If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

### Course: Arithmetic>Unit 4

Lesson 4: Fractions and whole numbers

# Representing 1 as a fraction

Let's explore various ways to represent the number 1 as a fraction, like 1/1, 2/2, and 3/3. We see how dividing a whole into equal parts and shading them in can represent 1 whole. We also use a number line to visualize these fractions, emphasizing that they all represent the same value: 1 whole. Created by Sal Khan.

## Want to join the conversation?

• would 1/1 be considered a fraction?
(32 votes)
• Absolutely! 1/1 is a fraction, with 1's in both the numerator and the denominator.
(37 votes)
• hi, why is a decimal considered a fraction?
(8 votes)
• Because a decimal is part of a whole number like a fraction.
(17 votes)
• why is 0/0 unidentified? Why can't 0/0 just equal 0.
(7 votes)
• Good question!

If we did 6/2, for example, we would ask ourselves
“what number times 2 is 6?”. The answer would be 3.

In the same way, when we do 0/0, we ask ourselves “what number times 0 is 0?”. Any number times 0 is 0. So 0/0 can be anything and is therefore called indeterminate.

Have a blessed, wonderful day!
(5 votes)
• Why is this easier than I thought
(6 votes)
• i dont understand
(1 vote)
• how can a fraction be represented on a number line?
(3 votes)
• Fractions exist between whole numbers, so the point representing a fraction would be between two points that represent whole numbers. For example, the fraction 1/2 would be between 0 and 1.

Draw a line and label a point 0 on the far left and another point 1 on the far right. Draw a point in the center of that line between 0 and 1, and write 1/2.
(6 votes)
• I am new to fractions. So is 8/8 1 whole?
(4 votes)
• Yes - 8/8 is the same thing as 1 - just shown in a different way.

Imagine the pizza. If it was cut into eight slices - 1 slice would be 1/8 of the pizza (1 of the 8 slices) while 8/8 (all 8 slices) would be 1 whole pizza.
(4 votes)
• At , "Sal said "one oneth", but meant "one over one".

What is the proper way to say 1/1? One over one, one onethS?
(3 votes)
• One over one is correct. I'm sure both can be used (correct me if I'm wrong), but one over one is generally the most universally used.
(4 votes)
• would 1/1 be considered a fraction
(3 votes)
• Anything counts, unless the denominator is `0`.
So yeah, `1/1` is a fraction. It equals `1` whole
(1 vote)
• is o/o a fraction
(3 votes)
• `0/0` is indeterminate, it could be equal to any real number but there's no single agreed-upon value for it.
If `0/0 = ?` then that means `0*? = 0`. But we know that anything times `0` equals `0`, so `?` and thus `0/0` could be anything.
Happy learning.
(2 votes)
• and is 8/5 real?
(2 votes)
• yes 8/5 is real
(3 votes)

## Video transcript

So let's say that this circle-looking thing represents a whole. We've already seen a couple of situations. We said, hey, look, we could divide this into two equal pieces. And if we shade in one of them-- so one of these equal pieces-- that would be 1/2. And then if we shade in two of them, this would be 2/2. So let me color that in a little bit better. So this right over here, I've divided into two equal pieces. And I'm shading in two of these equal pieces. So what fraction of the whole do I have shaded in? Well, we've seen this multiple times. This is 2/2 of the entire figure. And we see we've shaded in the entire figure. So this is equal to 1 whole. And we could do that. We don't have to just split it into two equal parts. We could split it into three equal parts. So let's say we were to split it into three equal parts-- let me do that, my best attempt to draw three equal parts. Three equal parts looks like a Mercedes symbol. And that's my best. I could draw a little bit better job of that. Let me be clear that I'm trying to make them equal. So that's three equal parts. And then if we were to actually shade in the three equal parts-- so that would be one of the three, so that's 1/3, 2/3, and 3/3. So once again, 3/3 is equal to 1 whole. Now, what if we were to do something, on some level, even simpler? What if we just take our whole and we divide it into only one equal section? Well, I've already done that. This is one equal section right over here. And then I were to select that one equal section-- so let me color it in. So I have one section, and I'm going to shade it in. So what fraction of the whole do I now have shaded in? Well, I had one equal section to begin with. And I shaded in that one equal section. So I have 1/1 of this shaded in. And this is also clearly an entire whole. So this is also equal to a whole. And I think you see a pattern here. 2/2, 3/3, or 1/1-- these all represent the exact same value. They all represent a whole. And you would also see this if you were to draw a number line. So this is 0. This is 1. We could keep on going. Well, this is 1/1. If I were to say, well, between 0 and 1, I just have 1, I divide it into one equal chunk, well, that's just this whole thing right over here. And if I were to move one of those equal chunks, I would get to 1. If I divide it into two equal chunks and if I make two jumps-- one, two jumps-- I still end up at 1. If I divide it into three equal sections-- so let's say one, two, three equal sections-- and I make three jumps-- one, two, three-- I end up at 1 again. So 2/2, 3/3, 1/1, or 1 over 1-- these all are different ways of representing the number 1, or 1 whole.