Less Than — Definition, Formula & Examples
Less than means one number is smaller in value than another number. You write it with the symbol , so means 3 is less than 5.
For any two real numbers and , the relation holds if and only if is a positive number. This defines a strict inequality, meaning cannot equal .
Key Formula
Where:
- = The smaller number (on the left side of the symbol)
- = The larger number (on the right side of the symbol)
How It Works
The less than symbol always points toward the smaller number. Think of it as an arrow or an open mouth that faces the bigger number. To check whether , subtract: if , then is indeed less than . On a number line, the smaller number always sits to the left of the larger one.
Worked Example
Problem: Is 7 less than 12?
Subtract: Compute the difference: 12 minus 7.
Check the result: Since 5 is positive, the first number is smaller than the second.
Answer: Yes, .
Why It Matters
Comparing numbers is something you do constantly in everyday life, from checking prices at a store to reading temperatures. In math class, the less than symbol appears in inequalities you solve in pre-algebra, algebra, and beyond.
Common Mistakes
Mistake: Mixing up the direction of the symbol and writing when you mean 5 is greater than 3.
Correction: Remember the symbol points at the smaller number. The open end faces the larger number: .