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### Course: Arithmetic (all content) > Unit 5

Lesson 10: Decomposing fractions# Decomposing a fraction visually

Sal uses a tape diagram to decompose 7/9. Created by Sal Khan.

## Want to join the conversation?

- How do you add numbers with different denominators (EXAMPLE: 3/9 + 2/6)?(18 votes)
- You would need to convert the fractions so that they have the same denominator, and then add them by adding the values in the numerators and keeping the denominator the same. To convert a fraction into a different denominator, you have to multiply the numerator and denominator by the same number (in order to keep the actual value the same). The easiest way to convert two fractions to the same denominator is to make each denominator the least common multiple of the two previous denominators. With all that out of the way, let's see that example:

3/9 + 2/6

The least common multiple between 9 and 6 is 18 (you can learn how to find LCMs by using the search box in the top of any Khan Academy screen, if you don't know already). So, we multiply each fraction to get 18

3/9 * 2/2 = 6/18

2/6 * 3/3 = 6/18

Now, you have two fractions with the same denominator, so you can add them as normal:

6/18 + 6/18 = (6 + 6) / 18 = 12/18 = 2/3

So, your final simplified answer is 2/3

(Note: you could have made the problem lots easier by simplifying the fractions at the beginning into 1/3 and 1/3 and then just adding those, but that would defeat the purpose of learning how to add unlike denominators.)(74 votes)

- can you do 1/9 + 6/9 - 1/9 + 1/9?(20 votes)
- I think of it this way:

(1/9 + 6/9) - (1/9 + 1/9)

= (7/9) - (2/9)

= 5/9

So the answer would be 5/9

I remember being taught the MDAS (Multiplication, Division, Addition, Subtraction) method (which tells you which operations you would do first in given equation). For the problem you posed, I added all terms that needed to be added then I moved on to tackle the terms that needed to be substracted....Hope this helped.(21 votes)

- what happends if you have a improper fration(23 votes)
- then you have to change to a mixed number for example if you have 5/2 you could change it to 2 and 1/2(12 votes)

- In Thailand, we didn't learn decomposing a fraction

I want to know how important is it?(14 votes)- It's very practical and applicable to real life. It's important.(10 votes)

- At1:28cant Sal use 4/9+3/9 instead of 2/9+3/9+2/9?(9 votes)
- Yes that would work too. In fact there are many more possibilities, can you find more?

There are actually infinitely many ways to represent 7/9 (or any number really). Sal just gave 3 examples here, hoping to give the viewers some insight into fractions.(8 votes)

- How do you add fractions with diffrent dennminators(4 votes)
- Check the top-voted answer.

In short, you need to convert the denominator into a common denominator.

You can do it by a method called cross multiplication (I'm not sure but at least that's what I called it).`a c`

- + -

b d

a * d + c * b

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

b * d

The cross means multiplying the denominator on the other side.`a c`

- \ -

b d

a c

- / -

b d(4 votes)

- could u take away the denominator and pretend that it is 2+3+2=7(3 votes)
- You would be multiplying the fractions by the denominator (if it's the same for all of them) but technically yes.(2 votes)

- Sal says "times two ninths" but meant "plus two ninths.(3 votes)
- what if the question was 2/5-4/5(2 votes)
- I doubt it will be that. If it was, the answer be negative 2/5.(3 votes)

- is 2/6574847 equal to 3/5?(2 votes)
- No 2/6574847 is equal to 3.04189587986e-07 which is way less than 3/5 which is equal to 0.6.(3 votes)

## Video transcript

So let's think about all
of the different ways that we can represent 7/9. So let's just visualize 7/9. So here I have 9 equal sections. And 7/9 you could represent
as 7 of those equal sections. So let me get myself a
bigger thing to draw with, so that I can fill this in fast. Actually, I don't
like how that looks. I'm going to use
the paint brush. So here we go. So that's 1, 2, 3,
4-- you know where this is going-- 5, 6, and 7. So that's one way
of representing 7/9. We already know that. That's not too interesting. But let's see if we
can represent 7/9 as the sum of other fractions. So let's imagine maybe
we can represent it as-- let's do it as 2/9. Let me use a
different brush here. So let's represent it as 2/9. 2/9 plus-- I don't know,
let's see, maybe 3/9. But that doesn't quite
get us to 7/9 yet. 2/9 plus 3/9 is going
to get us to 5/9. So we're going to need 2 more. So it's going to be
plus another 2/9. So what would this look like? So let's just draw
another grid here. So this is going to
look like-- and I'll try to do it right
below it, so that we can see how they match up. So we have 2/9, this
2/9 right over here. Well, we have each
of these as a ninth. We have 9 equal sections. So we're going to get 1 and 2. And then we're going
to add 3 more ninths. So 1, 2, 3. So we add 3/9 right over
there and then 2 more ninths, 1 and 2. So notice, when I added 2/9 to
3/9 to 2/9, this equals 7/9. And we know that when we
add a bunch of fractions like this that have
the same denominator, we can just add the numerator. And this is why. This is 2/9 plus 3/9 times
2/9 is going to give me 7/9. Let's do this one more time. This is actually a lot of fun. So let me draw my grid again. And then let's see
what we can do. So let me get my pen tool out. Let me make sure my
ink isn't too thick. Well, this is fine. And let's add a
couple of ninths here. So let's add first 1/9. And I'm going to draw
out all the 9's in blue. And let's add 2/9. And then we could add-- I don't
know, maybe we could add-- let me give some space here
so we can add more. And maybe we could add 3/9. And then we could add, let's
see-- actually, let me just write this out. I'm going to try to add
four fractions here. So let's say add first 1/9
and see where that gets us. So 1/9 is going to get
us right over here. So that's 1/9. So let's say we add 2/9 to that. I've got my little
paint brush going on. So that's 1 and 2 more, 2/9. So that still
doesn't get us there. This gives us a total of 3/9. 1 plus 2 is 3-- 3/9. So let's add 4/9. And I'll do that
in this blue color. So 4/9. That's different enough. So let's see where this gets us. Actually, well, why not? So 4/9. And so that's going
to get us 1, 2, 3, 4. So that looks like it
got us all the way, because 1 plus 2 plus 4 is
going to give us 7-- 7/9. So what could we put here? Well, we could say 0/9. Why not? So we could call this
one right over here 0/9. And how would we visualize that? Well, we're saying
none of these. No ninths right over here. So this is 1/9 plus 2/9
plus 4/9 is equal to 7/9. So these are all different
ways to decompose the exact same fraction.