How to Use the Less Than Symbol with Numbers and Examples
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. Recognizing 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 does the less than symbol (<) mean in math?
The less than symbol (<) indicates that the value on the left is smaller than the value on the right. For example, 5 < 10 means 5 is less than 10.
2. How is the less than symbol different from the greater than symbol (>)?
The less than (<) and greater than (>) symbols represent opposite comparisons. < shows a smaller value on the left, while > shows a larger value on the left. Remember, the smaller number 'points' to the smaller value using the pointy end of the symbol.
3. How do I type the less than symbol (<) on my keyboard?
The less than symbol (<) is typically typed by pressing the Shift key and the comma (,) key simultaneously. This works on most keyboards (Windows and Mac).
4. What are some examples of using the less than symbol in math problems?
Here are some examples: 3 < 7, 1/2 < 2/3, -5 < 0, x < 10 (where x represents a variable). The symbol is used to show inequalities.
5. What is the symbol for 'less than or equal to'?
The symbol for 'less than or equal to' is ≤. This indicates that the value on the left is either smaller than or equal to the value on the right.
6. What is the difference between < and ≤?
< (less than) means the left value is strictly smaller. ≤ (less than or equal to) means the left value is either smaller or equal to the right value. For example, 5 < 6 is true, but 5 ≤ 6 is also true, along with 6 ≤ 6.
7. Can I use the less than symbol with decimals and fractions?
Yes, you can use the less than symbol (<) to compare decimals and fractions. For instance: 0.5 < 0.75 and 1/4 < 1/2.
8. How do I compare negative numbers using the less than symbol?
When comparing negative numbers, remember that smaller numbers are further to the left on a number line. For example, -5 < -2 because -5 is to the left of -2 on the number line. It is important to visualize this relationship using a number line.
9. What are some real-life examples where I would use the less than symbol?
You use less than (<) in everyday comparisons: "I have less than $10", "The temperature is less than freezing", "She spent less than an hour studying".
10. Which symbol means 'is not less than'?
The symbol that means 'is not less than' is ≮. This is equivalent to 'greater than or equal to' (≥).
11. How do I remember the difference between less than and greater than?
Think of the less than symbol (<) as a tiny alligator mouth that always opens towards the bigger number. The alligator wants to eat the bigger value! This helps to remember which way the sign should point when comparing numbers. The greater than sign (>) is the opposite way.
12. What does the symbol ≮ mean?
The symbol ≮ means "not less than." This is the same as saying "greater than or equal to" (≥).
