The greater than and less than sign can be quite confusing.
If you are one of those people who confuse the other sign over the other, do not worry, you are not alone.
Both symbols look similar so it is not surprising that some people often mix up the two.
With that, we have created this guide to better help you understand the difference between them.
Table of Contents
Knowing the difference
Less than symbol
The less than symbol looks like the picture above.
It simply means the number on the left is less than the right.
This mathematical symbol first appeared in Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas (“The Analytical Arts Applied to Solving Algebraic Equations”) by Thomas Harriot in 1631.
After a century, it was then refined by Pierre Bouguer in 1734.
Rather than opt for the one used by Harriot, Bouguer slightly alters it by adding a line below the mathematical symbol like the ones below.
This less than sign symbol simply means less than or equal the number on the right.
Terminologies you can use for the less than symbol:
- Lower than
- Smaller than
- Fewer than
- Below
- Not greater than
Greater than symbol
The greater than sign looks like the one above.
It simply means the number on the right is greater than the left.
Since the greater than symbol is the opposite of the less than sign, it also has the same history.
It also appeared in Harriot’s book in 1631 and was later modified by Bouguer in 1734.
This greater than sign symbol means greater than or equal the number on the left.
Terminologies you can use for the greater than symbol:
- More than
- Higher than
- Over/above
- Beyond of
Equal Sign
The equal sign looks like the one above.
This simply means both numbers are equal or the numbers on the left and right sides have the same value.
The equal sign was first introduced in Robert Recorde’s book titled The Whetstone of Witte in 1557. As compared to the greater or less than sign, the equal sign is much older.
However, the equal sign was only formally defined by 1894. It was Cesare Burali-Forti who denote this sign as “equal by definition” in his book Logica Matematica.
Back then, he actually used the “=Def” rather than the modern “=” sign only.
Terminologies you can use for the greater than symbol:
- Same as
- Matches the
- Equivalent of
- On par with
How do you remember it?
There are several ways to remember these inequality symbols.
Our teacher (back when I was still a kid) also used these methods. I was able to better understand the difference between the greater than and the less than symbol because of the alligator method.
Hopefully, this guide can help you better understand the inequalities symbols as well.
Alligator Method
One of the most popular methods used by preschool and elementary teachers is the Alligator Method.
This method is pretty straightforward and highly effective among kids.
In the Alligator Method, the gator’s mouth is always open to the largest value. Since the alligator is always hungry, he is always eating the greater number.
See picture below
The gator’s mouth is open at the highest number on the left. This means 5 > 2 or you can read it as five is greater than two.
Another example below
The gator’s mouth is open at the highest number on the right. This means 12 < 15 or you can read is as twelve is less than fifteen.
So whenever you are confused, think of the alligator and his mouth. Just imagine which side of his mouth would his mouth be open.
L Method
Another way to remember the difference between the greater and less than sign is to think of the letter “L”
In order to have a better picture, we have illustrated it for you.
Since the above already means less than, then its counterpart is the opposite.
Fingers Method
You can simply use fingers to remember the difference between greater than and less than sign.
Just always remember that the opening should always point towards the highest number
Like this
5 > 3 or five is greater than three
10 < 15 or ten is less than fifteen
Worksheet
The worksheets below are from Corbettmaths. It is a website that offers free worksheets for students and teachers.
Practicing Inequality Symbols
| 8 | 6 | 4 | -1 | |||
| 2 | 3 | -4 | 6 | |||
| 7 | 10 | 9 | 9.4 | |||
| 5 | 0 | 0 | -1 |
Writing down inequality signs
- x is greater than 8
- x is less than 3
- x is less than or equal to 1
- x is greater than or equal to 0
- x is less than 7
- x is greater than or equal to −2
- x is less than or equal to −10
- x is greater than 5
Reading Inequalities
- x > 6
- x < 2
- x ≥ 1
- x ≤ 4
- x ≥ 0
- x ≤ −4
- x < −2
- x > 20
- x < y
- a ≥ b
- c > 5
- y ≤ 100
Application
Question 1: The cost, c, of a TV is less than £300. Write this as an inequality.
Question 2: To go on a rollercoaster, a person’s height, h, must be over 140 cm. Write this as an inequality.
Question 3: The value of a house, v, is £100, 000 or more. Write this as an inequality.
Question 4: There are 20 students in a class. The number of students present on a particular day is 20 or less. Write this as an inequality.
Question 5: Write down any integers (whole numbers) that satisfy both x > 4 and x ≤ 8
Question 6: Write down any integers (whole numbers) that satisfies both 2 < x ≤ 9 and x > 5
Conditions
- x is greater than 2, but less than 5
- x is greater than 0, but less than 4
- x is greater than 1, but less than or equal to 7
- x is greater than −5, but less than or equal to 2
- x is greater than or equal to −8, but less than 3
- x is greater than or equal to 10, but less than 20
- x is greater than or equal to 3, but less than or equal to 6
- x is greater than or equal to 8, but less than or equal to 11
You can view the answers here
Aside from the worksheet we cited below, there are many free websites that offer free worksheets and resources.
With a simple Google search, you would be amazed at the number of worksheets and practice problems available for free.
Websites for Worksheets
KS Learning
Founded in 2011, K5 Learning offers several worksheets and practice problems for free. Their website has had over 100 million visitors from teachers, tutors to current students and aspiring students.
Worksheet Genius
According to their website, Worksheet Genius is a free online website that generates differentiated and randomized worksheets. They offer unlimited worksheets for free.
Math-Aids
A free online resource website where you can download printable worksheets in PDF files. Their website boasts flexibility and textbook quality worksheets. So if you are looking for more practice problems, then this website might be the best one for you.
Common Core Sheets
This online website offers several worksheets and practice problems for download. One of the plus sides of this website is that it is available in different languages. Aside from that, they also have worksheets for different subjects like Social Studies, Writing, Spelling, Science, and many more.
Conclusion
The best advice we can ever give you is to practice reading inequality symbols and answer several practice problems as well.
This way, you would always remember the difference between the greater and the less than sign.
Hopefully, you managed to learn a thing or two about the topics we covered.
To briefly recap, we have discussed the following
We have also wrote a few fun articles that you can check out
Todd VanDuzer
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