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## Class 5 (Marathi)

### Unit 3: Lesson 5

Word problems on fractions# Subtracting fractions word problem: tomatoes

CCSS.Math:

Sal solves a word problem by subtracting mixed numbers with unlike denominators. 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.(18 votes)
- 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)

- I'm confused. How did 3 1/4 turn into 12/4+1/4?(11 votes)
- 12/4 is equal to 3, so either way of writing it is valid(10 votes)

- 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) - Whats a beefsteak tomato? because beefsteak and tomatos are two very different things(5 votes)
- beefsteak tomatoes are large tomatoes and also called cherry tomato beefsteak tomato.(2 votes)

- why chery tomatoes am I right(4 votes)
- 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(3 votes)

- can anybody please solve this for me?

Q.

50-21x2

------------

18x6-4(3 votes)- 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)

- 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)
- 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)

- what does created by sal khan mean?(2 votes)
- it means it was created by Sal Khan aka the creator of khan academy(3 votes)

- 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)
- 12/4 is actually just 3, as 12 divided by 4 is 3. 3+1/4 is 3 1/4 (duh).

Hope this helps!(0 votes)

- Really confused by this one, thought you would change the denominators first.(2 votes)
- 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.