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Equal, Greater or Less Than

Besides as the familiar equals sign (=) it is also very useful to evidence if something is not equal to (≠) greater than (>) or less than (<)

These are the of import signs to know:

=

When two values are equal
nosotros use the "equals" sign

 example: ii+two = 4
≠

When 2 values are definitely non equal
nosotros use the "not equal to" sign

 example: two+2 ≠ 9
<

When one value is smaller than another
nosotros use a "less than" sign

 example: three < five
>

When i value is bigger than another
we use a "greater than" sign

 example: 9 > 6

greater than sign

Less Than and Greater Than

The "less than" sign and the "greater than" sign wait like a "V" on its side, don't they?

To remember which style around the "<" and ">" signs become, just call up:

  • BIG > small
  • pocket-size < BIG
The "small" end always points to the smaller number, like this:

greater than sign

Greater Than Symbol: BIG > small

Example:

10 > 5

"x is greater than v"

Or the other way effectually:

5 < 10

"5 is less than 10"

Do yous see how the symbol "points at" the smaller value?

... Or Equal To ...

Sometimes we know a value is smaller, merely may also be equal to!

jug

Instance, a jug can hold up to iv cups of water.

So how much water is in information technology?

It could be four cups or it could be less than 4 cups: So until we measure out it, all we can say is "less than or equal to" 4 cups.

To testify this, we add an extra line at the bottom of the "less than" or "greater than" symbol similar this:

The "less than or equal to" sign:

 ≤

The "greater than or equal to" sign:

 ≥

All The Symbols

Here is a summary of all the symbols:

Symbol

Words

Example Use

=

equals

i + 1 = 2

≠

not equal to

one + 1 ≠ 1



>

greater than

5 > 2

<

less than

seven < nine



≥

greater than or equal to

marbles ≥ one

≤

less than or equal to

dogs ≤ 3

Why Utilize Them?

Because there are things nosotros practice not know exactly ...

... only tin still say something almost.

So nosotros accept ways of maxim what nosotros do know (which may be useful!)

marbles

Case: John had 10 marbles, merely lost some. How many has he at present?

Respond: He must have less than 10:

Marbles < x

If John withal has some marbles we can also say he has greater than zippo marbles:

Marbles > 0

But if we thought John could have lost all his marbles we would say

Marbles ≥ 0

In other words, the number of marbles is greater than or equal to zero.

Combining

We can sometimes say two (or more) things on the 1 line:

Instance: Becky starts with $10, buys something and says "I got change, too". How much did she spend?

Answer: Something greater than $0 and less than $10 (but Not $0 or $10):

"What Becky Spends" > $0
"What Becky Spends" < $10

This can be written down in just ane line:

$0 < "What Becky Spends" < $10

That says that $0 is less than "What Becky Spends" (in other words "What Becky Spends" is greater than $0) and what Becky Spends is also less than $10.

Notice that ">" was flipped over to "<" when nosotros put it earlier what Becky spends. Ever make sure the small finish points to the small value.

Changing Sides

We saw in that previous example that when we change sides nosotros flipped the symbol too.

This: Becky Spends > $0 (Becky spends greater than $0)
is the same as this: $0 < Becky Spends ($0 is less than what Becky spends)

Just make certain the small end points to the small-scale value!

Here is another case using "≥" and "≤":

Example: Becky has $10 and she is going shopping. How much will she spend (without using credit)?

Respond: Something greater than, or peradventure equal to, $0 and less than, or perchance equal to, $10:

Becky Spends ≥ $0
Becky Spends ≤ $10

This can exist written down in just one line:

$0 ≤ Becky Spends ≤ $10

A Long Example: Cut Rope

Hither is an interesting instance I idea of:

rope

Example: Sam cuts a 10m rope into two. How long is the longer slice? How long is the shorter piece?

Answer: Let us call the longer length of rope "Fifty", and the shorter length "Due south"

L must exist greater than 0m (otherwise it isn't a piece of rope), and also less than 10m:

Fifty > 0
L < 10

So:

0 < 50 < x

That says that 50 (the Longer length of rope) is between 0 and 10 (but not 0 or 10)

The same thing tin be said about the shorter length "S":

0 < S < 10

Only I did say in that location was a "shorter" and "longer" length, then nosotros also know:

S < L

(Do you meet how neat mathematics is? Instead of saying "the shorter length is less than the longer length", we can just write "S < Fifty")

We tin can combine all of that like this:

0 < S < Fifty < ten

That says a lot:

0 is less that the short length, the brusque length is less than the long length, the long length is less than 10.

Reading "backwards" we can also run into:

10 is greater than the long length, the long length is greater than the brusque length, the brusque length is greater than 0.

Information technology also lets u.s.a. see that "Southward" is less than x (past "jumping over" the "L"), and fifty-fifty that 0<10 (which we know anyway), all in 1 statement.


At present, I have one more trick. If Sam tried really hard he might be able to cut the rope EXACTLY in half, so each half is 5m, just we know he didn't considering we said there was a "shorter" and "longer" length, so we also know:

S<5

and

L>5

We can put that into our very smashing statement here:

0 < Due south < v < L < 10

And IF we idea the two lengths MIGHT be exactly 5 nosotros could change that to

0 < Southward ≤ five ≤ L < 10

An Example Using Algebra

OK, this example may be complicated if you don't know Algebra, but I idea you might similar to run into information technology anyway:

Example: What is 10+3, when we know that x is greater than 11?

If ten > xi , then x+3 > 14

(Imagine that "x" is the number of people at your political party. If at that place are more than eleven people at your political party, and 3 more get in, then there must be more than than 14 people at your party now.)

5250, 5251, 5252, 5253, 5254, 5255, 5256, 5257, 5258, 5259