How do you remember which way the less than and greater than signs face?

Think of the symbol as a mouth that opens toward the bigger number. Alternatively, remember that the pointed end (the small end) always points at the smaller number. Another trick: the less than sign $<$ looks like a tilted letter L, and "Less" starts with L.

What is the difference between less than and less than or equal to?

The less than sign ($<$) means strictly smaller — the two values cannot be the same. The less than or equal to sign ($\leq$) allows the two values to be equal as well. For example, $3 < 5$ is true, and $5 \leq 5$ is also true, but $5 < 5$ is false.

Can you use greater than and less than with negative numbers?

Yes. On a number line, numbers farther to the left are smaller. So $-8 < -2$ because $-8$ is farther left. A common mistake is thinking $-8$ is greater because 8 looks bigger than 2, but the negative sign reverses the order.

Equal, Less Than, Greater Than — Definition, Formula & Examples

Q: What is the difference between less than and less than or equal to?

The less than sign ($<$) means strictly smaller — the two values cannot be the same. The less than or equal to sign ($\leq$) allows the two values to be equal as well. For example, $3 < 5$ is true, and $5 \leq 5$ is also true, but $5 < 5$ is false.

Q: Can you use greater than and less than with negative numbers?

Yes. On a number line, numbers farther to the left are smaller. So $-8 < -2$ because $-8$ is farther left. A common mistake is thinking $-8$ is greater because 8 looks bigger than 2, but the negative sign reverses the order.

Equal, less than, and greater than are the three basic comparison symbols used to show how two numbers relate to each other. The equal sign (=) means two values are the same, the less than sign (<) means the first number is smaller, and the greater than sign (>) means the first number is larger.

For any two real numbers $a$ and $b$ , exactly one of three relationships holds: $a = b$ (the quantities are identical in value), $a < b$ (the value of $a$ is strictly less than the value of $b$ ), or $a > b$ (the value of $a$ is strictly greater than the value of $b$ ). This principle is known as the trichotomy property of real numbers. The symbols $<$ and $>$ are called inequality signs, while $=$ is the equality sign.

Key Formula

a < b \quad \text{or} \quad a = b \quad \text{or} \quad a > b

Where:

$a$ = The first number being compared
$b$ = The second number being compared
$<$ = Means a is less than b (a is smaller)
$=$ = Means a equals b (same value)
$>$ = Means a is greater than b (a is larger)

How It Works

To compare two numbers, picture them on a number line: the number farther to the right is greater, and the number farther to the left is less. If they sit at the same point, they are equal. A helpful trick for the

<

and

>

symbols is that the pointed end always faces the smaller number, like an arrow pointing at it. You can also think of the symbol as a hungry alligator mouth that always opens toward the bigger number. When you write

3 < 7

, you read it left to right as "3 is less than 7." When you write

7 > 3

, you read it as "7 is greater than 3."

Worked Example

Problem: Compare the numbers 12 and 5 using the correct symbol.

Step 1: Identify which number is larger. 12 is farther to the right on a number line than 5, so 12 is the larger number.

Step 2: Choose the correct symbol. Since 12 is larger than 5, we use the greater than sign (>). Remember, the open side of the symbol faces the bigger number.

Step 3: Write the comparison.

12 > 5

Answer:

12 > 5

— twelve is greater than five.

Another Example

This example involves an expression on one side that must be evaluated before comparing, and the result is equality rather than an inequality.

Problem: Fill in the blank with =, <, or >: 4 + 6 ___ 10

Step 1: Simplify the left side. Add 4 and 6.

4 + 6 = 10

Step 2: Now compare 10 and 10. Both values are the same.

Step 3: Since the values are identical, use the equal sign.

4 + 6 = 10

Answer:

4 + 6 = 10

Why It Matters

Comparison symbols appear in every math course from first grade through calculus, making them one of the most frequently used pieces of notation in all of mathematics. Understanding

<

=

, and

>

is the foundation for solving inequalities, writing compound inequalities, and interpreting interval notation in algebra. Outside school, you compare quantities whenever you check prices, read temperatures, or evaluate sports statistics.

Common Mistakes

Mistake: Mixing up the direction of < and >

Correction: Remember: the pointed end always aims at the smaller number. If you write 8 < 3, that says 8 is smaller than 3, which is wrong. It should be 8 > 3.

Mistake: Thinking a bigger-looking digit means a bigger number when negatives are involved

Correction: With negative numbers, a larger digit actually means a smaller value. For example,

-10 < -2

even though 10 looks bigger than 2. Always check position on a number line.

Mistake: Using the equal sign when values are only close, not exactly the same

Correction: The equal sign means the two sides have the exact same value. If

a = 4.9

and

b = 5

, then

a \neq b

; you must write

a < b

Check Your Understanding

Fill in the blank with <, =, or >: 9 ___ 15

Hint: Which number is farther to the right on a number line?

Answer:

9 < 15

True or false:

-3 > -1

Hint: Draw a number line and plot both numbers.

Answer: False.

-3 < -1

because

-3

is farther to the left on a number line.

Fill in the blank:

2 + 8

___

5 + 5

Hint: Calculate each side first, then compare.

Answer:

2 + 8 = 5 + 5

because both sides equal 10.