Is Greater Than 1 2
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Equal, Greater or Less Than
Besides equally 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 important signs to know:
| = | When 2 values are equal | example: 2+two = iv |
| ≠ | When two values are definitely not equal | example: ii+2 ≠ 9 |
| < | When one value is smaller than another | example: 3 < v |
| > | When 1 value is bigger than another | example: 9 > 6 |
Less Than and Greater Than
The "less than" sign and the "greater than" sign expect like a "V" on its side, don't they?
To remember which way around the "<" and ">" signs go, just remember:
- BIG > small
- small < Big
Greater Than Symbol: BIG > small
Example:
10 > 5
"ten is greater than 5"
Or the other style around:
5 < ten
"5 is less than x"
Do you lot see how the symbol "points at" the smaller value?
... Or Equal To ...
Sometimes nosotros know a value is smaller, only may as well be equal to!
Example, a jug tin can hold up to iv cups of water.
And so how much h2o is in it?
Information technology could be 4 cups or information technology could be less than 4 cups: So until we mensurate it, all we can say is "less than or equal to" 4 cups.
To show this, we add an extra line at the bottom 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 | Case Apply |
|---|---|---|
| = | equals | ane + 1 = 2 |
| ≠ | not equal to | 1 + one ≠ 1 |
| | | |
| > | greater than | 5 > 2 |
| < | less than | 7 < 9 |
| | | |
| ≥ | greater than or equal to | marbles ≥ i |
| ≤ | less than or equal to | dogs ≤ 3 |
Why Use Them?
Because there are things we do non know exactly ...
... but can still say something about.
So we take ways of saying what we do know (which may be useful!)
Example: John had 10 marbles, but lost some. How many has he now?
Reply: He must accept less than 10:
Marbles < 10
If John still has some marbles nosotros can also say he has greater than zero marbles:
Marbles > 0
But if we idea 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
Nosotros tin can sometimes say 2 (or more than) things on the one line:
Instance: Becky starts with $10, buys something and says "I got change, as well". 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 tin be written downward in merely 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 also less than $ten.
Find that ">" was flipped over to "<" when we put information technology before what Becky spends. Always make sure the minor stop points to the small value.
Changing Sides
Nosotros saw in that previous case that when nosotros modify sides we flipped the symbol likewise.
| 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 sure the pocket-size terminate points to the minor value!
Hither is some other example using "≥" and "≤":
Example: Becky has $ten and she is going shopping. How much will she spend (without using credit)?
Answer: Something greater than, or possibly equal to, $0 and less than, or possibly equal to, $ten:
Becky Spends ≥ $0
Becky Spends ≤ $10
This tin be written downwardly in but one line:
$0 ≤ Becky Spends ≤ $x
A Long Example: Cut Rope
Hither is an interesting example I thought of:
Example: Sam cuts a 10m rope into 2. How long is the longer piece? How long is the shorter piece?
Answer: Let us call the longer length of rope "L", and the shorter length "S"
L must be greater than 0m (otherwise it isn't a piece of rope), and besides less than 10m:
Fifty > 0
Fifty < 10
And so:
0 < Fifty < 10
That says that L (the Longer length of rope) is between 0 and 10 (only non 0 or 10)
The aforementioned affair can be said well-nigh the shorter length "S":
0 < S < 10
Just I did say there was a "shorter" and "longer" length, and so nosotros also know:
S < L
(Do you come across how peachy mathematics is? Instead of maxim "the shorter length is less than the longer length", we tin merely write "S < L")
Nosotros tin combine all of that like this:
0 < Southward < Fifty < x
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 ten.
Reading "backwards" we tin as well encounter:
x is greater than the long length, the long length is greater than the short length, the short length is greater than 0.
It also lets us see that "Southward" is less than ten (past "jumping over" the "L"), and fifty-fifty that 0<10 (which we know anyway), all in one statement.
At present, I have one more than trick. If Sam tried really hard he might be able to cut the rope EXACTLY in one-half, then each half is 5m, just nosotros know he didn't considering we said there was a "shorter" and "longer" length, and then we too know:
S<5
and
L>5
Nosotros tin put that into our very neat statement here:
0 < S < 5 < L < x
And IF we thought the 2 lengths MIGHT be exactly 5 nosotros could modify that to
0 < S ≤ five ≤ L < ten
An Example Using Algebra
OK, this example may be complicated if you don't know Algebra, only I idea you lot might like to see it anyway:
Case: What is x+iii, when we know that x is greater than 11?
If x > 11 , and so ten+3 > fourteen
(Imagine that "x" is the number of people at your party. If there are more than 11 people at your party, and 3 more arrive, so there must be more than than 14 people at your political party now.)
5250, 5251, 5252, 5253, 5254, 5255, 5256, 5257, 5258, 5259
Is Greater Than 1 2,
Source: https://www.mathsisfun.com/equal-less-greater.html
Posted by: geerdinduch.blogspot.com
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