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### Course: Class 7 (Foundation)>Unit 5

Lesson 3: Adding and subtracting

# Adding fractions word problem: paint

Learn how to add and subtract fractions with unlike denominators through a real-world problem. Watch as the problem is broken down step-by-step, practice finding common denominators, and apply this knowledge to determine if the sum or difference of the fractions meets a specific requirement. Created by Sal Khan.

## Want to join the conversation?

• question when looking for a common denominator
must it be the lowest you can find or can it be just any?
• A common denominator cannot be "any" number, because it has to fit both fractions. However, it can be "any" fitting number. The reason you want it to be a smaller number is that it makes adding and simplifying easier. (see simplifying fractions) I hope this helped!
• you are confusing me about splitting the bar graph
• Splitting the bar graph really isn't at all confusing.It means that you divide something into fractions so you can understand better.The best object to use is a bar graph.Sal divided the first two into different fractions.Then, when you converted the two into fractions with same denominators,you add them together.When you add it,you get the answer,which Sal demonstrated in the third bar graph. So it is not confusing at all.Thanks for reading this reply!
• thank u for helping me i think ima get a 100
• Hope you do
• "Since 5 and 2 are both prime numbers, the smallest number (least common multiple) is just going to be their product."

Is there an explanation for this?
• Yes there is. Your getting into number theory for why that is the case. As well as formal math logic and proofs. There is a key theorem involved which would require far more math to put into this small space. But
Fundamental Theorem of Arithmetic:
Every integer greater than 1 (because 1 isn't prime), either is prime itself or is the product of a unique combination of primes.

Now I'm not going to shove a formal proof down you. Just some thoughts. LCM is the smallest value that can be cleanly divided by both numbers. So if x = 2 * 3 * 7 = 42 and y = 2 * 2 * 5 = 20
I'll use | to seperate, but when say 2 occurs on one side and 2 * 2 = 2^2 on the other, eliminate the one with the smaller exponent.
3 * 7 | 2 * 2 * 5 - the two on the left can be eliminated.
3 * 7 | 2 * 2 * 5 well the LCM is now 2*2*3*5*7=420

I'll also expand it so that you know it's not just prime * prime that is the smallest x * y for LCM.

Two numbers are relatively prime if they share no prime numbers in common. Thus if x and y are relatively prime or prime then LCM = x * y

Example: x = 6 = 2 * 3, y = 65 = 5 * 13
2 * 3 | 5 * 13 no way to eliminate any primes so the LCM is 6 * 65 = 390
• At 4.40 from this video I see how to do this but what do you do if theres are three numbers to add or subtract. How do you do that?
• I don´t wanna watch the video i wanna work
• How come when you have prime numbers, the smallest common multiple is them times each other? (Example: 5 and 2.) At - , Sal said that when both numbers were prime, you just needed to multiply them times each other. Why does that work?
(1 vote)
• That works because the 2 numbers he's using have only 2 factors each(1&5) and (1&2) and since these 2 numbers have only these factors or they are considered prime,you will find that the smallest common multiple is just multiplying those 2 numbers together.
(1 vote)
• thanks for the help. But when i am doing a harder problem is there an easy and quick way to check if you got it right?
(1 vote)
• You can estimate. Sometimes this doesn't work, but it usually does. Sal, at the end of the video, estimated to check his answer (2/5 is less than half, so when added 1/2, it won't equal a whole).
(1 vote)
• its harder to understand with bars.
(1 vote)
• it really isnt because it helps you visulive the problem or equasion better
(1 vote)
• How do you solve 11/15 - (-3/5) =
(1 vote)
• Well first recognize that 11/15- (-3/5) is also equal to 11/15+3/5 (because when two negatives are by each other, they become a positive). So from here on it should be easy to solve, change 3/5 to 9/15. So 11/15 + 9/15 = 20/15. Simplifying it would make it 4/3, change it to a mixed fraction would make it 1 1/3.
Hope this helped!
(1 vote)