# Less Than Symbol

Less than symbol is one of the mathematical operators used to compare two entities. There could be two ways of expressing the results of the comparison. Firstly, you can write comparison sentences. And, secondly, you can use symbols to show the idea of less than/greater than. A comparison could be done for almost all things around you. But definitely, there are various parameters of comparison.

Let us try these questions!

Can you compare yourself and your friend sitting next to you?

Yes, You can.

What are the different parameters on which the comparison will be done?
Mathematically, the comparison could be made with everything that you can count. In mathematics, we compare two or more numbers.

How do you order a group of numbers in ascending or descending order?
Whenever there is inequality among the number of objects, there comes the word greater than or less than. For this purpose, two terms are extensively used: “greater than” and “less than”. Further, you will see that symbols are used for greater than and less than. These words can be replaced with the help of symbols. And you can explore how these symbols are used to show the relation between two numbers and how it saves time. The concept of comparison of numbers is fun and interesting. It is one of the fun lessons in mathematics.

Further, there are some tricks to remember the less-than symbol that could prove helpful in eliminating the confusion among different symbols encountered during the process of comparison. And, you will gradually encounter these tricks in this article. One of the common tricks is the alligator method to remember the less-than symbol.

## Less than Symbol

A less-than symbol is a mathematical symbol used to represent inequality between two numbers and denotes that one quantity is less than the other. The symbol for less than is “<“. It is an alternative way to represent less than sentences with the help of symbols. Further, the less than symbol is the opposite of the greater than symbol.

Let us try to understand the concept of less than and its representation with help of symbols.

Think!

Do you agree, representing the comparison of numbers would be tedious without these symbols?
No doubt, in this modern era everyone is looking forward to speed, accuracy, and compatible methods to deal with different types of questions. The whole world is busy exploring and discovering different methods to serve these purposes.

For Example:
If you have to compare 3 and 4.
Then you can write,
In sentence
Three is less than four.
Using symbol

You will explore the importance and uses of the less-than symbol in the following examples.

Example 1:
Compare the numbers 6 and 8.
Here, 6 is less than 8.
Mathematically,
You can write it as
6< 8.

Example 2:
Compare the numbers 6,345 and 6,346 using the less than symbol.
Solution:
Here,
6,345 < 6,346

Example 3: The cost of a pen is \$2.12. Sia bought 3 such pens. Compare the cost of one pen with that of 3 pens.
Solution:
Cost of one pen = \$2.12
Cost of three pens = 3 × 2.12
The cost of three pens is \$6.36.
Comparing 2.12 and 6.36
2.12 < 6.36

Note:

• When the number on the left side is less than the number on the right hand then this symbol is used (“<”).
• The symbol is towards the smaller number.
• The symbol is like two equal slant lines that meet at an acute angle toward the left side.
• To decide the symbol, you can use during comparison, the most crucial step is to decide which number has a greater value. And, then you can put the greater than or lesser than symbol accordingly.

## Equal to sign

Unlike the less than and greater than symbols, the equal to symbol represents the equality between two similar numbers. A symbol used is “=”.
Example-Compare the numbers 3025 and 3025.
Here,
3025 = 3025
Thus, here you have to use the equality sign.
Mathematically it is represented as,
3,025=3,025

## Forms of the less than symbol

We can use a combination of the less than and the equal sign to represent quantities that can be greater than or equal to. It is denoted by . If we say x is less than or equal to y then we write it as x y. This statement is true in both the cases of x < y or x = y.

Example: Fail grade (F) = 34 and below.

Shera scores 34 and Veera scored 17. Mathematically Shera’s score is equal to the fail grade while Veera’s score is less than the fail grade. Hence both of them receive the grade F.

We can write the condition as F = score 34.

TRICK TO REMEMBER THE SIGN:

• The angular bracket opens to that side which has a large number.

Example: Compare 10,000 and 12,000.56.
Here,
10,000 is less than 12,000.56.
Therefore, the inequality sign will be
10,000<12,000.56.

