Adding and subtracting fractions with unlike denominators
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Adding fractions with unlike denominators
Adding Fractions with Unlike Denominators
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 We're asked to add 4/9 and 11/12 and to write our answer
 as a mixed number, and then simplify and write our answer
 as a mixed number.
 So here we have two fractions we're adding together, but we
 have different denominators.
 So whenever you add fractions, the first thing you have to do
 is check the denominators.
 If they're the same, you can add, but if they're different
 like this, you have to make them have the same
 denominator.
 So what we have to do is find a number that both 9 and 12
 will divide into, and that will be our common
 denominator, and you'll see why both 9 and 12 have to
 divide into it.
 So let's think about what that number is, and there's two
 ways of coming up with that what we could call a least
 common multiple, the smallest multiple of both 9
 and 12 that is common.
 One way is just to kind of look at the multiples of 9 and
 see if any of them are divisible by 12.
 So if you start with 9 we can do it over here.
 So you have 9, that's not divisible by 12.
 18 isn't divisible by 12.
 27 isn't divisible by 12.
 36, well, that is divisible by 12.
 That is 12 times 3.
 So 9 goes into 36 and 12 goes into 36.
 So what we want to do is write a common denominator.
 So we're going to write 4/9 as something over 36, and we're
 going to write 11/12 as something over 36.
 Now, to turn your 9 into a 36, you have to
 multiply it by 4, right?
 9 times 4 is equal to 36.
 Now, you can't just multiply the denominator by 4.
 You also have to multiply the numerator by the same thing.
 So if you multiply the numerator by 4, you get 4
 times 4 is 16.
 So 4/9 is the exact same thing as 16/36.
 If you wanted to simplify this one to 4/9, you divide the
 numerator and the denominator by 4.
 Now, we do the same thing over here.
 36, 12 times 3, so we're multiplying 12 by 3 to get 36.
 Well, if we did that to the denominator, we also have to
 do that to the numerator, so 11 times 3 is 33.
 And just like that, we've now rewritten each of the
 fractions so that they have the same denominator.
 Both of their denominators is 36.
 So now we're ready to add.
 If you add these two things, we'll have 36, because we're
 considering kind of parts of 36 or fractions of 36, and
 then we have 16 plus 33 in the numerator.
 Let me write that down.
 16 plus 33 in the numerator.
 And 16 plus 33 is what?
 6 plus 33 would be 39 and then you have
 another 10, so it's 49.
 So it's equal to 49/36.
 Now, can we simplify this?
 49, it's 7 squared, so it has 1, 7 and 49 as factors.
 This has 1 it has a bunch of numbers, but it's not
 divisible by 7, so this is actually in simplest form, but
 this is an improper fraction.
 The numerator is larger than the denominator.
 So let's write it as a proper fraction.
 To do that, we divide 36 into 49.
 36 goes into 49 how many times?
 Well, it only goes one time, so it equals 1.
 And how much will be left over?
 If I divide 36 into 49 one time, or 1 times 36 is 36,
 then I have 13 left over to get to 49.
 So it's 1 and 13/36.
 And you can do that manually, if you like you.
 You'd say 36 into 49.
 36 goes into 49 one time.
 1 times 36 is 36, and then you subtract.
 9 minus 6 is 3.
 4 minus 3 is 1.
 You have a remainder of 13.
 So that's our answer: 1 and 13/36.
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This discussion area is not meant for answering homework questions.
why does the denominator have to be the same as the other denominator
Good question.
In mathematics, the concept of adding and subtracting fractions require the denominator to be common. The numerator does not need to be common but the denominator must be.
If the denominator wasn't common how would we work out the question?
E.g. 1/3 + 3/7 = ?
To work out this question, we would have to find the LCM (Lowest Common Multiple) of the denominators; in this case, 3 and 7. Then when we find that it is 21, we can adjust the numerators to 7 and 9. With that done, we can add 3 and 7 to make 10 over the denominator, which is 21.
This is why the denominators have to be common. There was no equation or formula built in the concept of adding and subtracting fractions that do not require the denominators to be common.
