56 | two and six divided by two is three . So | |
| 11:59 | I have eight and two thirds and that is the | |
| 12:01 | final answer . So this means if I start out | |
| 12:04 | with five pizzas plus 1/6 of another and I added | |
| 12:08 | +23 pizzas and +36 of another , I'm going to | |
| 12:11 | have eight whole pizzas but I'll have two thirds of | |
| 12:15 | a remaining pizza because when I combine these together and | |
| 12:18 | simplified it comes out and works out to be two | |
| 12:20 | thirds , eight and 2/3 . Alright problem number three | |
| 12:27 | , let's say we have three and 2/11 and we're | |
| 12:31 | going to add to that . Eight and 8/11 . | |
| 12:36 | What do we do first ? We add the whole | |
| 12:38 | numbers 89 10 , 11 , So eight plus three | |
| 12:41 | is 11 . But the common denominator is also 11 | |
| 12:45 | , so that goes in our answer and then we | |
| 12:47 | have eight plus two , which means we have 11 | |
| 12:52 | and then eight plus two is 10 And 11 goes | |
| 12:55 | down here , we have 11 and 10 11th . | |
| 12:59 | So we have 11 whole pizzas in the answer and | |
| 13:02 | then we have 10 out of 11 slices of another | |
| 13:04 | final pizza there in the answer as well . So | |
| 13:08 | it's almost 12 whole pizzas . If it was 11 | |
| 13:11 | out of 11 slices here , this would make another | |
| 13:14 | hole and we would turn this into a 12 , | |
| 13:16 | but we're not quite there . So we just leave | |
| 13:17 | it where we are there . So 10 , 11 | |
| 13:19 | and 10 11 is kind of a weird thing to | |
| 13:22 | say . That's how you say it now , here's | |
| 13:24 | our next problem . What about five and 1/8 ? | |
| 13:28 | And we're going to add to that four and 3/8 | |
| 13:33 | ? What do we do here ? We add these | |
| 13:34 | together , We add the whole numbers first . What | |
| 13:36 | is five plus four ? Five plus four is nine | |
| 13:41 | . Now we have a common denominator of an eight | |
| 13:43 | , so that just goes into our answer and then | |
| 13:44 | we have one plus 31 plus three , so we | |
| 13:48 | have 91 plus three is four , Then we have | |
| 13:51 | eight . Now can we simplify four and eight ? | |
| 13:55 | Of course we could divide top and bottom by two | |
| 13:58 | , But we also realize we can divide by four | |
| 14:01 | . So what we'll do is we'll say nine and | |
| 14:03 | 4/8 . We can divide top and bottom by whatever | |
| 14:07 | we want . So we'll divide this guy by four | |
| 14:09 | and we'll divide the bottom guy also by four . | |
| 14:13 | So we'll get an answer of 94 divided by four | |
| 14:16 | is one and eight divided by four is two . | |
| 14:19 | So the answer will get is 9.5 . So it | |
| 14:22 | doesn't seem like it makes sense . But it does | |
| 14:25 | actually When you think about it , because if I | |
| 14:26 | have five plus four that gives me nine pizzas , | |
| 14:28 | then I have 18 plus 3/8 . That's gonna give | |
| 14:31 | me 48 4/8 of a pizza is four out of | |
| 14:35 | eight slices . Four out of eight slices . It's | |
| 14:38 | the same thing as half of another pizza . That's | |
| 14:40 | why the answer came out to work out to beat | |
| 14:42 | 9.5 . 9 1/2 . All right . I think | |
| 14:48 | we're almost to the halfway point . Let's say we | |
| 14:50 | have six and 4/9 and we'll add to that . | |
| 14:55 | Eight and 5/9 . All right . What do we | |
| 14:59 | have here ? Six plus eight . How do we | |
| 15:01 | add those together ? 9 10 , 11 , 12 | |
| 15:04 | , 13 , 14 . So eight plus six is | |
| 15:07 | 14 . So we have a 14 here and then | |
| 15:09 | we have a fraction , we have the same common | |
| 15:11 | denominator of nine and then we have four plus five | |
| 15:15 | , so four plus five . So we have 14 | |
| 15:18 | and four plus five . Works out to be nine | |
| 15:20 | and then we have nine out of nine . Look | |
| 15:22 | this is the same thing that happened before . You | |
| 15:24 | know , we have one out of nine slices , | |
| 15:26 | two out of nine slices , three out of nine | |
| 15:28 | slices here , we have nine out of nine slices | |
