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Adding fractions: different denominators

To solve this problem, we need to find the least common multiple to get at the common denominator. Can you help? We bet you can!

Adding fractions: different denominators

Discussion and questions for this video
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 9 and 7 to make 16 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. :)
What does it mean to simplify the problem?
Simplifying a fraction just means putting it into the simplest form. For example, 3/6 can be simplified to just 1/2. They are the same thing, but 1/2 is simplified.
when im adding uncommon fractions, i keep getting it wrong. what im saying is i dont understand. please tell me the steps.
Well, let's do 17/10 + 3/2.

The first step is to find the least common multiples of the denominators ( 10 and 2).

The LCM of 10 and 2 is 10.

You have to multiply 10 1 time to get 10 so you also multiply the numerator by 1. The left side becomes 17*1/10*1

You have to multiply 2 5 times to get 10 so you also multiply the numerator by 5. The right side becomes 3*5/2*5

Your expression is now 17*1/10*1 + 3*5/2*5. 17*1=17. 10*1=10. The left side is now 17/10. 3*5=15 and 2*5=10. The right side is now 15/10.

Your final equation becomes 17/10 + 15/10. Now you add the numerators. 17 + 15 = 32. Your answer is now 32/10.

Now, you simplify. 32/2=16 and 10/2=5. Your final improper answer is 16/5.

The reason it may say you got the question wrong is because you have to convert to a mixed number. 16 goes into 5 3 times. 5*3=15. 16 - 15 = 1.
Your final mixed answer is 3 1/5.

I hope this was not too confusing :)
still not sure have problem 12/18 + 5/6 = Not sure of answer 1 9/18
You're correct! Just make sure to reduce 9/18 to 1/2, so your final answer is 1 1/2.
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.
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.~_~
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
Why do you have to get the common denominator, can't you just add?
No. If the denominators are unlike you are comparing two completely different things. Think of fractions like pizza. The total number of slices is the denominator. What happens when you increase the total number of slices while keeping the pizza the same size? The slices get smaller. A pizza with 4 slices will have smaller slices than a pizza with just 3 slices. So if you don't keep the denominator (or number of slices) the same your definition of what constitutes a slice (or fraction) changes and your answer no longer makes sense. It maybe easier to comprehend if you see it visualized, checkout http://mathmistakes.info/facts/AlgebraFacts/learn/fr/add.html
What about this but for subtracting where is that?
If you understand about adding the fractions together, and changing the denominators, see the video on subtracting fractions. (http://www.khanacademy.org/math/arithmetic/fractions/v/subtracting--fractions). There isn't one specifically on subtracting fractions with unlike denominators.
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
why do we use the same denominators, when we are doing the adding when we have a different denominators.
Hi there, I will show an example because this is better than explaining. If I explained it to you would be lost. So an easier way is easier to understand.

Mr. McFattenMeUp has 4/8 of a chocolate cake in his refrigerator. Later his friend Mr. MeFillMyTummy gave him 3/4 of a vanilla cake. How many cakes does Mr. McFattenMeUp has all together?

(0)(0)(0)(0)( )( )( )( ) 4/8
( 0 )( 0 )( 0 )( ) 3/4

I got this diagram ready. now if I were to add them both without converting them you would get 7/12 and the answer would look like this

[|][|][|][|][|][|][|]00000 7/12

And this would be false since if you combine my previous diagram you would get this

[(0)(0)(0)(0)( 0 )( 0 )] ( 0 ) 1 and 1/4

The reason why we change the denominator is because the pieces of chocolate and vanilla cake have different size. So to get the correct answer, we change the denominator to make the pieces of chocolate and vanilla cake have same size. I showed you the answer but lets do the math anyways.

(0)(0)(0)(0)( )( )( )( ) + ( 0 )( 0 )( 0 )( )
4/8 3/4

( 0 )( 0 )( 0 )( ) --> (0)(0)(0)(0)(0)(0)( )( )

3/4 times 2 on both sides is 6/8 and 2 x 4 is 8 so the slice changes from ( 0 ) to (0)

(0)(0)(0)(0)( )( )( )( ) + (0)(0)(0)(0)(0)(0)( )( )
4/8 6/8

And we add them up which we get:

[(0)(0)(0)(0)(0)(0)(0)(0)] (0)(0) 10/8 which is 1 2/8

Now we must simplify them.