I hope this clears everything up. :)
In mathematics, the concept of adding and subtracting fractions require the denominator to be common. The numerator does not need to be common but the denominator must be.
If the denominator wasn't common how would we work out the question?
E.g. 1/3 + 3/7 = ?
To work out this question, we would have to find the LCM (Lowest Common Multiple) of the denominators; in this case, 3 and 7. Then when we find that it is 21, we can adjust the numerators to 7 and 9. With that done, we can add 3 and 7 to make 10 over the denominator, which is 21.
This is why the denominators have to be common. There was no equation or formula built in the concept of adding and subtracting fractions that do not require the denominators to be common.
I hope this clears everything up. :)
It makes the process a lot easier, but you don't have to. Just find the common denominator and multiply, divide, add, or subtract. Using graphs or charts such as the pie chart also helps understand the basic concept of it.
In some cases denominators are equal to make some of the questions easier, like
Example: A person bought 8/10 kgs of sugar and another person bought 2/10 of it. So how much is left in the bag
Answer: Nothing
Example: A person bought 8/10 kgs of sugar and another person bought 2/10 of it. So how much is left in the bag
Answer: Nothing
The denomentar has to be the same because if you want to add , you have to have the same equal sized pieces.
Good help now to make another math problem adding multiple fractions eg)1/2 + 3/5 + 4/7= Actually Mom knows the method but the 15 year old can't figure out w/ a lot of examples from a good book. However KHAN makes an excellent teaching explanation!!!
You can't add or subtract unlike denominators unless you find a common denominator
This is a very necessary thing to learn....now I am not as smart as the guy on the videos, but
it is easy to add them when they are alike! It makes it way way way easier! :)
it is easy to add them when they are alike! It makes it way way way easier! :)
it has to be the same because then we need same denominators for adding fractions with an unlike denominator.
The integers would have different values and the numerator would be incorrect.
because say you want to add the 2 numbers the nmbers need to be the same in order to add them witch them means that the numbers need to be the same in order to add them but with subtracting you need to find common numbers that still work in order for you to do the subtracting but if you are multiplying the numbers you still need to find denomiters that will work for both. And for dividing then you need to still need find common denimatiors so then you need to dived the numbers the by the top then the bottom
It needs to be like that so you can subtract the numerators you cant do that with different denominators.
so you can divide
61 it is don't say it's wrong just think about it how about 11x11=4
22x22=16
Now 33x33=?
22x22=16
Now 33x33=?
It makes it easier to add the fractions.
so that you can add it evenly
because if you are not a math freak and can do it in your head than it's just easier.
because if you dont then you are not ready to add them. They need to be the same unlike when you are multiplying fractions
that is not logical Zach !
You'll get the awnswer wrong if you don't
so you can add or subtract it, realy pay attention !
I agree with everyone else
Why did he say to turn the nine in to a 36 and why multiply by 4 what.]
nine times four is thirty six but why cant the nine just be nine. I'm confused ):
and why do we have to multiply the numerator by 4 too.~_~
nine times four is thirty six but why cant the nine just be nine. I'm confused ):
and why do we have to multiply the numerator by 4 too.~_~
to add fractions, you need to have the denominator the same. these two fractions have denominators of 9 and 12. The lowest common multiple of these two numbers is 36. That requires multiplying by x4 and x3 respectively. We multiply the numerator and denominator by the same number so the number does not change.
4/9 * 4/4 = 16/36. 4/4 is the same as 1, so the number doesn't change
4/9 * 4/4 = 16/36. 4/4 is the same as 1, so the number doesn't change
at first i felt like you so i know what you mean. If you are multiplying with unlike denominators then you need to multiply the denominators by each other so that they are the same. Then you have to multiply the numerator by the other denominator as to make the number not change. If you didn't , it would be a totally different fraction!
If both denominators are prime numbers, is the only least common multiple between them always going to be the product of the two?
Well, yes because since both are prime numbers, and prime numbers can't divide into each other's multiples, it will have to be the product. For example, 1/5 + 1/7, 7 can't divide into 5's multiples and 5 can't divide into 7's multiples, so the denominator has to be the product. By the way the answer is 7/35 + 5/35 = 12/35
If both denominators are prime numbers, is the only least common multiple between them always going to be the product of the two
Why do the denominators have to be the same?
