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!
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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] = ?
Solution,
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 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 does the denominator have to be the same as the other denominator?
This is the tip of the actual people that understand this "adding or subtracting" it has different "rules" of what to do.... is all about process and know when to do the operations.
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.
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 ..um how do you do this but is there a easy way?
I don't get it at all. He is doing it right but, I don't get the part, I mean all the parts. The only part I get is when you got to times it to find the same number. Anyone can help me pleas do.......
Yes, that method works perfectly.
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