Buzz
A helpful trick for remembering the direction of the 'greater than' and 'less than' symbols is to imagine them as mouths eager to consume the larger number. (Image: Dream01 / Shutterstock)Greater than, less than, equal to: These are key mathematical terms used to compare two numbers or expressions. Once you understand these terms and the corresponding symbols, you'll be able to apply them effectively in a range of math problems.
What Are Inequality Symbols?
Inequality symbols are defined through negation. Unlike the equal sign (=), which shows that two values are identical, inequality symbols indicate that two numbers are not equal or may not be.
There are several inequality symbols, but we’ll begin with the two most commonly used: greater than (>) and less than (<).
These two symbols are straightforward. The 'greater than' symbol (>) indicates that the number before it is larger than the number after it. Similarly, the 'less than' symbol (<) means that the number before it is smaller than the number following it.
Examples of Inequalities
These mathematical expressions allow us to convey meaning without words. Unlike some complex math symbols, they can be easily converted into everyday English, as the examples below demonstrate. Since we read from left to right, switching the symbols with words is intuitive.
If you perform the arithmetic in the previous example, you'll find that 73 + 54 equals 127, and 148 – 15 equals 133. So, 127 < 133 (127 is less than 133).
3 Ways to Remember Greater Than and Less Than Symbols
Although the concept is simple, it can sometimes be tricky to remember which symbol is which. Fortunately, there are several easy and effective tricks to help you recall the correct symbol for any given situation.
1. The Alligator Method
This technique incorporates a fun visual. Imagine the greater than or less than symbols as the open mouth of an alligator, which will always face the larger number, as though it’s about to consume the greater value. Here's an example:
In this case, the alligator's mouth is wide open towards the second number, clearly showing that 83 is greater than 41.
2. The L Method
If you rotate the less than symbol slightly, it forms the shape of a capital 'L.' This makes it easier to translate the inequality into spoken English, as it shows you how to interpret the comparison.
This inequality can be read as '15 is less than 33.' When you view the less than sign as a rotated or squished 'L,' it clearly shows how the sentence should be read. The second number is greater, while the first is smaller.
3. The Crescendo Method
This method is ideal for those who are musically inclined. You might have noticed that the greater than and less than symbols resemble the decrescendo and crescendo markings found in sheet music.
In mathematics, the symbol opens up toward the larger value, similar to how the (de)crescendo symbols expand toward the louder volume in music.
This can be interpreted as '612 is less than 680.' When you view the less than symbol through the lens of music, you realize that the direction of the arrow represents increasing volume — or in this case, it signals the growing value towards the larger number.
3 More Symbols in Math Inequalities
There are other symbols used in math inequalities. At times, a simple equal sign, greater than, or less than symbol isn't enough to represent the relationship between numbers.
1. Greater Than or Equal To: ≥
This symbol is used to show that two numbers are either equal or that the first number is greater than the second, as the name implies.
In this example, we do not know the exact value of y, but the inequality indicates that y can be either equal to 1 or any number greater than 1.
2. Less Than or Equal To: ≤
On the other hand, this symbol is used between two numbers where the first number is less than or equal to the second.
In this case, the exact value of x is unknown, but the inequality symbol tells us that it can be any number equal to or less than 54.
3. Not Equal To: ≠
This symbol signifies "not equal to" and is essentially the inverse of the equal sign.
With a regular equal sign, both sides must display the same number, for instance, 72 = 72 or 64 = 64.
How to Know When to Use Greater Than or Less Than Signs
For most of the cases we've seen so far, it's pretty easy to decide which inequality symbol to use. However, there are times when the decision isn’t as clear. Consider the example of negative numbers. Is -50 greater than -35?
In situations like this, it can be helpful to refer to a number line. The number closer to zero represents the greater value. Since -35 is nearer to zero than -50, the inequality would be written as follows:
Greater Than and Less Than Symbols in Algebraic Equations
In some instances, mathematical inequalities will include variables, like in algebra. Solving such inequalities might require more than one step, and you might not end up with just a single value.
However, when the task is simply to determine which side of the equation holds the greater value, you can use the greater than and less than symbols to express the solution.
