Greater Than and Less Than Symbol

Introduction

One important math skill that is taught early in school is understanding comparison. When comparing two numbers, quantities, or values, the greater than and less than symbols are crucial. We can determine which value is larger or smaller with the aid of these symbols. Gaining skills with these mathematical symbols not only improves numerical abilities but also establishes a foundation for algebra, data processing, and logical thinking.

Today, we will explore the greater than and less than symbol, their meanings, how to teach them, tricks to remember greater and less than, and practical greater than less than examples to make learning easier.

 

Table of Contents

• What is the Greater Than and Less Than Symbol?
  • Greater Than Symbol (>)
  • Less Than Symbol (<)
  • Equal To Symbol (=)
• Tricks to Remember Greater Than and Less Than
• Greater Than and Less Than Examples
• Applications of Greater Than and Less Than Symbols in Algebra
• Solved Examples
• Conclusion
• FAQs on the Greater Than and Less Than Symbols

What is the Greater Than and Less Than Symbol?

In mathematics, the greater than and less than symbols are used to compare values or numbers. They help in distinguishing between larger and smaller numbers.

• “>” is the greater than symbol.

• “<” is the less than symbol.
  
  

They are comparison operators, just like equals to (=). For example:

• 9 > 6 (Read as "9 is greater than 6")

• 4 < 7 (Read as "4 is less than 7")
  
  

These symbols are commonly introduced at the elementary level, and their application extends through advanced mathematical concepts like inequalities, algorithms, and coding.

 

Greater Than Symbol (>)

The greater than symbol is used when the number on the left is larger than the number on the right.

Example:

• 9 > 6 → 9 is greater than 6

• 100 > 10 → 100 is greater than 10
  
  

Less Than Symbol (<)

The less than symbol is used when the number on the left is smaller than the number on the right.

Example:

• 3 < 8 → 3 is less than 8

• 15 < 20 → 15 is less than 20
  
  

Equal To Symbol (=)

The equal to symbol is used when both quantities are exactly the same.

Example:

• 5 = 5 → 5 is equal to 5

• 12 + 3 = 15 → both sides are equal
  
  

This symbol works alongside the greater than and less than symbol to make logical comparisons in mathematics.

 

Tricks to Remember Greater Than and Less Than

Teaching the greater than and less than symbol can be fun and engaging using simple tools and relatable visuals.

1. Alligator Mouth Trick

Think of the symbol as an alligator's mouth:

• The alligator always eats the bigger number.

• So 7 > 4 means the alligator mouth opens to the 7.
  
  

2. L for Less Than

• The less than symbol (<) looks like a slanted "L".

• So if you see "<", think L = less.
  
  

3. Visual Arrow

• Less than (<) points to the left → smaller numbers

• Greater than (>) points to the right → bigger numbers
  
  

4. Number Line Method:

• Place numbers on a number line and show how the symbol points to the smaller number.

By using these tricks to remember greater and less than, students can easily differentiate the symbols.

 

Greater Than and Less Than Examples

Here are some useful greater than less than examples to show how these symbols work:

 

Applications of Greater Than and Less Than Symbols in Algebra

In algebra, the less than (<) and greater than (>) symbols are crucial. They are used in domain definition, graphing, inequalities, and mathematical modelling of real-world situations. The main applications are listed below:

1. Solving Inequalities

Inequalities are mathematical statements that use the greater than and less than symbols to compare expressions in algebra.

Example:
x + 5 < 12
Subtract 5 from both sides:
x < 7
This means any value of x that is less than 7 is a solution.

 

2. Graphing Inequalities on a Number Line

Inequalities are often shown on a number line to represent a range of values.

Example:
x > 3
This means the graph starts just after 3 and continues to the right.
x ≤ -1
This means the graph includes -1 and continues to the left.

 

3. Defining Domains and Ranges

In functions, inequality symbols helps in defining the range of outputs or the domain of inputs.