You do not have to make them the same but it makes it far easier to do.
they make the adding process much easier. and drawing pie charts also helps to grasp the concept.
Because if you add them it messes up the question
They have to be the same because if you imagine it just drawn in your head then that would not make sence! LIke, for ex:3/5+8/11. Then really if you do it that way then the awenser would be 11/14.
if they arent the same you cant add or subtract
why does the denominater have to be greater than the top number?
Excellent question my friend. If you had two fractions like 6/5 and 7/5 you would get 13/5. That is what you would call a improper fraction. In arithmetic you wouldn't leave it like that because it's considered a improper fraction. You would need to change it into a mixed number. When you get to algebra 1 they will allow you to leave it as a improper fraction as an answer to a problem.
the denominator must be bigger because the numerator has to go into the denominator.
It doesn't have to but if you are in 5th grade, you haven't learned about that yet. If it is smaller, it is a proper fraction. If the numerator is larger than the denominator, that just means it is an improper fraction and it hasn't yet been reduced into whole numbers.
I don't get this it is hard can anybody help me?
it is quite simple if you ask me all you have do is this Whenever you add fractions with unlike denominators, you must make the denominators of the same value. In this example, the easiest approach is to multiply 8 x 3 to get 24. Here, you multiply by 3 to get . Then you multiply the second equation by 8 to get . Note that both addends have 24 as a denominator. Add in the same manner as with the unit Adding fractions with like denominators.
I don't get your question that you asking me women please be specific but I don't give up so im going to give you the awnser any way............................................... m2;00 so yes
i cant understand this, how did you get the x3 but the other x4?
Because it is a fraction you can multiply it by anything  it will still be the same fraction of a whole number. (1/2 * 2 is 2/4  but both are 0.5 in decimal terms)
The objective is to get the denominators the same.
The objective is to get the denominators the same.
Cause we took LCM of both 9 and 12 and they both are divisible by 3 and 3 times 3 = 9 and 3 times 4 = 12
and So, we get x3 and x4
and So, we get x3 and x4
can you divide fractions
yes you can beacuse fractions are the answer of 1 divide by a number so yes they can
What if you have a problem where one of the fractions has to be divided into a fraction, and the other number is whole?
If one number is whole, you put it over a denominator of 1. If you have 24/8  2, write:
24/8  2/1
Hope this helps!
24/8  2/1
Hope this helps!
I still don't understand. Please help me i have test next week.
Well when you add a fraction like 4/6 and 9/10 you have to get a common denominator. To do that multiply the denominator 6x10= 60 now the fraction would look like _/60 all we need to do is fine the numerator 6x what = 60 its 10 then we do 10x4 to get the numerator 40/60 do the same thing to the other one now we got 54/60 + 40/60 ok add the numarator 54+40=94 so now we got 94/60 we need t turn it into a mixed number. How much times can 94 go into 60 its 1 time so now we have 1 and 34/60 and thats not your answer yet you have to reduce. So divided by 2 = 17 then 60 divided by 2 is 30 so 17/30.
I DOn't Get It
Is multiplying a fraction as easy as adding and subtracting one?
Multiplying is even easier because you don't have to find any common denominators or anything. You just multiply across: the numerator times the numerator and the denominator times the denominator.
can both fractions be negativs
Right Patrick Crandon!
check the number line. can you add two negative numbers? the answer is yes.
I didn't know you can have negitave fractions!!
JMAtlason
JMAtlason
yes they both can be negtive
why does the denominator have to be the same?
The denominator has to be the same because then it makes it easier to add, subtract, multiply, or divide the fraction.
what if there was an x in the denominator like in the problem 1/x + 4/1
That is a more advanced type of problem, but you can still find a common denominator.
you could multiply 4/1 by x/x and get 4x/x
then add the numerators 1 + 4x, which can't be simplified further.
