The greater than sign (>) shows that the value on its left is larger than the value on its right. “7 > 4” is read “seven is greater than four”. The open, wide end of the symbol always faces the bigger number and the point faces the smaller one.
What does the greater than sign mean?
The statement a > b is true when a lies to the right of b on the number line. It is false when a is equal to b or smaller than b. So 10 > 3 is true, 3 > 10 is false, and 5 > 5 is false because 5 is equal to 5, not greater.
Greater than, less than and the related signs
| Symbol | Name | Example | Read as |
|---|---|---|---|
| > | Greater than | 9 > 2 | 9 is greater than 2 |
| < | Less than | 2 < 9 | 2 is less than 9 |
| ≥ | Greater than or equal to | x ≥ 18 | x is at least 18 |
| ≤ | Less than or equal to | x ≤ 60 | x is at most 60 |
| = | Equal to | 4 + 3 = 7 | 4 plus 3 equals 7 |
| ≠ | Not equal to | 4 ≠ 7 | 4 is not equal to 7 |
9 > 2 and 2 < 9 say exactly the same thing. You can always flip a comparison by swapping the two sides and reversing the sign.
How to remember which way the sign points
- Open end to the bigger number. The symbol is widest next to the larger value: 12 > 5, 5 < 12.
- Read left to right. Whatever comes first is the subject. If the first thing you meet is the wide end, say “greater than”; if it is the point, say “less than”.
- The “L” trick. With a little tilt, the less than sign < looks like the letter L, for “Less”.
Greater than sign examples
Whole numbers
15 > 11, 100 > 99, 1,000 > 999. All true.
Negative numbers
On the number line, numbers get larger as you move right. −2 sits to the right of −5, so −2 > −5. Students often get this backwards because 5 is bigger than 2. Think of temperature: −2 °C is warmer than −5 °C.
Also, any positive number is greater than any negative number: 0.1 > −1,000.
Decimals
Compare place by place from the left. Is 0.45 > 0.405? Line them up as 0.450 and 0.405. The tenths match (4), the hundredths are 5 and 0, so 0.45 > 0.405. The longer decimal is not automatically the larger one.
Fractions
Is 3/4 > 5/7? Cross-multiply: 3 × 7 = 21 and 5 × 4 = 20. Since 21 > 20, 3/4 > 5/7. (As decimals: 0.75 and about 0.714.)
Expressions
2³ > 3²? 2³ = 8 and 3² = 9, so the statement is false; in fact 2³ < 3².
Greater than in inequalities
With a variable, the sign describes a range of values rather than one number. x > 4 means x can be any number bigger than 4, such as 4.01, 5 or 1,000, but not 4 itself.
On a number line, x > 4 is drawn with an open circle at 4 and an arrow to the right. For x ≥ 4 the circle is filled, because 4 is included.
Solving an inequality
Solve 3x − 5 > 10.
- Add 5 to both sides: 3x > 15.
- Divide both sides by 3: x > 5.
Check with x = 6: 3(6) − 5 = 13, and 13 > 10. Correct.
The rule that trips people up
When you multiply or divide both sides by a negative number, reverse the sign. Solve −2x > 8: divide by −2 and flip, giving x < −4. Check with x = −5: −2(−5) = 10, and 10 > 8. Correct. If you forgot to flip you would get x > −4, and x = 0 would give 0 > 8, which is false.
Adding or subtracting (even negative numbers) never flips the sign.
Greater than sign in programming
In almost every language, > is a comparison operator that returns true or false.
marks = 72
if marks > 40:
print("Pass")
This prints “Pass” because 72 > 40 is true. Related operators: >= (greater than or equal), and in C, C++, Java and Python, >> is a right bit-shift, not “much greater than”. For example, 16 >> 2 = 4. See number systems and Boolean algebra for how shifts work on binary numbers.
A few other places you will meet the symbol:
- HTML: write > to display > on a web page, and < for <, because raw angle brackets start tags.
- Command line: in Windows and Linux shells, command > file.txt sends the output to a file (overwriting it); >> appends.
- Spreadsheets: =IF(B2>40,”Pass”,”Fail”) in Excel or Google Sheets.
Where the symbol came from
The > and < signs first appeared in print in Thomas Harriot’s algebra book Artis Analyticae Praxis, published in 1631, ten years after his death.
FAQs
What does > mean in maths?
It means “greater than”. a > b says a is larger than b, for example 8 > 3.
Which way does the greater than sign face?
The wide, open side faces the larger number and the point faces the smaller one, as in 20 > 7.
Is −3 greater than −7?
Yes. −3 is to the right of −7 on the number line, so −3 > −7.
What is the difference between > and ≥?
> excludes equality, ≥ includes it. x > 5 does not allow 5; x ≥ 5 does.
When do you flip the greater than sign in an inequality?
Only when you multiply or divide both sides by a negative number. −x > 2 becomes x < −2.