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Equal, Greater or Less Than

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

These are the of import signs to know:

=

When two values are equal
we utilise the "equals" sign

 example: 2+2 = 4
≠

When 2 values are definitely non equal
we use the "non equal to" sign

 example: 2+2 ≠ nine
<

When i value is smaller than some other
we use a "less than" sign

 example: 3 < 5
>

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

 example: 9 > half-dozen

greater than sign

Less Than and Greater Than

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

To call up which way effectually the "<" and ">" signs become, simply think:

  • Large > small
  • small < Large
The "small-scale" end always points to the smaller number, like this:

greater than sign

Greater Than Symbol: Large > modest

Case:

10 > 5

"10 is greater than 5"

Or the other way around:

v < 10

"5 is less than 10"

Do you 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

Case, a jug tin can hold upwardly to 4 cups of water.

And then how much water is in it?

Information technology could be iv cups or it could be less than 4 cups: And so until nosotros measure it, all we can say is "less than or equal to" four cups.

To show this, we add an extra line at the lesser of the "less than" or "greater than" symbol like 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 Apply

=

equals

one + i = 2

≠

not equal to

one + 1 ≠ 1



>

greater than

5 > 2

<

less than

seven < 9



≥

greater than or equal to

marbles ≥ 1

≤

less than or equal to

dogs ≤ 3

Why Use Them?

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

... simply can still say something most.

Then nosotros have ways of proverb what we do know (which may be useful!)

marbles

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

Answer: He must have less than ten:

Marbles < 10

If John still has some marbles nosotros can as well say he has greater than zero marbles:

Marbles > 0

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

Marbles ≥ 0

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

Combining

Nosotros can sometimes say two (or more than) things on the one line:

Example: Becky starts with $x, buys something and says "I got modify, too". How much did she spend?

Answer: Something greater than $0 and less than $x (simply NOT $0 or $x):

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

This can be written down in just one 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 too less than $10.

Discover that ">" was flipped over to "<" when we put it before what Becky spends. Ever brand sure the pocket-size end points to the small value.

Changing Sides

We saw in that previous example that when nosotros modify sides we flipped the symbol as well.

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

Just brand certain the pocket-sized end points to the small value!

Here is some other case using "≥" and "≤":

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

Answer: Something greater than, or perhaps equal to, $0 and less than, or possibly equal to, $10:

Becky Spends ≥ $0
Becky Spends ≤ $ten

This can exist written downward in just one line:

$0 ≤ Becky Spends ≤ $10

A Long Example: Cutting Rope

Hither is an interesting example I thought of:

rope

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

Answer: Let us call the longer length of rope "50", and the shorter length "S"

L must be greater than 0m (otherwise it isn't a slice of rope), and too less than 10m:

L > 0
L < 10

So:

0 < L < 10

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

The same thing can exist said about the shorter length "Due south":

0 < South < ten

But I did say there was a "shorter" and "longer" length, so we also know:

S < L

(Do you run across how bang-up mathematics is? Instead of saying "the shorter length is less than the longer length", we tin just write "South < 50")

We tin can combine all of that like this:

0 < S < L < 10

That says a lot:

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

Reading "backwards" we can besides see:

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

Information technology also lets us see that "S" is less than x (by "jumping over" the "L"), and fifty-fifty that 0<10 (which we know anyway), all in one statement.


NOW, I have one more trick. If Sam tried really difficult he might exist able to cut the rope EXACTLY in half, and so each one-half is 5m, only nosotros know he didn't because nosotros said there was a "shorter" and "longer" length, so we as well know:

South<five

and

Fifty>five

We tin can put that into our very groovy statement here:

0 < S < v < L < ten

And IF nosotros thought the two lengths MIGHT exist exactly 5 we could modify that to

0 < S ≤ 5 ≤ L < x

An Instance Using Algebra

OK, this example may be complicated if you lot don't know Algebra, but I thought you might like to meet it anyway:

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

If 10 > 11 , and then x+3 > 14

(Imagine that "x" is the number of people at your party. If there are more than 11 people at your party, and 3 more make it, so there must be more than 14 people at your party now.)

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