2/8 --factor--> (2)/(2 x 2 x 2)

We can cross off one 2 since it exists in both numerator and denominators and we get.
(2)/(2 x 2 x 2) --> 1/(2 x 2) --> 1 and 1/4 (I took out 1 temporary because adding it to the fraction while I was simplifying might have confused you)

So Mr. McFattenMeup has 1 and 1/4 of cakes altogether

Hope this helped and your curiosity has rewarded you with a +1 vote :D

P.S Would your Hopper care to cuddle with my Hopper?
at the end do you have to divide the numbers
Hi there, no you do not have to divide the number because 1 and 13/36 cannot be divided any further. However if the answer was 1 and 12/36, it would be divisible.

12/36 (2 x 2 x 3)/(2 x 2 x 3 x 3)
I factored them
Now I cross off the numbers that exist in both numerator and the denominator.
(2 x 2 x 3)/(2 x 2 x 3 x 3) --> 1/3 since there are 2 of 2 and 1 of 3 that exist in both sides. I placed 1 in the numerator on the top because all of the number in there has been crossed off. So the answer is 1 and 1/3

But in the problem that Sal gave us, 1 and 13/36 cannot be divisible any further.

Hope this helped and +1 vote for your curiosity :D
Here are some practice problems.
9/10 times 3/10

5/15 time 17/45
Not sure if you want me to solve them but I welcome your question.

9/10 x 3/10 = 27/100

5/15 x 17/45 = 85/675 --factor-->
(5 x 17)/(5 x 5 x 3 x 3 x 3) --cross off-->
17/(5 x 3 x 3 x 3)


You should have posted this on multiplying fraction but that's alright. I appreciated your problems and will give you +1 vote.
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.
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.
does it take away energy pints to vote
No. Voting is encouraged; in fact, there are badges for it.
Can we do another step like this:
3/4 + 1/2=answer in simplest terms
In order to add fractions, the denominators must be the same.
The lowest common denominator or multiple (LCD or LCM) is 4.
Whatever we multiply the denominator by, we must multiply the numerator by.
Therefore, 1/2 = 2/4.
So, 3/4 + 2/4 = 5/4 as an improper fraction or as 1 1/4 as a mixed number.
why do you need to multiply the numerator when you multiply the denominator to add or subtract fractions?
Good question. The answer is that if you didn't then you would change the value of the fraction. Like 2/3. If you multiplied both of them by 2, you would have 4/6. Both equal 0.66. If you multiplied the bottom only, then it would be 2/6 which is equal to 0.33. It would change the value.
can both fractions be negativs
Right Patrick Crandon!
How do You do tris
The formula is (HOCH^2)^3 CNH^2 , but this is math not chemistry.
Why does the denominator have to be the same as the other denominator?
Think of it this way:

When you are adding or subtracting two things, they must be the same in order to make it work. If you had 6 basketballs, could you subtract 3 iPhones from them? Of course not!

When working with fractions, the denominator describes the SIZE of the piece, so to do the addition or subtraction, you must make them the same size.

The numerator tells you HOW MANY of each "size" you have, so you only add or subtract the numerator, not the denominator (you aren't changing the "size" of the pieces).

Hope this helps.
i cant understand this, how did you get the x3 but the other x4?
If you're adding a fraction, you must have denominators that are alike. For example, if you are adding 1/4 + 1/3, you have to make both the denominators the same. So the lowest common denominator for 4 and 3 is 12, so you would multiply 1/4 by 3 and get 3/12. Then you would multiply 1/3 by 4 because you need to get the denominator to 12, and 3 times 4 is 12. So you would get 4/12. Now you would add 3/12 and 4/12 together and get 7/12.
I hope this helped and good luck!
can you divide fractions
No you can not. You have to flip the right fraction then multiply it. ;)
how do you subtract a broblem
You first use the same method as shown in this video to find common denominators.

Once the denominators are alike, the fractions can be added or subtracted.

Here is a video on "Adding and Subtracting fractions" with like denominators.
HI there so i was wondering if someone could help me with my math i really dont understand how to get the answer!

It is this: 3/4+ N= 4/5 and N-3/5=1/4
thank you!!
Wait... but lets say you have to add 3 fractions like um.... 1/2 3/4 and 3/8 how would you do that...?


