The greater than sign is one of the simplest mathematical symbols, yet it is easy to reverse when comparing numbers. The symbol looks like >, and it tells you that the value on the left is larger than the value on the right.
The greater than sign (>) means that the number or value before the symbol is larger than the number or value after it. For example, 8 > 5 is read as “8 is greater than 5.” The open side faces the larger value, while the pointed end faces the smaller value.
What Is the greater than sign?
The greater than sign is written as:
>
It is a mathematical inequality symbol used to compare two quantities that are not equal.
For example:
10 > 6
This statement means:
10 is greater than 6.
In mathematical notation, the symbol is placed between two values. The value on the left must be larger for the statement to be true.
Here are a few more examples:
| Comparison | Read as |
|---|---|
| 9 > 4 | 9 is greater than 4 |
| 25 > 12 | 25 is greater than 12 |
| 100 > 99 | 100 is greater than 99 |
| 2.5 > 2 | 2.5 is greater than 2 |
| 0 > -3 | 0 is greater than negative 3 |
The same principle works with whole numbers, decimals, fractions, negative numbers, variables, measurements, and many other types of mathematical values.
How to Remember the Greater Than and Less Than Signs
Many students understand number comparisons but accidentally reverse > and <.
A simple rule solves the problem:
The open side faces the larger number. The pointed side faces the smaller number.
Consider:
12 > 7
The wide opening faces 12 because 12 is larger. The narrow point faces 7 because 7 is smaller.
Now reverse the numbers:
7 < 12
The comparison still says the same thing, but it is read as:
7 is less than 12.
Both symbols effectively point toward the smaller value.
The alligator method
A popular classroom memory trick imagines the symbol as an alligator mouth.
The alligator wants to eat the larger number, so its mouth opens toward the bigger value.
For example:
15 > 8
Imagine the open mouth facing 15 because 15 is the larger number.
This can be useful for young learners, although understanding the mathematical rule is even better: wide side toward the greater quantity, point toward the smaller quantity.
Greater Than Sign vs Less Than Sign
The greater than sign and less than sign look similar but express opposite relationships.
| Symbol | Meaning | Example | How to read it |
|---|---|---|---|
| > | Greater than | 8 > 3 | 8 is greater than 3 |
| < | Less than | 3 < 8 | 3 is less than 8 |
| = | Equal to | 8 = 8 | 8 equals 8 |
| ≥ | Greater than or equal to | x ≥ 8 | x is at least 8 |
| ≤ | Less than or equal to | x ≤ 8 | x is at most 8 |
The equals sign describes two equal quantities. Greater-than and less-than symbols describe inequalities, meaning one quantity has a different order or magnitude from another.
Which way does the greater than sign go?
The greater than sign points toward the smaller number.
So:
20 > 5
is correct because the narrow point faces 5.
Writing:
20 < 5
would be false because that statement says 20 is less than 5.
greater than sign Examples With Numbers
The easiest way to learn the symbol is to compare actual values.
Whole numbers
30 > 20
Thirty is greater than twenty.
500 > 125
Five hundred is greater than one hundred twenty-five.
Decimal numbers
Decimals can also be compared:
4.8 > 4.2
Because both numbers have 4 as their whole-number part, compare the tenths digits. Eight tenths is larger than two tenths.
Another example:
7.05 > 6.99
The number 7.05 is greater because its whole-number portion is 7 rather than 6.
Negative numbers
Negative values sometimes cause confusion.
For example:
-2 > -7
Although 7 is numerically larger than 2 when both are positive, -2 is greater than -7 because -2 lies farther to the right on a number line.
Another example:
0 > -10
Zero is greater than every negative number.
The greater-than symbol therefore compares mathematical value, not simply the visible digits.
How to Use the greater than sign With Fractions
Fractions can be compared using the same symbol.
For example:
3/4 > 1/2
Three-fourths equals 0.75, while one-half equals 0.5.
Therefore:
3/4 > 1/2
Fractions with the same denominator are even easier:
7/10 > 3/10
Because the denominator is identical, compare the numerators. Seven tenths is greater than three tenths.
For fractions with different denominators, you can use decimal conversion, common denominators, or cross multiplication to determine which fraction is larger.
Greater Than Sign in Algebra
The greater than sign becomes especially useful when variables are introduced.
Consider:
x > 5
This does not identify one exact value of x. Instead, it describes an entire set of possible values.
Examples that satisfy the inequality include:
- x = 6
- x = 8
- x = 20
- x = 100
But:
- x = 5 does not satisfy it.
- x = 4 does not satisfy it.
That is because the expression specifically requires x to be greater than 5.
Greater than inequalities
Suppose you have:
x + 2 > 7
Subtract 2 from both sides:
x > 5
The solution is every number greater than 5.
One important algebra rule appears when multiplying or dividing an inequality by a negative number: the inequality sign reverses direction.
For example:
-2x > 10
Divide both sides by -2:
x < -5
This reversal is essential when solving inequalities correctly.
Greater Than vs Greater Than or Equal To
The symbols > and ≥ are related but do not mean exactly the same thing.
The greater than symbol:
x > 10
means x must be strictly larger than 10.
The greater than or equal to symbol:
x ≥ 10
allows x to be either 10 or anything larger.
Unicode identifies ≥ separately as the “GREATER-THAN OR EQUAL TO” symbol, with code point U+2265.
For example, imagine an amusement ride requires passengers to be at least 120 cm tall.
