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Subtracting fractions word problem: tomatoes

Sal solves a word problem by subtracting mixed numbers with unlike denominators. Created by Sal Khan.

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  • purple pi purple style avatar for user Phil
    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.
    (18 votes)
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    • cacteye green style avatar for user Nights Dawn
      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.
      (11 votes)
  • blobby yellow style avatar for user Marcos MacDonald
    I'm confused. How did 3 1/4 turn into 12/4+1/4?
    (11 votes)
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  • starky sapling style avatar for user Michaelr.Renaud
    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.
    (8 votes)
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  • aqualine ultimate style avatar for user Stella
    Whats a beefsteak tomato? because beefsteak and tomatos are two very different things
    (5 votes)
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  • starky sapling style avatar for user Antwan Dunmyer
    why chery tomatoes am I right
    (4 votes)
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  • leaf green style avatar for user Kshitiz Saxena
    can anybody please solve this for me?

    Q.
    50-21x2
    ------------
    18x6-4
    (3 votes)
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    • mr pants teal style avatar for user Aaron Rodriguez
      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

      Therefore: the answer is 8/104

      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
      (3 votes)
  • stelly yellow style avatar for user KaylaW
    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.
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      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.
      (4 votes)
  • eggleston blue style avatar for user theobertoni6
    what does created by sal khan mean?
    (2 votes)
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  • blobby green style avatar for user Tehphna Richardson
    he said 3 1/4 is the same as 12/4 + 1/4 but how is that? i need to understand that part better
    (4 votes)
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  • blobby green style avatar for user R.DEG
    Really confused by this one, thought you would change the denominators first.
    (2 votes)
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    • male robot hal style avatar for user Jesse T.
      You would still get the correct answer if you change the denominators first. To do that in this example, you would take the 1/4 and multiply the numerator and denominator by 2. This way 3 1/4 becomes 3 2/8.

      Next, you would turn 3 2/8 into an improper fraction. First, you need to find a way to represent 3 and 2/8 as a sum of two fractions. 2/8 is already a fraction, and 3 can be represented as 3/1, so you have (3/1 + 2/8). To create a common denominator, you will take 3/1 and multiply the numerator and denominator by 8, which gives you 24/8.

      So now 3 2/8 has become: (24/8 + 2/8). When you add it together, it is (26/8).

      Now you can do the same thing with 2 7/8. 7/8 is already a fraction, so you want to represent the 2 as 2/1, so you have (2/1 + 7/8). Then create a common denominator by taking 2/1 and multiplying the numerator and denominator by 8 to turn it into 16/8.

      So now 2 7/8 has become: (16/8 + 7/8). Add it together to get (23/8).

      Now you have (26/8) - (23/8), so you can easily subtract to get 3/8, which is the final answer.
      (3 votes)

Video transcript

Silvia is growing tomato plants and studying their heights. Here is her data. So the beefsteak tomato type had a height of 3 and 1/4 feet, Roma 2 and 7/8 feet, cherry 3 and 1/2 feet. And they ask us, what is the difference between the heights of the beefsteak, so that's that one right over there, and the Roma tomato plants? So they want us to find the distance between these two heights. So this cherry tomato height was really unnecessary for the sake of this problem. So we want to find the difference in these two heights. So we want to subtract the smaller of these from the larger of these. So we're really trying to evaluate what 3 and 1/4 minus 2 and 7/8 is. Now, the first thing that I like to do is convert both of these into mixed numbers. Sorry, they're already mixed numbers-- to convert both of these into improper fractions. So 3 and 1/4 is the same thing as 3 plus 1/4, which is the same thing as 12/4 plus 1/4. That's the same thing as 3 and 1/4. And from that, we're going to subtract 2 and 7/8. 2 and 7/8 is the same thing as 2 plus 7/8. 2 is the same thing as 16/8 plus 7/8. So this is essentially what we are trying to figure out. Now, what is 12/4 plus 1/4? It's 13/4, 13 over 4. And then, what's 16/8 plus 7/8? Well, that's 23/8. So this is going to be minus 23 over eight. Now, we're subtracting one fraction from another. But we have different denominators. So we can't make sense of this until we have the same denominator. And so what is the least common multiple of these two denominators, of both 4 and 8? What is the smallest number that is divisible by both 4 and 8? Well, 8 is divisible by 8. And 8 is also divisible by 4. So if we can rewrite 13/4 as having 8 as a denominator, then we are all set. So let's try to do that. So we're going to write both of these with 8 as the denominator. This one already has it. So 13/4, I'm going to have it with 8 as the denominator. So to get from 4 to 8, we have to multiply the denominator by 2. So in order to not change the value of the fraction, we have to multiply the numerator by that exact same value. We've got to multiply it by 2. So this becomes 26/8. And from 26/8, we're going to subtract 23/8. And so this is going to be over 8-- 26 minus 23, which is equal to, and we deserve our drum roll now, is 3. So it's 3/8. So the difference between the heights of the beefsteak and Roma tomato plants-- 3/8. And everything we've been doing insofar has been in feet, so 3/8 of a foot.