Like what if you had (10 1/2) ( 8 2/3) ( 3 1/3) (5 5/8) how would you do those as mixed numbers...?
If you have mixed numbers make them and improper fraction
10 1/2 this is how you convert it into a improper fraction
10x2 = 20
20+1 =21

the answer is 21/2
you get 2 as the denominator because the fraction is 1/2 and the denominator is 2.
how are fractions used in real life situations?
What if you have five people and one pizza.
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!
Is multiplying a fraction as easy as adding and subtracting one?
no....it is the same but you just multiply in stead of adding and subtracting...
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.
cant you use 3 as the donominator ??
Yes you can, but its easier to use the largest number that can go in both numbers because by using the number 3 instead of 12, you would have to keep simplifying over and over.
I was so mad at myself for forgeting how to add fractions but when you came through I was so relived
Dividing and multiplying fractions ??
Indeed, you can divide and multiply fractions.

Let's say I have a piece of pie, which is 1/4 of the whole pie.
I can say: "I'll take two of those pieces", which would be 2x(1/4) = 1/2
Or I could say: "I only need half of this piece", which would mean (1/4) : 2 = 1/8.
But let's say that I have a 1/4-piece of a pie, and I want to share my piece with two other people, so each of us would have 1/3 of that 1/4 piece. This would be (1/3) * (1/4) = 1/12. So each of us would get 1/12 of a whole pie.

So it is definitely possible to divide and multiply fractions. If you don't know how it works, I suggest to check out some of Sal's videos on that topic :)
Hello! I am a grade 5 student but I really need help with these kind of fractions can you help me?
what is the numerator and the denominator?
The top one is called the numerator, the bottom one is called the denominator, and these two numbers are separated by a line.
2 / 4
2 = numerator
4 = denominator
I am having trouble with converting 2/6 and 14/15 into like denomanators
Think about the denominators: 6 and 30.
Count by 6s (multiples of 6): 6, 12, 18, 24, 30, 36....
Count by 15s (multiples of 15): 15, 30 - oh, wait. Stop right there!

30 is the MAGIC NUMBER! It's in both lists. Use 30 as the common denominator.

Ok, so now you convert the fractions:
The 2/6 needs to be multiplied by 5/5 because 6*5=30.
2/6 * (5/5) = 10/30.
The 14/15 needs to be multiplied by 2/2 because 15*2=30.
14/15 * (2/2) = 28/30.
simplify 1/rt=1/r1+1/r2+1/r3,please show steps on solving thank you
I have no clue how to simplify that! 1/rt=1r1+1/r2+1/r3 does not make sense. Especially cause I am in 5th grade.
Why can't you just put each fractions in the lowest terms before you add like 1/3 and 2/6? I could just simplify 2/6 to 1/3 and equal 2/3. It's still the answer without all the work having to be done at the end. So why can't it be like that?
You can totally add fractions that way - well done.
how do you add a mixed number with an fraction for example 4 2/3 + 1/6
I would first add the fractions so make 2/3 into 4/6 and add that to 1/6.That equals 5/6 and then add that to the whole number (4) to get 4 5/6 as your solution. In other words add the fractions and then add the whole number.
What do you do if the numerator is odd and the denominator is even because I'm doing homework it tiled adding fractions with mixed numbers
whether the denominator is even or odd does not matter. What matters is whether you can find the greatest common factor to reduce it And if you cannot find one is not affected by it being odd or even. It simply means they have no common factor. For example, 3/42
3 is an odd number but 42 is even.
If you look at their factors. 3 is a factor of itself and a factor of 42.
This would therefore reduce to 1/14.
Because when you add or subtract you only add or subtract the numerator, and not the denominator. If you have a different denominator for each fraction, say you had 3/4 + 18,
you can, not, add the denominator AND numerator, because if you do, you get 6/12, which is the wrong answer and if that was the way we added fractions it would be way too easy.
So you need to find the common denominator, by listing the two denominators for each fraction:
then writing out the multiples,
4: 4, 8,
8: 8,
then once you find a common multiple, that common multiple becomes the denominator:
3/8 + 1/8
And since you changed the denominator for one of the fractions, you change the numerator for that fraction, according to the difference for what that fraction's denominator used to be, to what it now is:
3/4 -> 3/8
4 x 2= 8
So then you do that change to the numerator to even it out:
In 3/4, the numerator is= 3
So you do 3 x 2, which equals 6, so your new fraction and numerator is 6/8.
2 Votes