So the new form is the (1 + 4x)/x also written as
1 + 4x

x
This isn't really any simpler than the previous expression but they are equal.
you could multiply 4/1 by x/x and get 4x/x
then add the numerators 1 + 4x, which can't be simplified further.
So the new form is the (1 + 4x)/x also written as
1 + 4x

x
This isn't really any simpler than the previous expression but they are equal.
Good question. If we knew the number value for x, we could put that number in place of x and complete the equation.
However, x is usually used when we don't know the number. In which case, the x acts like its own number. A fraction with x in the denominator, then, could only be added to other fractions with the same denominator: an x.
Also, since we don't know the value of x, we can't just change other numbers into x to make the denominators the same. It would be like changing apples into cookies.
In the example you gave, the 4/1 could be simplified to 4 and we're left with 4 + 1/x, or 4 1/x.
I hope this helps.
PS: Your question about x makes me think you'll enjoy algebra. It's my personal favourite and I wish you all the best at whatever you're working on.
However, x is usually used when we don't know the number. In which case, the x acts like its own number. A fraction with x in the denominator, then, could only be added to other fractions with the same denominator: an x.
Also, since we don't know the value of x, we can't just change other numbers into x to make the denominators the same. It would be like changing apples into cookies.
In the example you gave, the 4/1 could be simplified to 4 and we're left with 4 + 1/x, or 4 1/x.
I hope this helps.
PS: Your question about x makes me think you'll enjoy algebra. It's my personal favourite and I wish you all the best at whatever you're working on.
I haven't learned algebra yet but I would think x means 4.
What if both numbers don't have a greatest common factor?
Hi William. Two numbers always have a greatest common factor. Sometimes, it is 1, but often it is larger.
What if the Denominator was different from the other Denominator?
O_o
O_o
That's what were talking about here. "Unlike Denominators" are fractions with literally Unlike denominators.
Try the Skill "Adding Fractions" when you're done!
Try the Skill "Adding Fractions" when you're done!
When numerator is greater than the denominator.. it is considered as improper fraction?
Yes it is a improper fraction so you need to turn it into a mixed number.
I do not get the mixed fractions, is there an easier way
What don't you understand about them?
we are doing this in math and i kinda understand it but its hard also
Agreed, I still think fractions is a pain in the neck, but just work hard and you'll understand it.
This website has helped me a lot in my school work. Although i am a little confuzzled on how he got his answer, like how did he turn it to a mixed #?
Take a improper fraction like 4/3. Divide the denominator by the numerator. That's 1. How much is left? 1/3, so the mixed number is 1 1/3. This problem doesn't need simplifying, but remember to in other problems if they need it. Hope this helps.
thank you so much! I have a test soon on this so u were just in time ^^ thanks again
do you have fractions with multiplication
Yes they do have fractions with multiplication khan academy.
i think you can also just multiply the denominaters by each other........right?
Not exactly... It does involve multiplication, yes, but, what you need to do is find the common denominator( a denominator that both of the fractions can multiply into and get)
like 4/5 and 6/30. the common denominator would be 30, cause 5 can multiply into 30. if you multiply 5 by 6 to get 30, you would also need to multiply the numerator by that same number that you multiplied the denominator by.
like 4/5 and 6/30. the common denominator would be 30, cause 5 can multiply into 30. if you multiply 5 by 6 to get 30, you would also need to multiply the numerator by that same number that you multiplied the denominator by.
yes, you can just multiply the denominators by each other, but when you use larger numbers, it becomes tedious to multiply all of those giant numbers. It is much simpler to work with smaller numbers, and you are less likely to make a mistake that way. Multiplying the two numbers together is sometimes the only way to get a common denominator.
what if the denominators of two fractions don't have a least common multiple
you work with them in the way as they are  they are already simplified ;)
what is he trying to say? it is confusing.
it is, why doesn't it have audio
Well not really if your getting this then why do you need the video? But if your having lots of trouble and you NEED help then you can go on youtube but it depends if you know the concept or not to answer your question
if you dont understand what he is saying then you are not ready to learn this skill
But what if you get a improper fraction do you have to turn it into a mixed number or can you just let it be.
