Less Than Symbol in Maths

Less Than Sign, denoted as “<,” is a mathematical symbol that 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.

Let’s discuss Less Than Symbol, its applications in Inequalities along with some solved examples.

What is Less Than Symbol?

Less than sign (“<“) is a symbol used between two values, which means the left value is smaller than right value.

• “<” 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.“

Less than Symbol Meaning

The less than symbol (“<“) is 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<53<5, it is stated that 3 is less than 5.

Less Than Symbol Examples

Here are some examples of Less Than Symbol:

• 3 < 5 (Three is less than five)
• -2 < 0 (Negative two is less than zero)
• 7 < 7 (Seven is not less than seven. It is equal to seven)

Table of Mathematical Signs – Less Than, Greater Than, and Equals to

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

Mathematical Signs – Meaning and Examples
Symbol/Sign	<	=	>
Name	less than	equals to	greater than
Indicates	left value is less than right one	left and right values are equal	left value is greater than right value
Example	5 < 7 5 is less than 7	5 = 5 5 is equal to 5	7 > 5 7 is greater than 5

How 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, Greater Than and Equal To Symbols

Now we are going to discuss Greater than, Less than, Equal to Sign in brief.

• Greater Than Sign
• Less Than Sign
• Equal to Sign

Greater Than Sign

Greater Than Sign ” > “ is used to express a specific type of comparison between two quantities, where the left value is greater than the right value.
Example: 10 > 5; (ten is greater than five)

Less Than Sign

Less Than Sign ” < “ is used to express a specific type of comparison between two quantities, where the left value is smaller than the right value.
Example: 5 < 10; (five is less than 10)

Equal to Sign

Equal to Sign ” = ” is used to show equality between two numbers or values. It express that both the left and right values are equal.
Example: 5 + 5 = 10 i.e. 10 = 10 (ten is equal to ten)

Above are the fundamental signs which are used for comparison, there are other signs which are formed by combination of signs. These are greater than equal to and less than equal to.

Less Than or Equal to Symbol

Less Than or Equal to Symbol “≤” is used when there is ambiguity between the magnitude of the quantity. Let’s say we have a statement which states The number of apples Ram has is less than or equal to that with Rohan. Then we can mathematically express it as x ≤ y where x is the number of apples with Ram and y is the number of apples with Rohan.

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.

Read in Detail: Greater Than and Less Than Symbols

Less Than Symbol in Inequalities

An inequality is a statement that compares two expressions, and the less than symbol indicates that the expression on the left is smaller than the one on the right. The less than symbol is frequently used in mathematical inequalities

Types of Inequalities

The inequalities are of two types named as,

• Strict Inequality
• Non-Strict Inequality

These two inequalities are discussed below:

Strict Inequality (<)

This type of inequality represents a situation where the left-hand side is strictly smaller than the right-hand side.

For example:

• 2 < 7
• x < 10; x is less than 10 this means x can be -∞ to 9

Strict Inequality on Number Line

To visualize inequalities using the less than symbol, you can plot the numbers on a number line. The number line provides a graphical 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.

Non-strict Inequality (≤)

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).

Non-strict Inequality on Number Line

Let’s consider an 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.

Less Than Symbol Examples

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:

Less Than Symbol Questions

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:

1. 5 < 8

1. 10 < 7

1. 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

People Also Read:

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FAQs on Less Than Symbol

What does Less Than Sign represent in Mathematics?

“Less Than” sign (“<“) is a mathematical symbol used to indicate that left value is smaller or of lower magnitude than right value.

What is Opposite of Less than Symbol?

The opposite of the less than symbol (<) is the greater than symbol (>), which denotes that one value is larger than the other.

What does Less Than Symbol look like?

Less than symbol look like tilted ‘L’. Please refer the image in the article.

What is the Use of Less Than Sign?

Less than sign (“<“) is used to indicate that one value is smaller than another. For example, in the statement “3 < 5”, it means that 3 is less than 5.

What is Difference Between Symbols of Greater Than, Less Than and Equal To?

Greater than symbol (>) indicates that the value on the left is larger than the value on the right, while the less than symbol (<) shows that the value on the left is smaller than the value on the right. The equal to symbol (=) denotes that the values on both sides are exactly the same.

Can Less Than Symbol be used with Variables?

Yes, the less than symbol can be used in inequalities involving variables. For example, “x < 10” means that the variable x is less than 10.

What is Difference Between Strict and Non-Strict Inequalities?

In a strict inequality (e.g., x < 5), the left-hand value must be strictly smaller than the right-hand value. In a non-strict inequality (e.g., x ≤ 5), the left-hand value can be equal to the right-hand value.