Less Than Symbol in Maths

Less than symbol (<) is a mathematical comparison symbol used for number comparison. It is denoted as ("<"), the less than symbol shows an inequality between two values. When we use the "<" symbol, it means that the value or quantity on the left-hand side is smaller than the value on the right-hand side. This symbol is one of the comparison operators, which also includes the greater than (">") and equal to ("=") symbols.

In this article, we will discuss the Less Than Symbol, its applications in Inequalities, and its role in mathematics along with some solved examples.

What is Less Than Symbol?

The less than symbol ("<") is a comparison symbol used in mathematics to indicate that the value on the left side of the symbol is smaller than the value on the right side. For example, in the expression 3<5, it is stated that 3 is less than 5.

• "<" symbol indicates "smaller than".
• Less-than symbol, denoted as (<), is used to represent the relationship between two numbers or quantities.
• Less than symbol is binary, meaning it requires two operands, and it is read as "less than" or "smaller than."

Examples

Here are some examples of Less Than Symbol:

1. 3 < 5 (Three is less than five)
2. -2 < 0 (Negative two is less than zero)
3. In expressions like 2x + 5 < 7, (the LHS is less than RHS)

Comparison Symbols - Less Than, Greater Than, and Equal to

The following table represents the mathematical symbols used for number comparison along with their name, meanings, and examples.

Tricks to Remember Less Than Symbol

Less than sign and its counterpart greater than have almost similar visual representation but in opposite direction. Hence, to avoid confusion, there are two tricks by which we can remember what is the sign of Less Than.

These methods are called L Method and Smaller Mouth Method.

L Method for Less Than Symbol

This method is simple - ”less than” starts with a letter L, so the symbol that looks most like an L is the one that means “less than.”

Closed Mouth Method for Less Than Symbol

Closed mouth on left side indicates less than symbol. The "closed" end of "<" points towards the smaller quantity.

Less Than Symbol on Number Line

To visualize number comparison using the less than symbol, you can plot the numbers on a number line. The number line provides a visual representation of how values compare to each other.

Let's consider an example:

x < 4. This inequality means that the value of x is less than 4. On the number line, you would represent this by shading the region to the left of 4.

Less Than or Equal on Number Line

Less Than or Equal to Symbol "≤" is used when we want to define a range with maximum limit.

The "less than or equal to" symbol (≤) is like a friendly rule that tells us how big or small numbers can be. Imagine you have a box that can hold up to 10 toys—no more, but less is okay. If you wanted to write this rule down, you could use the ≤ symbol like this: the number of toys in the box ≤10.

For Example:
x ≤ 4, this inequality means that the value of x is less or equals to 4 (including 4). On the number line, you would represent this by shading the region to the left and on the 4.

Not Less Than Symbol

Not Less than symbol "≮" is used when the quantity on the left side is not less than the quantity on the right hand side. This means that the quantity on the left side is either equal to or greater than the quantity of right side.

Let's say John's age is 'p' years and Andrew is 'q' years old and John's age is not less than Andrew's age. This means either John's age is equal to or greater than that of Andrew's age. We can mathematically express it as p ≮ q.

In this case, the left-hand side is may be smaller but can be equal to the right-hand side also.
For example: 3 ≤ 3 (Three is less than or equal to three).

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Examples Problems on Less Than Symbol

Here we have solved some example questions for you to learn.

Example 1: How to represent “10 is less than 50” symbolically?

Solution:

“10 is less than 50” is symbolically represented as 10 < 50

Example 2: Determine whether the following statements are true or false:

a) 8 < 12

b) -5 < -7

c) 6 < 6

Solution:

a) True (8 is less than 12)

b) False (-5 is not less than -7)

c) False (6 is not less than 6; they are equal)

Example 3: Find the possible whole number for 'x' ; where 10 < x < 15

Solution:

Given, 10 < x and x < 15

From 10 < x , x can be: ( 11, 12, 13, 14, 15, 16, 17..........∞)

From x < 15 , x can be: (-∞..... 9, 10, 11, 12, 13, 14, 15)

Taking range from both the statement we get x can be: 11, 12, 13, 14, 15, 16

Example 4: Solve for x: 3x < 15

Solution:

To find the value of x, divide both sides of the inequality by 3:

3x < 15

x < 15 / 3

x < 5

So, the solution is x < 5

Example 5: A rectangular garden is 12 feet long and 8 feet wide. Another rectangular garden is 15 feet long and 10 feet wide. Which garden has a smaller area?

Solution:

To compare areas, calculate areas of both gardens

First garden has an area of 12 feet × 8 feet = 96 square feet

Second garden has an area of 15 feet × 10 feet = 150 square feet

We know that, 96 < 150

First garden has a smaller area because 96 is less than 150

Example 6: For x < 15 , draw for x on the number line.

Solution:

On number line x < 15 is drawn as:

Practice Questions on Less Than Symbol

Here are some questions on Less Than Sign for your practice.

Q1. Ram has 5 toffees and Shyam has 8 toffees. Who has less toffees?

Q2. Bob sleeps for 1/2 hours and Alice sleeps for 60 minutes every day in the afternoon. Who sleeps for less time?

Q3. State whether the given statement is true of false:

• 5 < 8
• 10 < 7
• x < 100 ; where x = 20

Q4. Find the possible whole number for ' x ' ; where 5 < x < 10.

Q5. Draw for ' x ' on number line ; where x < 100.

Q6. Place Greater Than or Less Tham symbol in the following

1. 2 __ 5
2. 0.25 __ 0.252
3. -14 __ 0
4. 1/4 __ 1/3

Similar Reads

• Greater Than and Less Than Symbols in Maths
• Math Symbols
• Greater Than Symbol
• Greater Than or Equal to Sign in Mathematics
• Less than Equal to Sign

Conclusion

The less than symbol ("<") is comparison symbol in mathematics, used to compare two values where the left value is smaller than the right. Understanding and remembering this symbol, along with related symbols like greater than (>) and equal to (=), is crucial for solving inequalities and other mathematical expressions.