Greater Than and Less Than Symbols Definition

Mathematics uses symbols for various purposes, like comparing and relating numbers. Two of such symbols commonly used are the less than ( < ) and greater than ( > ) symbols. These signs are integral in aiding the comparison of quantities, the ordering of numbers, and the interpretation of mathematical statements. This blog will focus on the meaning of the greater and less than symbols, provide a definition for each, and explain how to properly use the greater and less than symbols in mathematical statements with examples.

Learn the definition of greater than and less than symbols with simple examples to compare numbers easily in math.

Greater Than and Lesser Than Symbols: Interpretation 

The greater than symbol ( > ) denotes that the numeral positioned to the left is greater in value than the numeral to the right. 

Example: 7 > 3 (7 is greater than 3). 

The lesser than symbol ( < ) denotes that the numeral positioned to the left is lesser in value than the numeral to the right.

Example: 3 < 7 (3 is less than 7). 

In combination, these denote inequality, because they represent values that are not equal. 

Hence, the meaning of the greater and lesser than symbols is straightforward: they are used to compare two numbers or quantities to determine which of the two is greater or smaller.

Definition of the Greater Than and Less Than Symbols

Let’s define them clearly:

Greater than ( > ): The symbol which indicates that the number on the left exceeds the number on the right.

Less than ( < ): The symbol which indicates that the number on the left is less than the number on the right.

Consider the following examples:

15 > 10 → 15 is greater than 10

8 < 20 → 8 is less than 20

Understanding and Applying the Greater Than and Less Than Symbols in Mathematics

The less than and greater than symbols often confuse students. The following steps and easy hacks can improve your understanding of the symbols:

1. The Alligator Method 

Picture the symbol as an alligator’s mouth, which is eager to eat the larger number.

Example: When comparing 12 and 9, it is 12 > 9 because the alligator’s mouth opens towards 12.

2. The Pointy End Method

The smaller, pointy end of the symbol always faces the smaller number, while the open, wide end faces the larger number.

Example: Since 4 < 6, the pointy end of the symbol faces 4, the smaller number.

3. The Number Line Method

Numbers grow larger as you go to the right on a number line. Therefore, the number located further to the right is larger than the number to the left.

Example: The number 5 is to the right of 2 on the number line, which means 5 > 2 is an accurate statement.

Less Than and Greater Than Examples

Let’s glance over the workings of these symbols in maths:

Looking at 45 and 23. 23 is less 45 hence 23 is less than 45 → 23 < 45

Looking at 81 and 65. 81 is greater than 65 hence 81 is greater than 65 → 81 > 65 

Looking at 100 and 100. Both numbers are equal hence the equal to sign is used → 100 = 100 

Looking at decimals 3.5 and 3.2. 3.5 is greater than 3.2 and written as 3.5 > 3.2

Looking at fractions 2/3 and 3/4

Given that 3/4 is equal to 0.75 and 2/3 is approximately 0.67.

Thus, 2/3 < 3/4

Why Do We Need Greater Than and Less Than Symbols?

Basic Arithmetic - They are critical when there is a need to compare two numbers or quantities.

Solving Problems - These are useful when solving word problems, especially those dealing with comparison of real life objects such as prices, weights or dealing with distances.

Advanced Arithmetic - Inequalities are the foundation of equations as well as graphing and more complicated problem solving.

Routine Activities - We compare quantities and numbers as part of daily activities (for example 2 kg of rice is less than 5 kg).

Common Mistakes

In the process of grasping the concept of greater than and less than symbols, students tend to slip up in the following ways:

Switching the symbols: 5 < 3 instead of 5 > 3.

Omitting the equals sign: Unlike > or <, the correct sign for equal numbers is =.

Not being cautious: Always make sure to re-check the bigger number before picking the symbol.

Practice Problems

Give these a try yourself:

Fill in the blank with >, <, or =:

18 ___ 25

72 ___ 50

9 ___ 9

4.6 ___ 4.2

Answers: 18 < 25, 72 > 50, 9 = 9, 4.6 > 4.2

Conclusion

The meaning of the greater than and less than symbols is straightforward—they compare two numbers to indicate which one is bigger or smaller.

Greater than ( > ) indicates the number to the left is bigger. Less than ( < ) indicates the number to the left is smaller.

Greater and lesser math symbols can be remembered easily with the “alligator rule” or “pointy side rule.”

With a bit of practice, students can become adept at using the symbols confidently in regular math problems.

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