If your asked to "simplify" the answer, turn it into an improper fraction. Other than that, it depends on whether or not your teacher wants you to.
You need to do the LCD if your Denominator is different at Adding Fractions.
why can't you add them wit the denomenator that the # come with
can you please show hard and not easy like 9 and 12 ha s denominator and some thing like 7 and 8
you cant answer that it dosent make sense fractions only
u are soo smart.. just what i need to no except can you do a vidio were you can like turn the inproper fraction into a proper one?? if that makes sence
flvsftschoolwork are you a boy or girl?
hey jcnz2011 u boy or girl
how do i get the answer whne one od the fractions is negatice e.g 3/5 +1/2 ??
This is the way I like to do it:
I just find out what 3/5  1/2 is (watch this video: https://www.khanacademy.org/math/arithmetic/fractions/Adding_and_subtracting_fractions/v/subtractingfractionswithunlikedenominators) and then make it negative
I just find out what 3/5  1/2 is (watch this video: https://www.khanacademy.org/math/arithmetic/fractions/Adding_and_subtracting_fractions/v/subtractingfractionswithunlikedenominators) and then make it negative
would is easier for you guys to complete 4/5 + 6/7 or 5/6 +1/2?
how do u add and subtracted fractions
With finding the LCM, my teacher taught me something called the ladder method. when i ask adults about it, they dont know what that is. is this method useful?
of course!
the ladder method is a modern way of finding LCM
that is why adults dont know about it
the ladder method is a modern way of finding LCM
that is why adults dont know about it
Why is this so difficult?
If you work harder, it will be easier.
yeah try to think positive maybe you'll feel motivation to do more math and so on :D
it takes practice! think positive and maybe take a break for a while till you can think clearly again.
Because it is math and math is difficult......it's only hard if you make it that way
Faulty kitty cruft URL inflation Khomeini
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Ugbofythfbb Vince oilfield
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what is common denominator in 6/7 + 8/21
how can i practice on kahn academy
Hi, I was wondering if you were going make 49/36 into a proper fraction like he did... it there any other possible way of doing that? Or is that the only way to covert the improper fraction into a proper fraction? Just wondering! Thanks!
how would i solve for 8/7+6/14+1/35+2/5. I say all of them go into 35 except the 6/14
Do you have to simplify both fractions before finding the common denominator?
Thanks this really helped me alot
why do you have to multiply by the same number
That is right, whatever you do to the denominator you have to do to the numerator.
You have to multiply the same number for the denominator and numerator because whatever you do to the bottom, you do to the top. If you don't do this your fraction would not be equivalent so you would get a different answer because you changed the value of the fraction completely. Hope this helped. :)
i still dont get nothing by the way dont put my question at the bottom
is there any videos on subtracting fractions with different denominators
why do we have to multiply?
why do you make it so complicated?
why do people simplify mixed fractions?
What do you mean by "mixed fraction?" If you mean mixed number (1 2/3), then those don't get simplified. They are already in simplest form. Fractions in general are simplified because it is easier to visualize fractions with smaller numbers than it is to visualize fractions with larger numbers.
why is this so hard i kinda understand but not really who agrees
the whole thing was confusing
Is there any other faster ways to do the problems instead of just wasting so much time on only one problem when i could be on the next one in just a minute or less?
Guys Mr. Khan is a smart guy and this is a learning program. What if somebody asks you to add fractions and you do the LCM way and get it wrong? what happens then?
Get the LCD(least common denominator) of the denominator then add. He explains things that is why the video is long..:)
Is LCM the only way to add fractions with unlike denominators?
thax f4 the help
Why do we have to find a common multiple? Why cant we just the numerators and the denominators together, like we multiply the numerators and the denominators when we are multiplying fractions. I'm confused. Help!
Thanks,
Tesla
Thanks,
Tesla
equations with whole number and fraction
hey im new to this and you dont have improper fractions
is there any way to do it without changing the denominators?
when you get the answer 1 and 13/39 can you make 13/39 as 1/3
I don't get why we have to multiply
what divides the 9and 12?????
voteif u agree that the person who made this website is trying to turn the unlike denominator into a common denominator to make it more easier
why do u need to do a common denominator
So do you just find the common denominator?
