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### Course: Arithmetic > Unit 9

Lesson 3: Decomposing fractions# Decomposing a mixed number

Sal uses fraction models to decompose 2 1/4. Created by Sal Khan.

## Want to join the conversation?

- Can someone link an article of the reason why 8/8 is not bigger than 1/1? I am interested in reading about this topic, please reply.(39 votes)
- 1/1 = 8/8 because 1/1 is 1 out of 1 which is 1, and 8 out of 8 which is 8. the fraction sign is also the division symbol, so 1 divided by 1 =1, and 8 divided by 8= 1.(41 votes)

- They help you with cooking. You will need fractions if you are trying to figure out how much sugar you need for a cake. (‾◡◝)(28 votes)
- i can't do anything with fraction is just too hard.(9 votes)
- So start with a 20x20 times table and learning equivalent fractions. Pick any two numbers (like 2 and 5) and start going down both lines 2/5 = 4/10 = 6/15 = 8/20 ... This is where I like to start talking about fractions. So if you have 25/65, you can see that they are both on the 5 line, so going backwards, you get 5/13. This helps to find and reduce fractions.

Next, learn to multiply fractions (3/2)(5/4) multiply top and bottom 15/8. Since there is no line (except the one line) that has both 15 and 8, it cannot be reduced. Move to multiplications that can reduce, (4/5)(10/2) so when you multiply, you get 40/10. Since both 40 and 10 are on the 10 line, you can go up to 4/1, and you do not need to divide by 1, so you get 4.

Once you get good at these, then you can start to learn to add and subtract fractions, divide fractions, and then start working with mixed numbers.(22 votes)

- Can a fraction be cubed?(10 votes)
- Sure can! Take 4/5 for example. 4 cubed is 64, and 5 cubed is 125. So 4/5 cubed is 64/125.(12 votes)

- We should find the l.c.m while addition and subtraction or we can use the same method for multiplication and division?(8 votes)
- When multiplying or dividing (which is basically multiplying the first fraction by the reciprocal of the second fraction, "flipped") fractions, you don't have to find the LCM for the denominator because you're multiplying the denominators. It's a good idea to simplify the fractions before, though, so the numbers you get at the end aren't too large.(6 votes)

- 8/8 is longer form for 1/1 I think(6 votes)
- I do not think that longer form is language we use in math, we would say that 8/8 and 1/1 are equivalent fractions (meaning they are equal to each other).(8 votes)

- Can a fraction be squared (with an exponent)?(4 votes)
- Yes a fraction can be squared 4/5 squared = 16/25 because 4 squared is 16 and 5 squared is 25 but it is not the same because you don't multiply the numerator( the 4) and the denominator( the 5) by the same thing(6 votes)

- How do you decompose 1 3/8(5 votes)
- You can compose it to the improper fraction,11/8(3 votes)

- Elysepat, it is MUCH easier than yee think, but still, very difficult sometimes. The top number is the Numerator. The Numerator is how much someone has of the fraction. The bottom number is the denominator. The denominator is how much there is of something in total. If you want to add or subtract fractions, LEAVE THE DENOMINATORS ALONE! You need to only affect the numerator. that is it. See you in like, 60 years I asume.(5 votes)
- how do i do the symbol on my question(5 votes)

## Video transcript

Let's now think
about different ways to represent a mixed number. And let's say that our
mixed number is 2 and 1/8. Actually, let's make it a
little bit more interesting. Let's make it 2 and 1/4. So let's first think about
the whole number part, the 2. Well, the 2 is
literally two holes. You could literally
view that if you want. Right here we've
drawn each hole. We've cut it up into sections
of 8, so it literally is 8/8. So let me just do it like this. So the 2 is this whole region
right over here, that's 1. So this right over here is 1. And then this right
over here is 2, 2 holes, so let me paint that in. So that is 2 holes. And then I have 1/4. So this last piece,
this last hole, is divided into 8 sections. So let me divide it
into fourths first. So that's one 1/4, 2/4, and 3/4. So we want one of
those four to be filled in-- one of
those four in orange. So one of those four to be
filled in, just like that. You might notice that I
filled in two of the eighths, and that's because 1/4
and 2/8 is the same thing. So there I've represented
this mixed number, 2 and 1/4. Let's see how we
can decompose this. So let's get our grids back. So how else could we do it? And I'm just going to throw
a bunch of fractions up there and see what I get. So the first thing I'm
going to throw out is 1/2. So how would I
represent 1/2 here? Well, if I take
one of these holes and I put it into two
sections right over here, 1/2 would be this
section right over there. So let me color that in. So we have 1/2. So I'm first going to add 1/2,
which is the same thing as 4/8. And you see that I just filled
in four out of the eight sections, which is exactly
half of this first hole. So we're making some progress. Now let's throw in 3/8. So what would 3/8 look like? Each of these boxes
are literally an 1/8 and I could fill it in
however I want, but let me just put this as 1, 2, and 3. And then let's fill
in plus another 8/8. Now, what's 8/8? Well, 8/8 is a whole, and
I'll do that over here. I still haven't filled
this one in yet, but I'll fill in this
one right over here. So let's do that. So 8/8-- so that's 1/8, 2/8,
3/8, 4/8, 5/8, 6/8, 7/8, and 8/8, and it's a whole. So I have a whole hole
here, so that's 8/8. I want to make this one a whole,
because I want to get to 2, so let me put in a 1/8 there. So plus 1/8, well, that's going
to be this one right over here, so that's my 1/8. And then let's add another
2/8, plus another 2/8. Well, this is in
eighths right over here, so 2/8 is going to
be two of these. And notice, you see that the
2/8 is the same thing as 1/4. If you took this 1/4
and split it into two, so you have two times as
many pieces, it becomes 2/8. And you see that if 1 times
2 is 2, 4 times 2 is 8. So that 1/4 is the
same thing as 2/8. You see the 8/8 is the
same thing as a whole. Now, you see, you could make
another whole out of 1/2, plus 3/8, plus 1/8, and
they add up to a whole. And just to make sense
of why that worked, 1/2 is the same thing
as 4/8-- because you see that, we filled in the
4/8-- then you have 3/8, and then you have 1/8. And if you add all of these
together, 4/8 plus 3/8 plus 1/8, you are going
to get, in terms of eighths, 4/8 plus 3/8
plus 1/8 is going to be 8/8. 4 plus 3 plus 1 is 8, so you get
8/8 which is this entire whole. So hopefully that helps give
you a visual understanding of what we're doing when
we're adding and decomposing these fractions a
little bit more.