| 15:31 | . So it's an entire new pizza because it is | |
| 15:34 | nine out of nine complete slices of another pizza . | |
| 15:36 | So , what we have here is 14 whole pizzas | |
| 15:39 | plus , like another whole pizza . The +999 is | |
| 15:43 | one whole pizza . You can also think that we're | |
| 15:46 | gonna get into this a little bit later , but | |
| 15:47 | you can also think of fractions as division . I | |
| 15:50 | know this is kind of a new concept , we | |
| 15:52 | haven't gotten into this too much but you can think | |
| 15:54 | of fractions as division , so when you have nine | |
| 15:58 | on the top and nine on the bottom , it's | |
| 15:59 | like nine divided by 99 divided by nine is one | |
| 16:02 | . You already know that . So you can think | |
| 16:03 | of it as nine out of nine slices , give | |
| 16:05 | you one whole pizza or you can think of it | |
| 16:08 | as nine divided by nine which is also another hole | |
| 16:10 | one , 14 plus one is what ? 15 ? | |
| 16:14 | So it doesn't look possible . But when you add | |
| 16:16 | these fractions together , you don't get like a new | |
| 16:18 | fractional answer , You get 15 whole slices because if | |
| 16:22 | I were to arrange these four out of nine and | |
| 16:24 | five out of nine and put them together , it | |
| 16:26 | would make one whole complete pizza which would add to | |
| 16:28 | this to give me 15 . Alright problem # six | |
| 16:36 | , let's say we have two and 1/5 and we'll | |
| 16:40 | add to that . Four and 2/5 . We add | |
| 16:45 | the whole numbers first . What do we have ? | |
| 16:47 | Four plus 24 plus two . Works out to be | |
| 16:50 | six . Common denominator of five means we have five | |
| 16:53 | in our denominator and one plus two . We add | |
| 16:56 | these fractions . One plus two , gives us six | |
| 16:58 | and 3 56 and 3/5 . Can we simplify that | |
| 17:03 | ? No , we can't because three and five we | |
| 17:04 | can't divide them to make them really any simpler . | |
| 17:07 | So the answer is just six and 3/5 . So | |
| 17:11 | all right . Getting close to the answer here actually | |
| 17:13 | , let's go over here . I think we'll have | |
| 17:14 | a little more room to do it here . What | |
| 17:16 | about eight and 1/4 ? And we'll add to that | |
| 17:20 | Five and 2/4 . What do we do ? eight | |
| 17:25 | plus 5 add the whole numbers . Eight plus five | |
| 17:28 | works out to 13 . So we put a 13 | |
| 17:30 | here And then we have a fractional part four and | |
| 17:33 | 4 on the bottom means four goes in our answer | |
| 17:36 | , and then we have one plus to add enumerators | |
| 17:39 | , Which gives us 13 . And what do we | |
| 17:41 | have here ? three fourths . Can we simplify the | |
| 17:45 | 3/4 ? We can't because we cannot divide top and | |
| 17:48 | bottom by anything to make that any simpler . So | |
| 17:50 | we just leave it and say that that is the | |
| 17:52 | final answer . Okay . I think we have a | |
| 17:55 | little bit of space down below . So let's go | |
| 17:59 | ahead and do problem number eight . What about what | |
| 18:02 | ? About five and 3/8 ? And we'll add to | |
| 18:07 | that the same exact thing . five and 3/8 . | |
| 18:10 | Well , what is five plus five ? Course you | |
| 18:14 | all know ? Five plus five is 10 and the | |
| 18:17 | fractions have the same common denominator of eight . So | |
| 18:20 | it goes in our answer and then we add the | |
| 18:22 | three plus the three . So we have three plus | |
| 18:24 | three is going to be 10 , and then three | |
| 18:27 | plus three is six out of eight . And we | |
| 18:30 | ask ourselves can we simplify the 68 ? Yes , | |
| 18:33 | we can . They're both even numbers . So let's | |
| 18:35 | go ahead and just slide over here and say 68 | |
| 18:39 | what am I going to divide by two , divide | |
| 18:41 | by two Because they're both even numbers . So we'll | |
| 18:43 | divide this by two and this also by two . | |
| 18:47 | So I'll have a 10 , 6 divided by two | |
| 18:51 | is three and eight divided by two is four . | |
| 18:55 | So the answer I'll get is 10 and 3/4 again | |
