The greater than sign is one of the first comparison symbols students encounter in mathematics. It looks simple, but its direction is easy to mix up with the less than sign—especially when negative numbers, decimals, fractions, and algebra enter the picture.
The greater than sign (>) shows that the value on the left is larger than the value on the right. For example, 8 > 5 is read as “8 is greater than 5.” The wide, 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 numbers, quantities, variables, or expressions.
For example:
10 > 6
This statement means:
10 is greater than 6.
Because 10 has a larger numerical value than 6, the comparison is true.
The basic form can be written as:
a > b
This means the value represented by a is greater than the value represented by b.
The symbol is also sometimes called the greater-than symbol or more than sign. In mathematical writing, it is normally placed between the two values being compared.
Greater than sign examples
| Comparison | Read as |
|---|---|
| 9 > 4 | 9 is greater than 4 |
| 20 > 15 | 20 is greater than 15 |
| 100 > 99 | 100 is greater than 99 |
| 2.5 > 1.8 | 2.5 is greater than 1.8 |
| 3/4 > 1/2 | Three-fourths is greater than one-half |
| 0 > -5 | Zero is greater than negative five |
The same idea works whether you are comparing whole numbers, integers, decimals, fractions, measurements, or algebraic expressions.
How to Remember the greater than sign
The easiest rule is:
The wide side faces the bigger value, and the pointed side faces the smaller value.
Look at:
12 > 5
The wide opening faces 12, the greater number.
The pointed end faces 5, the smaller number.
This rule works for both greater than and less than signs. The narrow point always points toward the smaller value.
The alligator trick
A common classroom memory trick is to imagine > and < as an alligator’s open mouth.
The hungry alligator wants to eat the larger number.
For example:
9 > 3
Imagine the mouth opening toward 9 because 9 is larger.
This mnemonic can be helpful when first learning comparison symbols, but understanding the wide-side/big-number rule is more reliable as mathematics becomes more advanced.
Think BIG > small
Another quick memory aid is:
BIG > small
So:
50 > 10
Once you remember that the larger value goes on the open side, you do not need to memorize which direction the sign “faces.”
Greater Than vs Less Than Sign
The greater than sign (>) and less than sign (<) are closely related, but they describe opposite relationships.
| Symbol | Meaning | Example | Read as |
|---|---|---|---|
| > | Greater than | 9 > 5 | 9 is greater than 5 |
| < | Less than | 5 < 9 | 5 is less than 9 |
| = | Equal to | 9 = 9 | 9 is equal to 9 |
| ≥ | Greater than or equal to | x ≥ 9 | x is at least 9 |
| ≤ | Less than or equal to | x ≤ 9 | x is at most 9 |
| ≠ | Not equal to | 8 ≠ 9 | 8 is not equal to 9 |
The same two numbers can often be written in either direction.
For example:
8 > 3
and:
3 < 8
Both statements express the same numerical relationship.
Which way does the greater than sign go?
When the larger number appears first, use >.
For example:
25 > 11
When the smaller number appears first, the relationship becomes:
11 < 25
A useful check is to ignore the name of the symbol for a moment and look at its shape. The open end should face 25 because 25 is larger.
Greater Than and Greater Than or Equal To
The symbols > and ≥ do not mean exactly the same thing.
> means strictly greater than.
≥ means greater than or equal to.
Consider:
x > 5
The value 5 itself is excluded. Possible values include:
6, 7, 10, 100 and 5.1.
Now consider:
x ≥ 5
This includes 5 itself as well as every value greater than 5.
So:
5 > 5 is false.
But:
5 ≥ 5 is true.
This distinction becomes especially important in algebra, programming, statistics, eligibility requirements, and mathematical modeling.
How to Use the greater than sign to Compare Numbers
Using the greater than sign becomes straightforward when you follow a simple process.
- Identify the two numbers or quantities.
- Determine which one has the greater value.
- Put the larger value on the open side of the symbol.
- Make sure the pointed end faces the smaller value.
- Read the complete comparison to check whether it makes sense.
Suppose you need to compare 47 and 21.
47 is larger.
Therefore:
47 > 21
Read it aloud:
“47 is greater than 21.”
Comparing multi-digit numbers
For whole numbers with the same number of digits, compare place values from left to right.
