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.

## Arithmetic (all content)

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

Lesson 5: Comparing fractions

# Comparing fractions with like numerators and denominators

Created by Sal Khan.

## Want to join the conversation?

• Where did denominator and numerator come from? And who invented it? Also, who invented fractions? And when?
• how do i tell to use less or greater than? i am having trouble figuring it out and what i mean is sometimes i have like 4/5 and 1/2 obviously 4/5 is greater then i put the greater sign and check my answer but it says less than.. how can i know and remember which one to use?
(1 vote)
• The denominator of a fraction tells you how many pieces / parts will make up a whole unit. If the denominator = 10, then 10/10 = 1 whole unit. The larger the denominator becomes, the smaller the size of each piece. 1/10 is larger than 1/100
Hope this helps.
• Is the bigger fraction always going to be smaller than the smaller fraction? Ex:3/4 > 3/9.
(1 vote)
• Yes the denominator of a fraction is bigger than the other it is smaller if the numerator is the same
(1 vote)
• when did fractions become a thing?
(1 vote)
• You could find this with an internet search, which is what I did. There is evidence that fractions were used by ancient Egyptians in 1800 BC.
• Interesting video
I understood completely now
(1 vote)
• how do i get you as a avitar hopper?
(1 vote)
• so if i sead 3/5 is = to 2/6
(1 vote)
• have great day hope this made someone laff did i metion im realy in to body hair
(1 vote)
• Sal says 4/7 can be rewritten as 4 x 1/7. And 5/7 as 5 x 1/7. Can I always take the top number off and put a 1 there?
(1 vote)
• No. unless you want to do a longer problem. 4 x 1 = 4 right? so you can put 4/7. You can't put the 1 there unless the problem is telling you it really IS a 1. It is your choice if you want to make the problem a bit bigger.
(1 vote)

## Video transcript

Let's compare the fraction 4/7 to the fraction 5/7. And what I want you to do right now is to pause this video and think about which of these fractions represents a larger quantity. I'm assuming you've had a go at it, and the one thing that might jump out at you is that they both have the same bottom number, which we call the denominator. They both have a denominator of 7. So one way to think about it is this is literally 4 sevenths. This is literally 5 sevenths. So we could rewrite 4/7 as literally 4 times 1/7. And we can rewrite 5/7 as literally 5 times 1/7. It's 5/7. So now if I have 4 of something versus 5 of something, which is going to be a larger quantity? Well, clearly 5 of this 1/7 is going to be more. So 4/7 is smaller, 5/7 is larger. And so what we can do is we can write a less than symbol. The way that I remember less than and greater than, is that the point, the small side of the symbol, always is on the same side as the smaller number. So this could be read as 4/7 is less than 5/7, or that 4 times 1/7 is less than 5 times 1/7. Now, let's do another scenario, but instead of having the same denominator, let's have the same numerator. So let's say we want to compare 3/4 versus-- let's say versus 3/9. Which of these two fractions is a larger number? And once again, pause the video and try to think about it on your own. Well, as we mentioned, we don't have the same denominator here. We have the same top number instead. Here is the same bottom number, same denominator. Here we're going to have the same numerator. We have the 3 right over there. And we could view 3/4 as literally 3 times 1/4. And we could view 3/9 as literally 3 times 1/9. So we have 3/4 and we have 3/9. So we really just have to about what's larger, a fourth or a ninth? Well, think about if you start with a whole-- think about starting with a whole like this. And let me make a whole right over here, so the same sized whole. A fourth is literally taking the whole and dividing it into 4 pieces. While a ninth is taking the whole and dividing it into 9. 9 equal sections, I could say. So let's divide this into 4 equal sections. So my best attempt to hand draw equal sections. So that's 2 equal sections and then that looks pretty close to 4 equal sections. So that right over there is 1/4. And let me draw ninths here. So let me first split this into 3 equal sections. So those would be third. And then split each of those into 3 equal sections. So this is my best attempt at that, at hand drawing 9 equal sections, splitting the whole into 9 equal sections. So when you see here-- and you might have already realized this-- if you divide something into 4 equal sections, each section is going to be bigger than if you divide it into 9 equal sections. A ninth is smaller than a fourth. A ninth is smaller than 1/4. So 3/9 is going to be smaller than 3/4. So once again, when you want to do less than or greater than, you want to put the point, the small side of the symbol, on the same side as the smaller number. So it would look like this. And this is the greater than symbol, because what you have on the left is the larger number. 3/4 is greater than 3/9. And if you actually wanted to represent not just 1/4 and 1/9, we could actually color it in. 3 times one fourth, well that's 1, 2, 3. While 3 times 1/9, or 3/9, is 1, 2, 3. And when you look at it that way, it's pretty clear. But the important thing to realize is, is that when the denominator is larger, you're dividing the whole into more pieces so each piece will be smaller. So making the denominator larger makes the fraction smaller. Making the numerator larger makes the fraction larger.