Less Than Symbol In Mathematics- Definition, Meaning, and Solved Examples

In Mathematics, the less than symbol is defined as a term that describes the inequality between two values, fractions, or quantities. It is used to compare two given values, fractions, or quantities, where one value or quantity is smaller than the other. When we need to check which of the two given values is smaller than the other, we use the less than sign. While using this symbol, we should always focus on the left side of the symbol and compare it with the right side of the symbol.

This Maths symbol assists students in comparing quantities and determining the relationship between any two numbers. This is a very basic, yet fundamental concept in mathematics. This symbol can be used for the representation of a series of ascending numbers from a smaller to a greater number. 

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

What is the symbol for less than in Maths?

The “Less than” symbol is represented using “<”.

How to use the less than symbol for different numeric values and quantities?

Let us understand the use of the less than symbol for different numeric values and quantities in detail:

Less than symbol with whole or natural numbers

The less than symbol is used directly by pointing towards the smaller value among the given values. 

For example, if there are two numbers, 56 and 25, and we have to represent the smaller number among the two numbers using the less than symbol. By looking at the numbers, it is obvious to see that 25 is smaller than 56. Using the less than symbol, it can be represented as 25 < 56.

Less than symbol with decimal numbers

The less than symbol with decimal numbers almost works the same way as it works with natural or whole numbers. The symbol simply points towards the smaller value between the given values.

For example, if there are two decimal numbers, 0.6 and 1.7, and we have to represent the smaller number among the two numbers using the less than symbol. By looking at the numbers, it is obvious that 0.6 is smaller than 1.7. Using the less than symbol, it can be represented as, 0.6 < 1.7.

Less than symbol with negative integers

For negative integers, the less than symbol is used by pointing towards the greater value among the given values, because when we deal with negative numbers, a greater number is treated as a smaller number and vice-versa. Hence, -1 is the greatest negative number.

For example, if there are two numbers, -9 and -80, we have to represent the smaller number between the two numbers using the less than symbol. The given numbers are with a negative sign, so the greater number is considered the smaller number, and vice-versa. Hence, -80 is smaller than -9. Using the less than symbol, it can be represented as -80 < -9.

Let’s take another example, suppose there are two numbers -6 and 9, and we have to represent the smaller number between the two numbers using the less than symbol. Here, -6 is smaller than 9 because when we compare a positive number with a negative number, negative numbers are always smaller than positive numbers. Using the less than symbol, it can be represented as -6 < 9.

Less than symbol with fractions

To use the less than symbol with fractions, we need to first convert the fractions into natural numbers. So, for that, we need to perform cross-multiplication. For that, we will multiply the numerator of the first fraction with the denominator of the second fraction to get the first number. Similarly, we will multiply the numerator of the second fraction with the denominator of the first fraction to get the second number. And finally, we compare the two newly obtained numbers using the symbol.

For example, if there are two fractions, 4/5 and 14/20, and we have to represent the smaller fraction between the two fractions using the less than symbol. Since, both fractions have different denominators, we will rationalize them first:

4/5 and 14/25, since 25 is a factor of 5, let’s use 25 as the common denominator. Now, multiply 5 with the numerator and denominator to create an equivalent fraction with denominator 25.

(4×5) / (5×5)= 20/25

So, the final fractions are 20/25 and 14/25. Now, we have a common denominator, i.e., 25.

Between the two factors, let’s see which is the smaller one. As the denominator is common, see the numerator. Between the numerator 14 is clearly smaller than 20.

Hence, 4/5 < 14/25.

Less than sign with different quantities

To use the less than symbol with different quantities we need to focus on the units. Both the given quantities should have the same unit, only then we can determine which quantity is smaller than the other.

For example, if there are two quantities, 400 meters, and 1 kilometer, and we have to represent the smaller quantity among the two given quantities using the less than symbol, then first we will need to make sure that both quantities have the same unit. Here, either we need to convert kilometers to meters or meters to kilometers. On converting 1 kilometer to meters, it will be equal to 1000 meters.

Now, we will have to do a comparison between 400 meters and 1000 meters. It is pretty clear that 400 meters are smaller than 1000 meters. Using the less than symbol, it can be represented as, 400 < 1000.

Solved Examples

Question 1: Find the value of x as per the given expression:
22 + 3x < 88
Solution:
Given equation is, 22 + 3x < 88
On taking 22 to the right-hand side and subtracting from 88, we get
3x < 88 – 22
3x < 66
On taking 3 to the right-hand side and dividing by 66, we get
x < 66/3
x < 22
So, the value of x can be any value less than 22.

Question 2: Write the following numbers in ascending order using the less than symbol.
3, 9, 77, 0, 62, -51, 29, 18
Solution:
Ascending order refers to the arrangement of numbers from the lowest number to the highest number.
It is clearly visible that among all the given numbers, -51 is the lowest number and 77 is the greatest number.
So, the numbers can be represented in ascending order:
-51 < 0 < 3 < 9 < 18 < 29 < 62 < 77

Question 3: Which symbol is less than in the following options?
Option 1: =
Option 2: <
Option 3: >
Option 4: None of the above.
Solution:
Option 2 – “<” is the symbol of the less than sign.

Question 4: How to express less than 70 with a symbol?
Solution:
Let us assume that we want to express 70 is less than 80.
Hence, we can express less than 70 using a symbol as follows:
70 < 80.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

FAQs

What is the less than or equal to symbol?
“Less than” or equal to symbol is used to compare any two numbers, fractions, or quantities. When we need to check whether the first number, out of the two given numbers, is smaller than or equal to the second number or not, we use the less than or equal to symbol. It is represented by “⩽”.

What do you mean by the less than symbol and when do we use it?
The Less than symbol is used to compare any two numbers, fractions, or quantities. When we need to check whether the first number, out of the two given numbers, is less than the second number or not, we use the less than symbol. It is represented by “<”.

Which is smaller among 7 and -101?
Negative numbers are always smaller than positive numbers, so here 7 is a positive number and -101 is a negative number.
Hence, -101 < 7.

What are the other terms used to describe the less than symbol?
The other terms used to describe the less than are smaller than, fewer, not greater than, etc.

How to write 30 is not greater than 50?
Mathematically, you can write that 30 is not greater than 50 as 30<50.

We hope you understood all the basics of the less than symbol and that we have answered your queries related to this topic!