How to add fractions that have 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!
Back

How to add fractions that have different denominators

Discussion and questions for this video
why does the denominator have to be the same as the other denominator
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. Such as 1 3/5 + 1 2/3. A calculator does make this handy if you have one. Just turn it into an improper fraction and add. This process simplifies the complications of this branch of math a lot.
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 :)
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
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.
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)
So...

(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?
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)

17/135

You should have posted this on multiplying fraction but that's alright. I appreciated your problems and will give you +1 vote.
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
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.
No. Voting is encouraged; in fact, there are badges for it.
Can we do another step like this:
3/8+5/9=(3*9)+(5*8)/72=27+40/72=67/72
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.
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.
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!