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### Course: Arithmetic > Unit 13

Lesson 4: Adding and subtracting fractions with unlike denominators- Adding fractions with unlike denominators introduction
- Add fractions with unlike denominators
- Subtracting fractions with unlike denominators introduction
- Subtracting fractions with unlike denominators
- Adding and subtracting 3 fractions
- Solving for the missing fraction
- Add and subtract fractions

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# Adding fractions with unlike denominators introduction

To add fractions with different denominators, such as 1/2 and 1/3, you need to find a common denominator. The least common multiple of 2 and 3 is 6, so you can rewrite the fractions as 3/6 and 2/6, respectively. This allows you to add the numerators together, resulting in a sum of 5/6.

## Want to join the conversation?

- Still so confused' i have watched it twice and thought i was getting the hang of it but i was doing it wrong. Haha i'll figure it out eventually hopefully.(55 votes)
- Howdy Cheyenne,

It isn't that we can't literally add two fractions with unlike denominators; if we converted the fractions to decimals then we could add them simple enough.

But since we are humans we don't really have super good calculators in our head we need a system of easily adding fractions.

So while it may not seem the easiest it is a great way to add fractions once you get skilled at it. :-)

If we have 3/4 of a cherry pie, and we would like to add that to 2/5 of another cherry pie, how could we write down that much? Well, we could go around saying that we have "3/4 + 2/5 of cherry pie", simply carrying around those pie slices together.

But... as you can tell that isn't all that elegant. It would be nice if we could represent it as one fraction.

Let's imagine that we slice up these pies into "smaller" pieces. If we do this the right way, we could create fractions of the pies with like denominators.

For an example, to give "2/5" and "3/4" a "like" denominator we could easily multiply "2/5" by 4 (numerator & denominator) and "3/4" by 5 in the same way. Remember, if we multiply the numerator & denominator by the same number the value of the fraction doesn't change. All we are doing is cutting up our PIE differently.

(3 * 5)/(4 * 5) = 15/20

(2 * 4)/(5 * 4) = 8/20**NOTE**: The way I found the "like" denominator so easily is that if we have a denominator x and a different denominator y we know that both x & y can go into (x * y), or*the product*of y. So anytime you can't find the smallest number that both can go into, just multiply the numbers by each other!

Now since we have pies that have the same cut slices (like denominators), we can more easily add the slices together. If we have 8/20 of a PIE and 15/20 of PIE we can easily (visually) add this together to get 23/20 of a PIE. Hey, it looks like we actually have more of a PIE left over!

Hope this helps!

- Convenient Colleague(56 votes)

- I still understand. The way you kinda explain it is kinda confusing.(38 votes)
- Multiple denominator and nominator and you get your answer. Example: 5/2 + 5/4 multiple 4 2 times sense other is 2 and you get 8 and then multiple 5 together 25/8(3 votes)

- please vote me for a badge(37 votes)
- i have rewatched this video 7 times and i still dont understand(17 votes)
- 3/4 + 4/12 you have to multiply 4 by 3 to get twelve, since you multiplied by 3 on the denominator, you also have to do it to the numerator.(11 votes)

- this is the only video i have seen that is hard.(13 votes)
- I'm still so confused I watched the video 50 times(5 votes)
- Hello

So what Sal was trying to say is that when you get two fractions, for example, 1/4 and 1/3, you would need to add. in my opinion, it is easier to convert the fractions to denominators that are the same.

like:

|-----|-----|-----|-----| and |------|------|-----| right, so you need to find the common factor of 4 and 3 is 12 so to make 4 to 12 you would need to times that by 3 and 1/4 times three on the bottom you need to times the top as well so that would equal 3/12.

After you find the common factor between them that is 12 after you converted them into the most common factor, then you add in this case that is 4/12 + 3/12, and when you add 4 and 3, that is seven, so the answer to 1/3 and 1/4 is 7/12 (please ignore my horrible spelling and punctuation.)

Hope this helps(11 votes)

- Stop saying sixths like that!(8 votes)
- Im telling you! Its so annoying!(5 votes)

- stop bragging its actually annoying, and some advice, don't give your grade out online.(6 votes)
- y u so pressed(5 votes)

- This is sooooo confusing i watched this vid for about 30 times and I still don’t get it can someone help me (this is probably the most hardest vid I’ve ever seen so far idk how people get this)(4 votes)
- just try your best i keep on trying and trying until i get it im still learning ok 😁.(8 votes)

- DoNt sAy SiXtHs lIkE tHat!(7 votes)

## Video transcript

- [Instructor] In this video
we're gonna try to figure out what 1/2 plus 1/3 is equal to. And like always, I encourage
you to pause this video and try to figure it out on your own. All right, now let's work
through this together. And it might be helpful
to visualize 1/2 and 1/3. So this is a visualization of 1/2 if you viewed this entire bar as whole, then we have shaded in half of it. And if you wanted to visualize
1/3 it looks like that. So you could view this as this half plus this gray third here, what is that going to be equal to? Now one of the difficult
things is we know how to add if we have the same denominator. So if we had a certain
number of halves here and a certain number of halves here, well then we would know how
many halves we have here. But here we're trying
to add halves to thirds. So how do we do that? Well we try to set up
a common denominator. Now, what do we mean by
a common denominator? Well what if we could
express this quantity and this quantity in terms
of some other denominator. And a good way to think about it is is there a multiple of two and three and it's simplest when you
use the least common multiple and the least common multiple
of two and three is six. So can we express 1/2 in terms of sixths and can we express 1/3 in terms of sixths? So we can just start with one over two and I made this little fraction
bar a little bit longer 'cause you'll see why in a second. Well if I wanna express
it in terms of sixths, to go from halves to sixths, I would have to multiply
the denominator by three. But if I want to multiply
the denominator by three and not change the value of the fraction, I have to multiply the
numerator by three as well. And to see why that makes
sense, think about this. So this, what we have in green, is exactly what we had before but now if I multiply it the numerator
and the denominator by three, I've expressed it into sixths. So notice, I have six
times as many divisions of the whole bar. And the green part which you
could view as the numerator, I now have three times as many. So these are now sixths. So I now have 3/6 instead of 1/2. So this is the same
thing as three over six and I want to add that or if
I want to add this to what? Well how do I express
1/3 in terms of sixths? Well the way that I could do
that, it's one over three, I would want to take each of these thirds and make them into two sections. So to go from thirds to sixths
I'd multiply the denominator by two but I'd also be
multiplying the numerator by two. And to see why that makes sense, notice this shaded in gray part is exactly what we have here but now we
took each of these sections and we made them into two sections. So you multiply the numerator
and the denominator by two. Instead of thirds, instead
of three equal sections, we now have six equal sections. That's what the denominator times two did. Instead of shading in just one of them, I now have shaded in two of them because that one thing that I shaded has now turned into two sections. And that's what multiplying
the numerator by two does. And so this is the same thing as 3/6 plus this is going to be 2/6. And you can see it here. This is 1/6, 2/6, and now
that everything is in terms of sixths, what is it going to be? Well it's going to be a
certain number of sixths. If I have three of something
plus two of that something, well it's going to be
five of that something. In this case, the something is sixths. So it's going to be 5/6. I have trouble saying that. And you can visualize it right over here. This is three of the
sixths, one, two, three, plus two of the sixths,
one, two, gets us to 5/6. But you could also view
it as this green part was the original half and this gray part was the original 1/3, but
to be able to compute it, we expressed both of
them in terms of sixths.