Consider:
583 and 538
Both numbers have 5 in the hundreds place.
Move to the tens place:
8 > 3
Therefore:
583 > 538
If one positive whole number has more digits than another, it will generally be larger.
For example:
1,000 > 999
Comparing decimals
Decimal numbers use exactly the same comparison symbols.
For example:
4.8 > 4.2
If necessary, line up the decimal places:
4.80
4.20
Both have 4 ones, so compare the tenths. Eight tenths is greater than two tenths.
Another example:
0.75 > 0.7
You can rewrite 0.7 as 0.70:
0.75 > 0.70
Comparing fractions
Fractions can also be compared using >.
For fractions with the same denominator, compare the numerators:
7/10 > 3/10
For fractions with different denominators, find a common denominator, convert them to decimals, or use cross multiplication when appropriate.
For example:
3/4 > 2/3
Using a common denominator:
3/4 = 9/12
2/3 = 8/12
Because:
9/12 > 8/12
we know:
3/4 > 2/3
Quick Takeaway: The symbol does not change when you move from whole numbers to decimals or fractions. You still determine which value is larger and place the open side toward it.
Using the greater than sign With Negative Numbers
Negative numbers are a common source of mistakes.
On a number line, numbers farther to the right have greater values.
For example:
5 > 2
But also:
-2 > -5
Although 5 has a larger absolute value than 2, -5 is farther left on the number line, making it smaller than -2.
Think about temperature:
-2°C is warmer than -5°C.
Therefore:
-2 > -5
Zero is also greater than every negative number:
0 > -1
0 > -100
And every positive number is greater than zero:
1 > 0
A common negative-number mistake
It is incorrect to write:
-10 > -3
The correct comparison is:
-3 > -10
For negative numbers, the value closer to zero is greater.
greater than sign in Algebra and Inequalities
The greater than sign becomes especially useful in algebra because it can compare expressions and describe a range of possible values, rather than only two fixed numbers.
Consider:
x > 4
This does not identify one exact value for x.
Instead, it says that x can be any number greater than 4.
Examples that satisfy the inequality include:
5, 6, 10, 100, 4.5 and 4.01.
But 4 itself does not satisfy the condition because the symbol is >, not ≥.
Solving a greater than inequality
Consider:
x + 3 > 8
Subtract 3 from both sides:
x > 5
So every value greater than 5 satisfies the original inequality.
Check x = 6:
6 + 3 > 8
9 > 8
The statement is true.
When does the inequality sign reverse?
One of the most important rules in solving inequalities is that the sign reverses when you multiply or divide both sides by a negative number.
For example:
-2x > 10
Divide both sides by -2.
Because you divided by a negative number, reverse > to <:
x < -5
You can verify this using x = -6:
-2(-6) > 10
12 > 10
True.
Forgetting to reverse the inequality is one of the most common errors students make when solving algebraic inequalities.
greater than sign on a Number Line
A number line gives a visual way to understand inequalities.
For:
x > 3
3 itself is not included, so 3 is represented with an open circle. The solution continues toward numbers greater than 3, so the line or arrow extends to the right.
For:
x ≥ 3
3 is included, so a closed or filled circle is used instead.
The rightward direction makes sense because values increase as you move right on the standard number line.
This also explains why:
-2 > -7
-2 appears farther to the right than -7.
Greater Than Sign in Real-Life Comparisons
Comparison symbols are not limited to classroom exercises. They provide a compact way to describe numerical conditions in everyday situations.
Suppose one student scores 92 marks and another scores 84.
You can write:
92 > 84
If one building is 150 meters tall and another is 90 meters tall:
150 m > 90 m
Other examples include:
- A bank balance of $800 compared with $500: 800 > 500
- A temperature of 25°C compared with 18°C: 25 > 18
- A distance of 12 km compared with 8 km: 12 > 8
- A team with 30 points compared with one with 27: 30 > 27
- A product weighing 5 kg compared with one weighing 3 kg: 5 > 3
The quantities and units may change, but the underlying comparison remains the same.
greater than sign in Computers and Programming
The greater than sign also functions as a comparison operator in many programming languages.
A condition such as:
age > 18
tests whether the value stored in age is greater than 18.
If age is 25, the comparison is true.
If age is 18, it is false because > does not include equality.