Yes, that is what you do.
instead of listing the factor could you just multiply them please respond :D
where are the problem exercises?
With this problem couldn't Sal have simplified each fraction and then added them?
Yes, but it would've made the process much harder. It is easier to add, subtract, etc... them with common denominators than to have different denominators.
I thought you have to divide 36 to 4/9 and to 11/12 ???
Why Does This Video Have To Be So Short?
I Don't Understand!
I Don't Understand!
why do we need to know this?
how can this help us in the future?
how can this help us in the future?
Why do the denominators have to be the same?
I am not sure how to add fractions at all how do i
do you know how to do 4
still difficult thanks sal :[
It took me forever to get this. I think I did over 200 problems on the moduel before I was concidered "proficient". Whew, all done.....now....*leaps* to tackle Algebra 1 *pounces on Algebra 1*
why do u have to multiply the top to
When you find a common denominator are you allowed to divide instead of multiply 9x2=18 ,9x3=27and blah blah blah ?
Can you please make a video on simplifying fractions? That is what I am struggling with.
Is there any other way to do it? I do not understand it very well.
how to find a common multiple?
this was awesome! Now i can do another thing in my Kahn Academy project.
At 1:29 Sal says three, even though he meant four.
at2:00 how does it work
If you mean by counting the multiples of 9 to find one that is divisible by 12, you can check every single one (but it's not very efficient), or you can learn the multiples of 9 and 12 up to a certain point. If you mean the multiplying of the denominator as well as the numerator, my teacher always says: "what you do to the bottom you do to the top!" so you make an equivalent fraction.
why would the improper fraction have to changed
Here He is also Simplifying Fractions, there's a video for that too.
is their a easer way to make the denominator the same
i don't understand this formula its a little bit tricky.can some one help me.
Thanks for the video but I was sort of confused with how you got the 3.
need help with trying to find the lcd of 3/55+9/77
The lowest common denominator of 3/55 and 9/77 is 11.
If the numbers are in negative form and if they're denominators are unlike and are negative then how can we solve them?
How would you do M over (2m+3) + M over (m+3) ?
how about if we have like 36, and we have to find a GCF, and we have to do 2. what can save me from doin all that work?
i dont know but good question.
Make a video that tells me how to simplify a fraction that is NOT an improper fraction!
what are "signs" in adding fractions with different signs
/, x, , and + are all different signs. Is that what you meant?
on rylireback's comment so just cross multiply
if the question has a hole number do you just leave it and at the end add or subtract it
Nope. If you have a whole number, you call that a mixed number. You have to turn it into a improper fraction and then do the calculation.
ex: 2 3/4 + 3/5 = (2*4+3)/4 + 3/5 = 11/4 + 3/5
ex: 2 3/4 + 3/5 = (2*4+3)/4 + 3/5 = 11/4 + 3/5
what did he say I still don't get it
it is conufseing me i don't now why
why is it only sometimes we have to simplify and other times not?
but do you need to simplify to get the answer? of is it just to make a question easer?
Sometimes, you don't need to simplify. For example, 1/3 + 1/6 = 2/6 + 1/6 = 3/6. Here, you need to simplify because 3/6 = 1/2 and it's much simpler (and for other reasons). However, in 1/2 + 1/3, you cannot simplify the answer (5/6, see if you can get that!)
Hopes this helps!
Hopes this helps!
Why do the denominater go inside a common denominater
where is the test?
Why does this guy repeat himself soooooooo much? It confuses me. :(
It's realtime, and he can't speak as fast as he writes. It also helps reinforce what you're learning, but if you don't like it, just turn the subtitles on in English and read his words instead of hear them.
Because you can only add or subtract the numerator .
how would you multiply 5/20 * 8/5
Well you would cancel some of the numbers. the 5 and the 5 could cancel out, and that would leave you with 8/20.
10,020,396 over 300,285,932 plus 125 over 70,000,000. Seems hard. bet you I can fool ya. :)
Report a mistake in the video
Example:
At 2:33, Sal said "single bonds" but meant "covalent bonds."
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