Deciphering 'Greater Than,' 'Less Than' and 'Equal To' Symbols

One way to remember which way greater than and less than symbols point is to think of them as mouths that want to eat the bigger number. Dream01 / Shutterstock

Greater than, less than, equal to: These terms are mathematical expressions that allow the user to compare two numbers or equations. Once you've become familiar with these terms — and the symbols used to represent them — you'll be able to apply them to various math problems.

What Are Inequality Symbols?

The relevant symbols we'll be discussing are defined through negation. Unlike the classic, familiar equal sign (=), which denotes two values that are equal, an inequality symbol tells us that two numbers are not or may not be equal.

There are a few different inequality symbols, but we'll start with the two most common: greater than (>) and less than (<).

These are both about as straightforward as you can get. Greater than means that the number that precedes the symbol (>) is greater than the number that follows it. In the same way, the less than sign (<) means that the number before it is of smaller value than the number after it.

Examples of Inequalities

These mathematical expressions are ways to relate meaning without using words. Unlike some of the more advanced math symbols, they can be easily translated to standard English, as the below examples illustrate. Since we read from left to right, substituting the symbols for the words is simple.

6 > 2 (6 is greater than 2.)

12,459,003 < 12,485,770 (12,459,003 is less than 12,485,770.)

73 + 54 < 148 – 15 (73 plus 54 is less than 148 minus 15.)

When you do the arithmetic in that last example, you can see that 73 + 54 is 127, and 148 – 15 is 133. Thus, 127 < 133 (127 is less than 133).

3 Ways to Remember Greater Than and Less Than Symbols

While the concept is straightforward, if you're not used to the greater than and less than symbols, it can be tricky to recall which one means which. Fortunately, there are some simple, easy-to-remember tricks that can help identify which symbols fits in a given context.

1. The Alligator Method

This trick has a nice visual component. If you think of the greater than or less than symbols as the open mouth of an alligator, you can imagine that the alligator's mouth is going to be open towards the bigger number, as if it's about to eat the greater value. Take the following example:

83 > 41

Here, the alligator mouth is open wide towards the second number, clearly indicating that 83 is greater than 41.

2. The L Method

If you rotate the less than symbol slightly, you get a capital letter "L." This makes the translation into spoken English very easy, since it tells you how to read the inequality.

15 < 33

This example can be read as "15 is less than 33." If you look at the less than sign as a tilted or squashed L, you can see how the sentence ought to read. The second number is the greater number, and the first number is has the smaller value.

3. The Crescendo Method

This method is for the musically inclined. You may have noticed that the greater than and less than symbols resemble the decrescendo and crescendo symbols you'll find on sheet music.

In math, the symbol widens toward the larger value, just as the (de)crescendo symbols widen toward the louder volume.

612 < 680

This example can be read as "612 is less than 680." If you look at the less than sign as you would in music, you remember that the arrow in this direction means the volume will grow louder — or in this case, it will grow larger, towards the bigger number.

3 More Symbols in Math Inequalities

There are other symbols that can be used in these kinds of problems. Sometimes, what's called for isn't simply an equal sign, greater than or less than symbol.

1. Greater Than or Equal To: ≥

This sign is used between two numbers that are, as the name suggests, either equal, or where the first number is greater than the second.

y ≥ 1 (3 is greater than or equal to 1.)

Here, we don't know the exact value of y, but the inequality symbol tells us that it can be equal to 1 or any value greater than that.

2. Less Than or Equal To: ≤

On the flip side, this symbol is used between two numbers where the first number is less than or equal to the second.

x ≤ 54

Again, we don't know the exact value of x, but this sign tells us that it could any number equal to or less than 54.

3. Not Equal To: ≠

This symbol means "not equal to" and can be thought of as the opposite of an equal sign.

72 ≠ 64 (72 is not equal to 64.)

If you were to use a traditional equal sign, you'd need to show the same number on each side of the symbol, such as 72 = 72, or 64 = 64.

How to Know When to Use Greater Than or Less Than Signs

In most of the examples so far, it isn't hard to compare two numbers and decide which sign to use. Sometimes, however, greater than and less than aren't so obvious. Take the example of negative numbers. Is -50 greater than -35?

In this case, it can be helpful to look at, or even to imagine, a number line. In this case, the number of greater value will be the point on the number line that is closer to zero. Since -35 is closer to zero than -50, the inequality would read:

-50 < -35 (-50 is less than -35.)

Greater Than and Less Than Symbols in Algebraic Equations

Sometimes, math inequalities will involve variables, such as in algebra. More than one step must be taken to solve the inequality, and you might not get a single value.

But if all that needs to be done is determine which side of the problem has a greater value, you can express the solution using the greater than and less than symbols.