Programming languages may combine the symbol with other operators. For example, >= commonly represents greater than or equal to in source code, even though standard mathematical notation uses ≥.
Greater than sign in spreadsheets
Spreadsheet software can use the same comparison operator.
For example:
=A1>10
tests whether the value in cell A1 is greater than 10.
If A1 contains 15, the expression evaluates as true. If A1 contains 8, it evaluates as false.
The symbol can therefore appear in formulas, logical tests, filters, conditional rules, databases, and data analysis—not just handwritten mathematics.
How to Type the greater than sign
The symbol you may want to copy is:
>
On many standard Windows and Mac keyboard layouts, you can type the greater than sign by pressing:
Shift + .
The period key usually shares the > character.
On smartphones and tablets, open the numbers or symbols section of the on-screen keyboard and select >.
The greater-than character is also standardized in Unicode; the character > corresponds to U+003E GREATER-THAN SIGN.
Greater than sign in HTML
Because the symbol has a special historical role in markup, HTML also provides the character reference:
>
which displays as:
>
The letters “gt” stand for greater than.
Greater than sign in LaTeX
In ordinary LaTeX math mode, the character can be entered directly:
$a > b$
which represents the mathematical comparison:
a > b
This is useful when preparing mathematical documents, assignments, research papers, and technical material.
Common Mistakes With the greater than sign
Most errors with > come from the direction of the symbol or from misunderstanding the values being compared.
1. Pointing the symbol toward the larger number
Incorrect:
3 > 9
Correct:
9 > 3
Remember that the pointed end faces the smaller value.
2. Confusing > with <
These two statements have different wording:
8 > 4 means 8 is greater than 4.
4 < 8 means 4 is less than 8.
Both are true, but the comparison is being read from different directions.
3. Treating > as greater than or equal to
If a requirement says:
x > 10
then x = 10 does not qualify.
If 10 should also be included, write:
x ≥ 10
4. Comparing negative numbers incorrectly
Remember:
-2 > -8
On the number line, -2 is farther to the right and therefore has the greater value.
5. Forgetting to reverse an inequality
When solving an inequality, multiplying or dividing both sides by a negative number reverses the inequality symbol.
For example:
-x > 4
Multiply by -1 and reverse the sign:
x < -4
History of the Greater Than Symbol
The symbols > and < have been used for centuries. The earliest known published use is associated with English mathematician Thomas Harriot in Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas, published posthumously in 1631.
Their compact form made it possible to express numerical relationships far more efficiently than repeatedly writing phrases such as “is greater than” and “is less than.”
The symbols later became fundamental not only to arithmetic and algebra but also to logic, computing, programming languages, markup, and data processing.
Practice Examples
Try determining whether each comparison is true or false.
Example 1
14 > 9
True. Fourteen is greater than nine.
Example 2
7 > 20
False. Seven is less than twenty.
The correct relationship is:
7 < 20
Example 3
0 > -4
True. Zero is greater than every negative number.
Example 4
-5 > -2
False.
The correct comparison is:
-2 > -5
Example 5
0.9 > 0.75
True.
Nine tenths is greater than seventy-five hundredths.
Example 6
5/8 > 1/2
True.
Convert 1/2 to eighths:
1/2 = 4/8
Therefore:
5/8 > 4/8
Example 7
Write “x is greater than 20” mathematically.
Answer:
x > 20
Example 8
Write “a is greater than or equal to 12.”
Answer:
a ≥ 12
The equal line matters because 12 itself is allowed.
What Does > Mean?
Whenever you see >, read it as:
“is greater than.”
So:
30 > 12
means:
“30 is greater than 12.”
The rule remains the same for variables and expressions:
x > 10
means x has a value greater than 10.
And:
a + b > c
means the value of a + b is greater than c.
If you are unsure which way to write the symbol, first identify the larger value. Put the wide, open side toward the larger value and the point toward the smaller one.
Final Takeaway
The greater than sign (>) is a comparison symbol showing that the value on its left is larger than the value on its right. In 15 > 7, for example, 15 is greater than 7.
Remember one visual rule: the open side faces the greater value, while the point faces the smaller value. Once that is clear, the same greater than sign can be used confidently with whole numbers, negative numbers, fractions, decimals, algebraic inequalities, number lines, spreadsheets, and programming.