• Alligator Method:

The alligator method is a way where you can easily relate the greater than and less than signs with the open mouth of a crocodile. Imagine the symbol as the mouth of a crocodile. And the crocodile opens its mouth to that side where there is a greater number. This method helps a kid to memorize the symbol with its meaning in the early phases of learning about these symbols.

Application of Tricks to Use the Less than Symbol
Example 1: Compare the greatest two-digit number with the smallest three-digit number.

The greatest two-digit number = 99
The smallest two-digit number = 100
Clearly,
99 is smaller than 100.
So, a crocodile will open its mouth towards the right side.
Symbolically, it can be represented as,
99 < 100
The number 44 is less than 78.
The number 44 is greater than 78.
So, a crocodile will open its mouth towards the right side.

44 < 78.

Example 2: Compare the numbers 989 and 4,560.
The number 989 is less than 4,560.
So, the crocodile will open its mouth towards the left side.
Hence, we will write this as
989 < 4,560.

Example 3: Compare the numbers 34,567 and 78,906.
The number 34567 is less than 78906.
So, the crocodile will open its mouth towards the right side.
Hence, 34567 < 78906.

Example 4: Compare the numbers 34,567 and 78,906.
The number 34,567 is less than 78,906.
So, the crocodile will open its mouth towards the right side.
Hence, 34,567 < 78,906.

Example 5: Compare the product of 4 and 7 with 77.
The product of numbers 7 and 4 is 28 which is smaller than 77.
So, a crocodile will open its mouth towards the right side.
28 < 77.

Example 6: Compare the numbers 0.222 and 1.
The number 0.222 is smaller than the whole number 1.
So, a crocodile will open its mouth towards the right side.
0.222 < 1.

## SOME EXAMPLES OF LESS-THAN SIGNS:

Comparing Integers

• -44 and 64.
-44 is less than 64.
Therefore, -44 < 64.
• -130 and -100.
-130 is less than -100.
Therefore, -130 < -100.

Comparing Fractions
3/2 and 6/2
3/2 is less than 6/2.
Therefore, 3/2 < 6/2.

Comparing Decimals
0.00006 and 0.06.
0.00006 is less than 0.06.
Therefore, 0.00006 < 0.06.

Comparing Exponents
3^2 and 3^3.
3^2= 3×3 = 9 and 3^3 = 3×3×3 = 27.
Therefore, 3^2 < 3^3.

Example: 10 and 12
Here,
12 is greater than 10.
Therefore, the inequality sign will be like
10 < 12.
Hence,
10 is less than 12.
Similarly, between -12 and 10.
Here, 10 is greater than 12.

Food for thought!
We usually know that multiplication makes numbers bigger. Is it true for all numbers?
What happens to the product of ⅓ times 1/3? It is 1/6. But ⅙ < ⅓. Why do you think it is so?
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PROBLEMS

Question 1) What are different inequality signs?

Answer: There are two inequality signs in maths greater than and less than symbols.

Question 2) Can you use a less-than symbol to show the comparison between numbers 7.89 and 7.89?

Answer: No, the Inequality sign cannot be used as the numbers are equal. Instead, the equality sign will be used to show the comparison between the two numbers.

Question 3) Draw the alligator mouth to show less than a symbol for the following questions.
2.345    3.245
6598    965693
59    69
312    912

2.345 < 3.245
6598 < 965693
59 < 69
312 < 912

Question 4)
Can you compare Roman numbers?

Answers: Yes, you can compare even the Roman numbers as Roman numbers do have a numeric value.
The comparison involves the same method after you get the numeric value of the Roman number.

Question 5)
In a library there are books on Physics, Chemistry, Biology, and Astrology. And their numbers are 59874,58974,6789 and 45689 respectively. Arrange these numbers in increasing order.

Answer: Total number of Physics books=59874
Total number of chemistry books=58974
Total number of Biology books=6789
Total number of Astrology books=45689
Hence, 6789 < 45689 < 58974 < 59874

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