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Lesson 5: Adding and subtracting fractions with unlike denominators word problems

# Subtracting fractions word problem: tomatoes

Learn how to solve word problems involving the addition and subtraction of fractions with unlike denominators. Watch examples being worked out step-by-step, and practice applying the same techniques to solve similar problems. Created by Sal Khan.

## Want to join the conversation?

• This could have been solved much easier. What does it take for 2 7/8 to get to 3? 1/8. What does it take for 3 to get to 3 1/4? 1/4. Therefore the answer is 1/4 + 1/8 which is 3/8.
• For this case, that is an excellent way to do it. I commend you for seeing it that way.

I think many can't see the shortcuts yet, and the long way helps demonstrate the individual steps of the path.

Over time, with much practice, people will also find the fast way like you have already mastered.
• I'm confused. How did 3 1/4 turn into 12/4+1/4?
• 12/4 is equal to 3, so either way of writing it is valid
• What is the point of fractions?(I'm serious).
• Think of fractions like this: Suppose you solve a 2x2 Rubik's Cubes in half a second, somebody else solves it in 1/3 of a second, and another person solves it in 11/12 of a second. You want to find the average all the 3 solves. You would have to use knowledge about fractions, or else you won't be able to find the average of the solves, or even express the solve time!
• 0/0 is undefined, meaning that it can be a lot of different things, and therefore doesn't make sense as a fraction. As Kim says above, dividing by 0 is a nonsensical concept. Still, there can be times when 0/0 pops up in legitimate math questions, and it's useful to understand what it's close to, if not what it actually is (which is no particular number).

For example, imagine that I have some number of tomatoes (call this number n) and I'm always going to divide this number of tomatoes amongst that number of friends. In other words, each friend will always get n/n tomatoes. It's somewhat obvious that each friend will always get 1 tomato (for example, if I have 5 tomatoes and divide them among 5 friends, each one gets one). But what if I have 0 tomatoes and divide them amongst 0 friends? The answer doesn't make sense. However, it's useful to still know that if there were any friends, they would each get 1. So in this case, even though 0/0 is an undefined fraction, it acts like 1. In calculus, they would say that "the limit of n/n as n approaches 0 is 1."

Now let's imagine the same scenario, except where I have twice as many tomatoes, (2n), and I'm dividing them amongst n friends. Each friend gets 2n/n tomatoes. In this case, each friend will always get 2 tomatoes. But imagine I have 0 friends and 0 tomatoes. Again, the fraction 0/0 pops up, and it's still undefined, but this time it mostly means "2," whereas previously it mostly meant "1." Again, those who study calculus would say "the limit of 2n/n as n approaches 0 is 2."

We can think of similar examples for all possible numbers, which is why 0/0 is undefined. However, we can imagine that it's more of a context-dependent fraction than a fraction itself, and sometimes the number 0/0 can mean something, even though, in general, it doesn't mean anything.
• i feel like sal is making this too confusing, does any body agree with me?
• If you are confused, I recommend going back into the curriculum into something you're a bit more comfortable with, then, when you feel ready, you can get back to what was challenging before. Chances are, it will be a lot easier the second time.
• I have a question? i worked it out on paper and got 3/8 what if the whole number is lesser than the fraction then what do i do.
• What do you mean that the whole number is less than the fraction. Whole numbers are like: 0, 1, 2, 3, 4, 5, etc. The only whole number that can be smaller than a fraction is 0. Or do you have an improper fraction where the numerator is larger than the denominator? If you still need help, I suggest you post the actual numbers and the problem you are trying to do so that someone can help you.
• why chery tomatoes am I right
• Many times in these questions, they will add a little more info, to see how if you can get find your answer or get confused with the numbers. It's really all about how your brain processes the information
• can anybody please solve this for me?

Q.
50-21x2
------------
18x6-4
• The numerator:
50 minus 21 times 2 is equal to:
-> 50 - 42 (because 21*2=42)
-> 8 (because 50-40 = 10 -2 = 8

Denominator:
18 times 6 minus 4
(because there is no "parentheses," Order of Operations dictates that we multiply before subtracting, thus):
18 * 6 = (10*6) + (8*6) - 4 =
= (60 + 48) - 4
= (60 + 40) + (8) - 4
= 108 - 4
= 104

However, if you want to simplify then it must be noted that 104 is divisible by 8 as it relates to the denominator, and 8 is divisible by 8 as it relates to the numerator. Thus the simplified answer is:
1/13
• Wy do you have your videos so long and don't teach shortcuts.
• Okay so I'm not tryna be rude or anything like that, but I just have to say... what you said was pretty rude and also really unnecessary. Buuuuut for some unknown reason you posted it anyway so now I'm going to answer your mean questions:

First of all the videos are long because Sal has to teach things. I'd like to see you try and squish lots of stuff about subtracting fractions into a two-minute video. The videos are to help people learn, and sometimes that can take a while, but it's worth it to share knowledge.

Second: Sal doesn't teach shortcuts because they're kind of a lazy way to get through math questions. He teaches structured ways that can help you in many problems instead of just having you remember an algorithm. It's better to actually apply yourself than just remember a shortcut.

I hope you take what I said to heart because I really did spend a lot of time answering your questions when they really weren't very good questions at all and were quite petty and rude to Sal. In future, it would be appreciated if you please didn't use this chat page -- which is meant to ask people for help with math -- to complain. Thank you and enjoy your day.