| 18:58 | . 10 and 3/4 doesn't look like it would come | |
| 19:00 | out of it , but because of the way the | |
| 19:02 | pieces combined , the answer we get of 10 and | |
| 19:05 | 68 is exactly the same thing as 10 and 3/4 | |
| 19:08 | . When you put the models together , you'll see | |
| 19:10 | that they're exactly the same thing . Okay . All | |
| 19:13 | right , let me have two more problems . They're | |
| 19:15 | pretty straightforward . So let's go slide over here and | |
| 19:18 | try to do the next one . Let's say we | |
| 19:20 | have three and four sevens and we'll add to that | |
| 19:25 | . Five and 3/7 add the whole numbers three plus | |
| 19:29 | five comes out to eight , we have a seven | |
| 19:33 | and a seven in the denominator of our fraction . | |
| 19:35 | So that goes there and then four plus 34 plus | |
| 19:38 | three . So what do I have ? Eight and | |
| 19:41 | four plus three works out to be 7/7 . Look | |
| 19:43 | what we have here . So if it was one | |
| 19:46 | out of seven or two out of seven pieces or | |
| 19:47 | three out of seven , it would just be a | |
| 19:50 | part of a whole . But seven slices out of | |
| 19:52 | 77 out of seven is another whole pizza . Or | |
| 19:55 | you can think of it as division seven , divided | |
| 19:58 | by seven is another one whole . So really I | |
| 20:01 | have eight plus one hole , which is nine . | |
| 20:04 | So if you grab models and and put them together | |
| 20:07 | the four sevens and the three sevens will come together | |
| 20:10 | to make an entire new hole that will add to | |
| 20:13 | the nine or to the eight here to give you | |
| 20:15 | a total of nine . All right , only one | |
| 20:18 | last problem . What's it going to be ? Let's | |
| 20:23 | say we have six and 26 and we'll add to | |
| 20:29 | that four and one stick . So how do we | |
| 20:32 | do this ? Six plus four ? We add the | |
| 20:34 | whole numbers six plus four is 10 and then we | |
| 20:38 | have six and six for our denominator . So that | |
| 20:41 | goes in our answer and then two plus one , | |
| 20:44 | two plus one is three . So it becomes 10 | |
| 20:46 | and 36 Can we simplify the fractional part ? Yes | |
| 20:50 | , we can because we can divide top and bottom | |
| 20:52 | by three . So let's write it as 10 and | |
| 20:55 | 36 And we're going to divide the top by three | |
| 20:59 | and we'll divide the bottom by three . So we'll | |
| 21:01 | have 10 and three divided by three is one and | |
| 21:05 | six divided by three is too . So it works | |
| 21:07 | out to be 10.5 . And that makes sense because | |
| 21:09 | the answer we got was 10 and 363 Out of | |
| 21:13 | six slices . If you have a pizza and take | |
| 21:15 | three out of six slices you have half of the | |
| 21:17 | pizza . So it works out to be 10.5 . | |
| 21:20 | So we've introduced the idea of what a mixed number | |
| 21:23 | and we've also talked about how to add them . | |
| 21:25 | So a mixed number is when you have a whole | |
| 21:27 | number of objects and then you have some fractional . | |
| 21:30 | In addition to that , we call that a mixed | |
| 21:33 | number . You add mixed numbers together by just adding | |
| 21:35 | the whole parts separately and then add the fractional parts | |
| 21:38 | separately and then you get to your final answer . | |
| 21:41 | Sometimes the final answer in the fractional part ends up | |
| 21:44 | becoming a new hole . Seven out of seven for | |
| 21:46 | instance is a new hole . If that ever happens | |
| 21:48 | , just add it to the hole to give you | |
| 21:49 | a new whole pizza or whatever you're thinking about . | |
| 21:52 | I'd like you to work through these when you feel | |
| 21:54 | like you understand the concepts and you're getting the right | |
| 21:56 | answers . Follow me on the part two . We'll | |
| 21:58 | wrap up our practice with adding mixed numbers |
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Adding Fraction & Mixed Numbers w/ Common Denominators - Part 1 - [23] is a free educational video by Math and Science.
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