The condition can be written:
height ≥ 120 cm
A person exactly 120 cm tall qualifies.
Writing:
height > 120 cm
would exclude someone who is exactly 120 cm.
That small horizontal line beneath the greater-than shape changes the meaning.
How to Read Greater Than Statements
When you encounter the symbol, read the expression from left to right.
45 > 21
Read:
“45 is greater than 21.”
x > 100
Read:
“x is greater than 100.”
3.7 > 3.4
Read:
“3.7 is greater than 3.4.”
The phrase “more than” often expresses the same basic relationship in everyday language.
For example:
“Sarah has more than 20 books.”
Mathematically, if b represents the number of books:
b > 20
Notice that this means Sarah must have at least 21 whole books. Exactly 20 would not satisfy the statement.
Using the Greater Than Sign on a Number Line
A number line provides a visual way to understand inequalities.
Numbers increase as you move to the right.
For example:
7 > 3
Seven appears to the right of three on the number line.
Similarly:
-1 > -6
Negative one appears to the right of negative six, which explains why -1 is greater even though both numbers are negative.
This rule is useful:
A number farther to the right on a standard number line is greater than a number farther to the left.
Number lines are especially helpful when working with negative numbers and algebraic inequalities.
Real-Life Uses of the greater than sign
The greater than sign is not limited to classroom exercises. Comparisons appear throughout daily life, science, finance, statistics, and technology.
Age requirements
Suppose an activity is available only to people older than 18:
age > 18
This strictly excludes someone who is exactly 18.
Temperature
If today’s temperature is 30°C and yesterday’s was 25°C:
30°C > 25°C
Money
If one product costs $90 while another costs $75:
$90 > $75
The first price is greater.
Sports scores
If Team A scores 4 goals and Team B scores 2:
4 > 2
Measurements
If one object weighs 15 kg and another weighs 11 kg:
15 kg > 11 kg
Price comparisons, measurements, scores, budgets, and other numerical comparisons are common practical applications of inequality symbols.
Greater Than Sign in Programming
The symbol also appears throughout computer programming.
In many programming languages, > is a comparison or relational operator.
For example, in JavaScript:
5 > 3
evaluates to:
true
while:
3 > 5
evaluates to:
false
JavaScript’s greater-than operator returns true when the left operand is greater than the right operand and false otherwise.
A program might use the comparison in a condition:
age > 18
The application can then perform an action depending on whether the condition evaluates as true or false.
Languages in the C family and many other programming environments also use related operators such as:
>=
to represent greater than or equal to.
This is one reason the symbol is familiar far beyond traditional mathematics.
Greater Than Sign in HTML and Unicode
The standard greater than character is:
>
Its Unicode code point is:
U+003E
The character also corresponds to decimal value 62 in common character encoding references.
In HTML, the named character reference commonly used for the symbol is:
>
It renders as:
>
Related Unicode mathematical symbols include:
| Symbol | Meaning | Unicode |
|---|---|---|
| > | Greater than | U+003E |
| ≥ | Greater than or equal to | U+2265 |
| ≫ | Much greater than | U+226B |
| ≯ | Not greater than | U+226F |
Unicode therefore distinguishes the ordinary mathematical comparison sign from several related mathematical operators.
Who Invented the Greater Than Sign?
The history of > goes back several centuries.
The earliest known use commonly credited in mathematical history appears in work by English mathematician Thomas Harriot. His book Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas was published posthumously in 1631 and used the greater-than and less-than symbols to express comparisons.
The symbols proved useful because they allowed mathematicians to represent relationships between quantities compactly.
Instead of repeatedly writing:
“a is greater than b”
one could write:
a > b
That compact notation remains standard mathematical language centuries later.
Common Mistakes When Using the Greater Than Sign
Most errors come from confusing the direction of > and <.
Mistake 1: Looking only at the point
A learner may see:
9 > 4
and think the arrow-like point somehow represents the larger number.
It does not.
Remember:
The open side faces the larger number.
Mistake 2: Confusing > with ≥
These expressions are different:
x > 5
and:
x ≥ 5
The first excludes 5. The second includes it.
Mistake 3: Mishandling negative numbers
Consider:
-3 > -10
This is correct.
On the number line, -3 sits to the right of -10 and is therefore greater.
Mistake 4: Forgetting to reverse an inequality
When solving algebraic inequalities, multiplying or dividing both sides by a negative number reverses the comparison symbol.
For example:
-x > 4
Multiplying both sides by -1 gives:
x < -4
Missing this reversal produces an incorrect solution.
Greater Than, Less Than, and Equal Symbols at a Glance
Here is the fastest way to distinguish the main comparison symbols:
| Statement | Meaning |
|---|---|
| A > B | A is greater than B |
| A < B | A is less than B |
| A = B | A equals B |
| A ≥ B | A is greater than or equal to B |
| A ≤ B | A is less than or equal to B |
| A ≠ B | A is not equal to B |
For > and <, remember one visual rule:
The open side faces the greater value, and the point faces the smaller value.
So:
100 > 10
and:
10 < 100
both express the same numerical relationship from opposite directions.
Final Takeaway
The greater than sign is >, and it shows that the value on its left is larger than the value on its right. For example, 12 > 7 means “12 is greater than 7.”
To remember the direction, look at the shape: the wide opening faces the larger number, while the pointed end faces the smaller number. Once that rule is familiar, distinguishing greater than (>), less than (<), and greater than or equal to (≥) becomes straightforward in arithmetic, algebra, programming, and everyday comparisons.