Less Than Symbol Definition Examples and Number Line Explanation
Understanding the less than symbol (<) is a crucial skill in mathematics, especially for comparing numbers, solving inequalities, and building a solid base for advanced topics. Recognising and using the less than sign accurately helps students excel in school maths, entrance exams like JEE, and in day-to-day problem-solving scenarios.
What is the Less Than Symbol?
The less than symbol is represented as < in mathematics. It is used to show that the number or value on the left is smaller than the number on the right. For example, the statement 2 < 5 is read as "2 is less than 5."
This symbol is a key part of comparing quantities and understanding basic arithmetic. At Vedantu, we make sure students gain a clear understanding of such fundamental concepts for strong mathematical foundations.
Explaining the Less Than Sign
The less than symbol (<) has a narrow point towards the smaller number, and an open side to the larger number. This orientation makes it easy to distinguish from the greater than symbol (>), which faces the other way. When comparing two values, the less than sign always "points" toward the smaller value and "opens" towards the bigger value.
| Symbol | Name | Example | Pronunciation |
|---|---|---|---|
| < | Less Than | 4 < 9 | 4 is less than 9 |
| > | Greater Than | 8 > 2 | 8 is greater than 2 |
How to Use the Less Than Symbol
When you want to show that one number is smaller than another, simply place < between them. It works with whole numbers, decimals, negatives, fractions, and even variables.
- Numerical Comparison: 7 < 12 (7 is less than 12)
- Decimals: 0.4 < 0.9 (0.4 is less than 0.9)
- Negatives: -6 < 3 (-6 is less than 3)
- Variables: x < 10 (x can be any value less than 10)
- Fractions: 1/3 < 1/2
Less Than vs Greater Than: How to Remember
Many students get confused between < and >. Here are two common tricks:
- Alligator Method: Imagine the symbol as an alligator's mouth. The alligator always wants to eat the bigger number, so the open side faces the larger value:
- 5 < 9 → The alligator "mouth" opens to 9 (the greater number).
- L-Shape Method: The less than sign (<) almost looks like a sideways letter "L" for "less".
Related Symbols to Less Than
It's important to distinguish < from similar-looking symbols:
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| < | Less Than | Smaller than right-side value | 3 < 8 |
| ≤ | Less Than or Equal To | Smaller than or equal to right-side value | 6 ≤ 6 |
| ¬< | Not Less Than | Not smaller than (greater than or equal to) | 12 ¬< 10 |
Typing the Less Than Symbol
- Windows: Hold Shift and press the comma key (
Shift + ,). - Mac: Hold Shift and press the comma key (
Shift + ,). - Mobile: Tap the numbers or symbols keyboard to find <.
Worked Examples
Example 1
Determine if 4 < 7 is true.
- Compare 4 and 7.
- 4 is less than 7, so the statement is true.
Example 2
Use < or > to fill in the blank: -3 ___ 2
- -3 is less than 2, so -3 < 2.
Example 3
Which is correct: 0.8 < 1 or 1 < 0.8?
- 0.8 is less than 1, so 0.8 < 1 is correct.
Practice Problems
- Write the correct symbol (< or >): 10 ___ 15
- Compare: -5 ___ 0
- Is 3/4 < 1/2? Explain your answer.
- Solve for x: x < 12 and x is a positive integer less than 12.
- Arrange in ascending order using <: 2, 5, 9
Common Mistakes to Avoid
- Confusing < with >: Always check which number is smaller.
- Forgetting "less than" points to the smaller value (left side).
- Mixing up < and ≤ or other related symbols.
- Placing the larger number on the left of < (which makes the statement false).
Real-World Applications
The less than symbol is all around us: comparing discounts when shopping, recording scores in sports, setting upper limits (e.g., speed limits), or defining age limits for competitions. In science and coding, < is critical for making decisions and controlling logic—just as it is when comparing results in experiments or setting conditions in algorithms.
On Vedantu, topics like Greater Than Less Than Symbol, Math Symbols Overview, and Linear Inequalities provide deeper insight into the use of comparison signs and help you practice more advanced applications.
In summary, mastering the less than symbol (<) empowers you to compare quantities efficiently, solve inequalities, and apply maths confidently in and out of the classroom. At Vedantu, we help you build these comparison skills step by step so you'll never be confused by "less than" again.
FAQs on Understanding the Less Than Symbol in Maths
1. What is the less than symbol in Maths?
The less than symbol is < and it shows that one number is smaller than another number. It is used to compare values in arithmetic and algebra. For example:
- 3 < 7 means 3 is less than 7.
- -2 < 1 means −2 is less than 1.
2. How do you use the less than symbol?
You use the < symbol to compare two numbers and show that the number on the left is smaller than the number on the right. Follow these steps:
- Compare the two values.
- Place < between them if the first number is smaller.
- Example: 5 < 9.
3. What does the less than symbol mean?
The less than symbol (<) means that the value on the left is smaller than the value on the right. It represents an inequality between two quantities. For example:
- 10 < 15 shows 10 is smaller than 15.
- On a number line, numbers to the left are less than numbers to the right.
4. What is the difference between less than and greater than?
The difference is that < means smaller than, while > means larger than. Key differences include:
- 4 < 9 → 4 is smaller than 9.
- 9 > 4 → 9 is greater than 4.
- The open side of the symbol faces the larger number.
5. How do you remember the less than symbol?
You can remember the less than symbol (<) by thinking that the symbol opens toward the larger number. Helpful tricks include:
- The symbol looks like a hungry mouth that “eats” the bigger number.
- In 2 < 8, the mouth opens toward 8 (the larger number).
6. How do you write a less than inequality?
A less than inequality is written using the symbol < between two expressions. For example:
- x < 5 means x is any number smaller than 5.
- y + 2 < 10 means y is less than 8 after solving.
7. What is an example of the less than symbol with negative numbers?
An example with negative numbers is -5 < -2, which means −5 is less than −2. On a number line:
- Numbers further left are smaller.
- −5 is to the left of −2, so it is less.
8. How is the less than symbol shown on a number line?
On a number line, numbers to the left are less than numbers to the right. For example:
- If a point is at 3, all numbers left of 3 satisfy x < 3.
- An open circle at 3 means 3 is not included.
9. What is the less than or equal to symbol?
The less than or equal to symbol is ≤, and it means a number is either smaller than or equal to another number. For example:
- x ≤ 6 means x can be 6 or any number less than 6.
- On a graph, a closed circle shows inclusion.
10. What are common mistakes when using the less than symbol?
A common mistake is reversing the less than symbol (<) and confusing it with >. Avoid these errors:
- Placing the open side toward the smaller number instead of the larger number.
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
- Misreading negative number comparisons.
