Less Than
If you ever wondered how to identify where to put the lessthan symbol or the greater than symbol, think of the alligator.
The alligator’s mouth will open in the direction of the larger food item, in this case, a number. Once you get a hang of the symbols, you will understand numbers and fractions that are less than 1, as well as the concept of less than or equal to. Checkout the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page.
Lesson Plan
What Is Less Than?
In mathematics, we use numbers for comparisons.
To compare means examining the difference between quantities or values to decide which is greater than, or equal to, or smaller than the other quantity.
We do comparisons in terms of weight, the volume of liquids, etc.
In mathematics, we have important symbols or signs to understand bigger numbers, smaller numbers, and equal numbers.
We use certain signs for comparing these numbers, and "less than" is one such sign.
One of the ways to compare numbers is by using a number line.
Let's try the simulation shown below.
Enter any two numbers between 4 and 8
You can then observe them on the number line along with the symbol showing their relationship.
Define Less Than
Less than is used to describe the relationship between two values.
Less than meaning: Less than indicates that one value is lesser than the other.
The sign for less than is <
Using this symbol, we can compare numbers, weights, distances, etc.
We can show these numbers as: 3 > 1, 2 < 9
1. Write the following statement using mathematical symbols.
a) 5 is less than the sum of 3 and 4
b) The product of 8 and 2 is equal to the product of 2 and 8
What Is the Symbol of Less Than?
This sign is called the less than sign in math.
This is used to show that one value is lesser than the other value.
We know that the statement "16 is less than 18" is true.
Hence, we can write it as 16 < 18 using the less than symbol.
The wideopen side of the sign with its two points always faces the bigger number, whereas the smaller endpoint faces the smaller number.

One of the easiest ways to remember the "greater than" and "less than" signs is to imagine them as hungry alligators that always eat the larger number.
Hence, the wideopen side of the sign faces the larger number.

Another way to memorize them is to observe that the sign "<" looks similar to the alphabet "L". In other words, "<" means "Less than."
When to use Less Than?
Let's compare the twodigit numbers, 32 and 14
While comparing the twodigit numbers, we first compare the tens digits.
If the tens digits are the same, we will compare the ones digits.
Here, we can see that 1 is less than 3
Thus, we can say that 14 is less than 32
Mathematically, we can write it as 14 < 32 using the less than symbol.
Less Than 1
Representing numbers on a number line makes it easy to identify which numbers are greater or lesser.
A number on the left is less than a number on the right.
Hence, all the numbers which are on the left of 1 are less than 1
Use of Less Than in Algebra
In mathematics, the less than and the greater than symbols describe the inequality between two values.
The symbol “< “ is used to represent less than inequality.
 Make the smallest fourdigit number using the digits: 7, 1, 4, and 2 in such a way that no digit is repeated.
 For the numbers 0.12 and 0.21, form a mathematical statement using "less than symbol".
Solved Examples
Example 1 
Observe the figure below.
On the right side, there are 6 stars.
On the left side, there are 4 stars.
Insert the appropriate sign between the numbers.
Solution
The number 4 is smaller than the number 6
Hence, the alligator's open mouth faces number 6
Here, we can say that 4 < 6
\(\therefore\) 4 < 6 
Example 2 
Amrita had to collect various kinds of leaves and paste them in 2 sheets.
In order to place them all in two sheets, she pasted 8 on one sheet and 9 on the other.
Which sheet has fewer leaves?
Solution
As a part of her assignment, Amrita pasted 8 leaves on one page and 9 on the other.
The number 8 is less than the number 9
Thus, the sheet with 8 leaves has fewer leaves.
\(\therefore\) The sheet with 8 leaves has fewer leaves. 
Example 3 
A cow weighs 720 kilogram.
The weight of her calf is 180 kilogram.
Which of them weighs less?
Use symbols to represent this information.
Solution
Weight of the cow = 720 kilogram
Weight of the calf = 180 kilogram
Let's observe the numbers, 720 and 180
They are threedigit numbers.
7 and 1 are at the hundredths place.
By comparing them, we can say that 1 is less than 7
Thus, the information is represented as 180 < 720
\(\therefore\) The information is represented as 180 < 720 
Example 4 
(i) Which of them weighs less?
(a) (b)
(ii) Which of them (the bottle or the cartons) holds less amount of liquid?
Solution
\(\therefore\) (i) (a) weighs less. (ii) The carton each of capacity 100 ml holds less than the 1 litre(1000 ml) bottle. 
Example 5 
Varun is working on an assignment for his class.
He has a list of states which need to be arranged in ascending order according to their 2016 wheat harvest.
States  Volume (in million tonnes) 
Uttar Pradesh  6812 
Haryana  5805 
Punjab  6206 
Can you help him complete this task?
Solution
Arranging the numbers in ascending order means to arrange them from the lowest to the highest.
You can notice that all these numbers are not singledigit numbers.
Hence, we will start comparing from the leftmost digit in each number.
Thus, we get, 5805 < 6206 < 6812
That is, 5805 million tonnes < 6206 million tonnes < 6812 million tonnes.
\(\therefore\) 5805 million tonnes < 6206 million tonnes < 6812 million tonnes 
Interactive Questions
Here are a few activities for you to practice.
Select/Type your answer and click the "Check Answer" button to see the result.
Let's Summarize
We hope you enjoyed learning about Less Than with the simulations and practice questions. Now you will be able to easily solve problems on less than symbol, less than meaning, less than or equal to symbol in words, and less than 1
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Frequently Asked Questions (FAQs)
1. Are 0.5 and 0.05 the same?
No, 0.5, and 0.05 are not the same. They are not equal.
0.05 = \(\dfrac{5}{100}\) and 0.5= \(\dfrac{5}{10}\)
0.05 = \(\dfrac{5}{100}\) < 0.5= \(\dfrac{50}{100}\)
0.05 < 0.5
2. Can less than be represented on a number line?
Yes, less than can be represented on the number line.
3. What number is less than a negative number?
On the number line, negative numbers are to the left of zero.
The greatest negative integer is 1. There is no smallest negative integer.