# Greater than and less than symbols | Applying mathematical reasoning | Pre-Algebra | Khan Academy

Most of us are familiar with

the equal sign from our earliest days of arithmetic. You might see something

like 1 plus 1 is equal to 2. Now, a lot of people might

think when they see something like this that somehow equal

means give me the answer. 1 plus 1 is the problem. Equal means give me the

answer and 1 plus 1 is 2. That’s not what

equal actually means. Equal is actually just trying

to compare two quantities. When I write 1 plus 1

equals 2, that literally means that what I

have on the left hand side of the equal sign is the

exact same quantity as what I have on the right hand

side of the equal sign. I could have just as easily have

written 2 is equal to 1 plus 1. These two things are equal. I could have written

2 is equal to 2. This is a completely

true statement. These two things are equal. I could have written 1 plus

1 is equal to 1 plus 1. I could have written 1 plus 1

minus 1 is equal to 3 minus 2. These are both equal quantities. What I have here on

the left hand side, this is 1 plus 1 minus 1 is 1

and this right over here is 1. These are both equal quantities. Now I will introduce

you to other ways of comparing numbers. The equal sign is when I

have the exact same quantity on both sides. Now we’ll think

about what we can do when we have different

quantities on both sides. So let’s say I have the number

3 and I have the number 1 and I want to compare them. So clearly 3 and

1 are not equal. In fact, I could

make that statement with a not equal sign. So I could say 3

does not equal 1. But let’s say I want to figure

out which one is a larger and which one is smaller. So if I want to have some

symbol where I can compare them, where I can tell, where I can

state which of these is larger. And the symbol for doing that

is the greater than symbol. This literally would be

read as 3 is greater than 1. 3 is a larger quantity. And if you have trouble

remembering what this means– greater than– the larger

quantity is on the opening. I guess if you could view

this as some type of an arrow, or some type of symbol, but

this is the bigger side. Here, you have this

little teeny, tiny point and here you have the big

side, so the larger quantity is on the big side. This would literally

be read as 3 is greater than–

so let me write that down– greater than,

3 is greater than 1. And once again, it just doesn’t

have to be numbers like this. I could write an expression. I could write 1 plus 1 plus 1 is

greater than, let’s say, well, just one 1 right over there. This is making a comparison. But what if we had things

the other way around. What if I wanted to make

a comparison between 5 and, let’s say, 19. So now the greater than

symbol wouldn’t apply. It’s not true that 5

is greater than 19. I could say that 5

is not equal to 19. So I could still

make this statement. But what if I wanted to make

a statement about which one is larger and which

one is smaller? Well, as in plain

English, I would want to say 5 is less than 19. So I would want to say–

let me write that down– I want to write 5 is less than 19. That’s what I want to say. And so we just have to think

of a mathematical notation for writing “is less than.” Well, if this is

greater than, it makes complete sense that

let’s just swap it around. Let’s make, once

again, the point point towards the smaller

quantity and the big side of the symbol point to

the larger quantity. So here 5 is a smaller

quantity so I’ll make the point point there. And 19 is a larger quantity,

so I’ll make it open like this. And so this would be read

as 5 is less than 19. 5 is a smaller quantity than 19. I could also write this

as 1 plus 1 is less than 1 plus 1 plus 1. It’s just saying that this

statement, this quantity, 1 plus 1 is less

than 1 plus 1 plus 1.

I would explain it like you did, but when I was in school, we learned that the symbols are like a mouth of a crocodile which wants to eat the larger thing.

best use for lesser and greater symbols must be >.<

with love!

lol yeah i learned it that way too. but when i got older i realized the easiest to remember was think of a number line that has two arrow heads on each side. the arrow to the left is less than, right greater than.

Okay, WHO didn't know about greater and less than symbols?

What is that chalkboard thing you are drawing on… Software name

This was really helpful!

It took me years to get over the confusion surrounding the equal sign which was instilled in me by ignorant low tier educators.

'The greater number is on the bigger side' thing is a great way to remember it; I've always heard stupid little things like 'the bigger number is being eaten by the sign', but it always made me confused and think the analogue was 'the bigger number eats the smaller one'.

Thank u!

not fun

I never had issues with ><. it happens instantly in my mind. 15>5 or 5<15 for example. what I can't figure out is how to do it mathematically. the shorthand is I'm trying to write a program to compare binary numbers. I can tell you if a=5 and b=10, b is greater than a and if a-b=0 then a=b else a is either < or > than b. in this case the computer can't tell if the results are positive or negitive thus I'm lost…..

Thank you

<<sigh>> It's the "is less than" (<) and the "is greater than" (>) symbol. The "greater than" symbol is actually the plus sign (+) and the "less than" symbol is the minus sign (-). For example, Billy's age, b, is less than Cindy's age, c. That is b<c. However, if you say Billy's age is 5 less than Cindy's age, that would be b=c-5. Shame on you KA!

Are these symbols of used for mundane life doings? I mean, aside recalling how to used them on paper at school so won't have to write long words to show that I know that

6 + 100 – 46 is greater then 38

5 equals 5

and

-15 is less then 2…

Curious what's ze purpose of them? ðŸ˜—

I've always wondered, though, why do we need both? Why couldn't you just switch the placement of the numbers and always use the "greater than"?

Thanks

Fun! Algebra! Studying!

I really love your penmanship.

I was taught opposite in school. We were taught that you look at it like an alligators mouth eating the smaller of the two. 10<5, 930>1050, etc

the greater than and less than symbols are from the two ends of our number line…think about determining where 3 is in relation to 1 on the number line. 3 is to the right of the 1 on the number line which is why the symbol > is used to compare 3 & 1. If it was 1 & 3, you would ask yourself where is 1 in relation to 3 on the number line and the < symbol would be used. There is mathematics related to the symbols. It has never been rooted in alligators or the bigger part of the symbol toward the bigger quantity.

boring

2:30 & 4:20

I didn't know that that's what the equal sign stood for.