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

Lesson 4: Fractions and whole numbers# Whole numbers as fractions

Let's explore how to represent whole numbers as fractions. We shade circles to demonstrate 3/1 equals 3, and discuss how the fraction symbol represents division. We then illustrate the concept on a number line, connecting fractions to whole numbers. Created by Sal Khan.

## Want to join the conversation?

- What if I have 1 whole, and I have nothing shaded in? Will that just be 0/1?(32 votes)
- Yes. The whole represents the denominator. There are 0 parts, so 0 as the numerator. 0 over 1. 0/1. So it is definitely 0/1. Thanks for asking!(14 votes)

- Then how about 5/1 ? It is read as five one or five ones ?(13 votes)
- Five ones. This fraction means 5 wholes.(29 votes)

- can fractions have negative or decimal numbers inside?(16 votes)
- Yes! Fractions are essentially a form of division, so you can have a decimal or another fraction as the numerator or denominator.(5 votes)

- Seriously, where would this be used? Is the point something other than math. I understand whats happening here but how would this be used in the real world?

I'm a paranoid person and this question is a mental health tool.(7 votes)- Oh I PROMISE YOU, you need to be able to do fractions

So they haven't explained it yet but fractions are actually just a different way of expressing division in equations

so the fraction 10/2 is literally 10 divided by 2

And if you did the division section you'll know that division helps in separating groups equally.

If you need to spilt 10k between 10 people how many will received money?

If I have 3 pencils and 3 classes how many pencils can I have for each class

Then when the number doesn't spilt evenly fractions are there to explain what part of a whole part is needed to be given

Once again like with money: If my business made $47 today and I need to split it among 3 workers how much money does each worker get?

$15.66 (not rounded because we don't have extra money to give to all three)(6 votes)

*Why*is every single discussion locked and*how*do I do that?(7 votes)- not every discousion(2 votes)

- can a whole number be written as a fraction with a denominator of 1?(6 votes)
- Yes, all whole numbers can be written as a fraction with a denominator of 1.(2 votes)

- what yall talking about tell me pls forreal forreal ok tell meEMMA(3 votes)
- we are talking about stuff from the video and we are talking about fractions(5 votes)

- ummmmmmm ya what they sed(5 votes)
- what does this mean? 8/3 cuz idk(4 votes)
- /
*_____3_wholes_______*\

| 1_2_3 | 1_2_3 | 1_2_3 |*___________________*^8th number

so, it's 8-equal-parts/3-wholes.

On ward!(3 votes)

- why does he change the colors when writing?(3 votes)
- to split the 2 different subjects(4 votes)

## Video transcript

Let's say that this circle right
over here represents one whole. And we've divided this circle
into one, two, three, four, five equal sections. So each of these sections
represents 1/5 of the circle. And we've seen this already. 1/5, 1/5, 1/5, and 1/5. And if we were to then
color in some of this-- So, let's say we were to color
in three of these sections. So, that's one of the
sections right over there, another one right over here. So, we've colored
in two of the fifths and then three of the fifths. Notice, you put those
three 1/5's together, how much have we now shaded in? We've shaded in
3/5 of the whole. So the fraction that's
actually shaded in now is 3/5. 3/5 is what's shaded in. Now let's do something
in some ways a little bit simpler but also in some
ways kind of interesting. Let's start with
the whole again. So, once again,
this is one whole. Let me label it. One whole. And instead of dividing it
into five equal sections, I'm just going to divide
it into one equal section. So, if I were to shade
this in just like that-- so I'm shading in my one
whole, my one equal section, how many of the equal
sections are now shaded in? Well, just to remind ourselves,
there is one equal section, and I have shaded in exactly
one of those one equal section. I've shaded in the whole thing. Or I could say that 1/1--
which you'll never hear someone actually say-- is
shaded in, or I could say that the whole
thing is shaded in. So this is equal to one whole. So that's a whole. That's interesting. And I want you to keep
in mind, remember, look. We literally have one,
two, three fifths, and we literally call that 3/5. Now, this is one whole. Now, what happens if we were
to do this multiple times? Let me copy and paste that. So now I have another
one whole and then another one whole
right over here. So now, in total, how
many wholes do I have? Well, I have three. One, two, three wholes. And I've actually
shaded in three holes. So this one right over
here is equal to-- Let me make sure I label it right. This right over
here is equal to, if I were to take
the combination, this is equal to 3. 3 holes. Or if I were to think of it in
terms of numbers, just a number line, literally, this would
represent the number 3. But what's another way
I could represent it? Notice when I took a 1/5,
another 1/5, and another 1/5, I could call that 3/5. So now if I take one 1/1,
another 1/1, and another 1/1, well, I should be able to
call this 3/1, or 3 firsts, or however you want to call it. So I could call this 3 firsts. So this is interesting. Now we're seeing where the
top number on a fraction is larger than the bottom one. But another way of thinking
about this fraction symbol is that it's division. So you could view this as 3
divided by 1 is equal to 3. Or you could say, well,
look, 1 over 1 is a whole, and I now have three of them,
so this is equal to 3 wholes. So 3/1 is the same
thing as the number 3. And let me make sure,
let me emphasize that. Let me draw this
on a number line. So once again, let me
go all the way to 3. So 0, 1, 2, and 3. So one whole gets us exactly
one jump on the number line. So this right over here,
that gets us to 1/1. We do another jump, now
we've gotten 2 firsts, I guess you could say. We've essentially taken
two of these jumps. Each jump is 1/1. Now we are at 2/1, which
is the same thing as 2. You take another jump,
and we essentially get to, or we do get to 3/1, which
is the exact same thing as 3.