Example:
For the function f(x) = √x,
The domain is: x ≥ 0
Square roots of negative numbers are not real, so x must be greater than or equal to 0.

 

4. Piecewise Functions

Using inequalities to divide the intervals, piecewise functions are defined by distinct expressions based on the value of x.

Example:
f(x) =
x + 2, if x < 0
x², if x ≥ 0

The inequalities show which formula to use for each x-value.

 

5. Real-Life Word Problems

Inequalities are used in algebra to model real-world situations such as budgets, speed limits, or minimum requirements.

Example:
A person has at most ₹100 to spend.
Let x be the amount spent.
Then, x ≤ 100

This means the person can spend up to ₹100 but not more.

 

6. Systems of Inequalities

A system of inequalities involves solving two or more inequalities at once, often shown graphically.

Example:
x + y ≤ 10
x ≥ 0
y ≥ 0

This system describes a region on a graph where all the conditions are satisfied.

 

7. Expressing Constraints or Limits

In algebraic problems involving maximum or minimum values, limits are established using the lesser than and greater than symbols.

Example:
A machine should run at less than 80 degrees Celsius.
This can be written as:
temperature < 80

 

Solved Examples

Problem 1:
Ravi scored 78 marks in Math, and Sita scored 85 marks.
Who scored more? Use the appropriate symbol.

Solution:
Compare 78 and 85
78 < 85
Sita scored more.

Answer: 78 < 85 (Sita scored greater marks)

Problem 2:
A pencil costs ₹12, and a pen costs ₹18. Which is cheaper?

Solution:
12 < 18
Pencil is cheaper than the pen.

Answer: ₹12 < ₹18 (Pencil < Pen)

 

Problem 3:
Rahul is 15 years old, and his brother is 12 years old.
Who is older?

Solution:
15 > 12
Rahul is older than his brother.

Answer: 15 > 12 (Rahul > Brother)

Problem 4:
A car travelled 120 km, and a bike travelled 85 km.
Which vehicle went farther?

Solution:
120 > 85
The car travelled farther.

Answer: 120 > 85 (Car > Bike)

 

Problem 5:
Today’s temperature is 32°C and yesterday’s was 35°C.
Was today’s temperature greater or less?

Solution:
32 < 35
Today’s temperature is less than yesterday’s.

Answer: 32 < 35 (Today < Yesterday)

 

Conclusion

More than just a simple mathematical tool, the greater than and less than symbol is essential to understanding functions, comparisons, inequalities, and real-world problems. Together with the equal to sign, these symbols provide a solid basis for early mathematics and are still helpful for more complex ideas like algebra, graphing, and logical reasoning.

 

Related links

Math Symbols - Unlock the meaning behind essential math symbols to improve your comprehension and problem-solving speed.

Set Theory Symbols - Learn the key symbols used in set theory to understand and express mathematical relationships effectively.

Frequently Asked Questions (FAQs) on Greater than and less than symbol

1. Which is greater and less: <>?

Answer:
The symbols are:

• ">" means greater than

• "<" means less than

So:
5 > 3 means 5 is greater than 3
2 < 6 means 2 is less than 6

2. How to use <>?

Answer:
Use ">" when the number on the left is larger than the one on the right.
Use "<" when the number on the left is smaller than the one on the right.

Examples:

• 10 > 4 → 10 is greater than 4

• 3 < 8 → 3 is less than 8

Remember:
The open side of the symbol always faces the larger number.

 

3. What is the meaning of ≥ and ≤?

Answer:

• "≥" means greater than or equal to

• "≤" means less than or equal to

Examples:

• x ≥ 5 → x can be 5 or more

• y ≤ 10 → y can be 10 or less
  
  

4. How do you write greater than 5?

Answer:
Use the greater than symbol:
x > 5
This means x is any number greater than 5, but not equal to 5.

 

5. How do I write greater than 7?

Answer:
Write it like this:
x > 7
This means x is more than 7 (like 8, 9, 10, etc.).

 

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