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.