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!

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
First understand that x/y means "x" parts of a "whole" which is divided into "y" parts..
Now an example:
Suppose a class has 100 students, for a particular task 1/4 students were selected, and other 1/5 students were selected for a 2nd task. Find how many students have been selected from the class in all. [(1/4 + 1/5) * 100] = ?
1/4 of the class will be 1/4 * 100 = 25 ; 1/5 of the class will be 1/5 * 100 = 20
25+20 = 45; the answer will be 45 students
But if we directly add both the fractions we get 1/4 + 1/5 = 2/9 ; 2/9 * 100 = 22.22 students; which is not the correct answer.
To solve this problem we need to first find a LCM (Lowest Common Multiple) of the denominators (4 & 5) which is 20.
Now 1/ 4 becomes 5/20 and 1/5 becomes 4/20;
So 1/4 + 1/5 is now = 5/20 + 4/20 = 9/20
9/20 * 100 = "45" the correct number of students.
Thus finding LCM means finding a common number of parts; which also keep the ratio same; 1/4 = 5/ 20 and 1/5 = 4/20.
Hope this helps..
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.
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
If you understand about adding the fractions together, and changing the denominators, see the video on subtracting fractions. ( There isn't one specifically on subtracting fractions with unlike denominators.
I already knew how to do this, but it gave me a couple pointers.
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
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.
Please put this in the Tip/Thanks comment section, not here.
(I am not a moderator, but I'm fairly sure this goes against the rules as irrelevant)
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.
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.
This should be in the tip/thanks section. (I am not a moderator, but I'm pretty sure this is against the rules as irrelevant)
wow it really helped me ;) ive got a question how do you do this but is there a easy way?