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268 LearnersLast updated on December 12, 2025
Not Equal
When two quantities are different, we represent them using the "not equal" or "not equal to" sign. The "not equal sign (≠)" can be used to indicate inequality when two values are not equal. In this article, we will be discussing the “not equal” symbol and its applications.
What is the “Not Equal Sign” in Math?
The not equal to sign (≠) is the mathematical symbol that indicates that two values are not equal. It is the opposite of the equal sign (=).
When you see ≠, it means:
- The number on the left is different from the one on the right.
- The two quantities do not equal.
The symbol looks like an equal sign with a slanted line through it, clearly indicating that the values are unequal.
Let’s see an example:
5 ≠ 3
Because five is not the same as 3
How to Show “Not Equal”?
The not equal sign (≠) is used to show the relation between two unequal quantities. These quantities can be whole numbers, real numbers, fractions and even decimals. Not equal can be also be used in equations when performing arithmetics operations, or solving complex problems.
For example:
- 5 + 4 ≠ 6 → because 5 + 4 equals 9 and not 6.
- 2.3 ≠ 4.1
- 1/3 ≠ 4/2
- 2 3/5 ≠ 1 3/2
x ≠ y → This means the value of x is not equal to the value of y.
Where do we use the Not Equal in Math?
The not equal sign (≠) is used in math to indicate that two numbers, expressions, or values are not equal. We use it in many situations, like:
1. Comparisons: To show that one number is different from another.
Example:
7 ≠ 9
Because seven is not equal to 9
2. Equations and Inequalities: To say that the variable cannot be a specific value.
Example:
x ≠ 4
(x cannot be 4)
3. Domain Restrictions: To show that the values that make an expression undefined.
Example:
1x is undefined when x = 0
So, we write: x ≠ 0
4. Checking Correctness: To point out that the two results do not match.
Example:
5 + 3 ≠ 10
Because 5 + 3 = 8, not 10
The not-equal sign clearly shows that the two sides of a statement do not match or cannot be equal.
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Comparison Signs in Math
In mathematics, comparison signs help us quickly compare two numbers, quantities, or expressions. These symbols make it easier to show the relationships without writing the long sentences like “greater than” or “less than.”
The equal to sign (=) shows that the value on the left-hand side (L.H.S.) is the same as the value on the right-hand side (R.H.S.). The does not equal to sign (≠) indicates that the values on both sides are not equal.
Here is the common comparison symbol and its meaning
| Comparison Symbol | Meaning |
| = | Equal to |
| < | Less than |
| > | Greater than |
| \(\neq\) | Not equal |
| \(\leq\) | Less than or equal to |
| \(\geq\) | Greater than or equal to |
Tips and Tricks to Master Not Equal
Understanding not equal sign can be one of the simplest topics in mathematics. Here are a few tips to help to master not equal:
- Assume the parallel lines as a regular path, and when the line is drawn crossing the path. It means that now the path is broken into two different parts which are not the same.
- When checking inequality for decimal numbers, check the whole parts and fractional parts both.
Example 2.32 and 2.12
Here, the whole parts are equal: 2 = 2, but the fractional parts are not equal: 0.32 ≠ 0.12.
⇒ 2.31 ≠ 2.12
- To verify if two fractions are equal or not, always simplify the ratios first. For example, 1/2 and 2/4 can be seen as not equal, but when 1/4 is simplified it gives 1/2. Hence, both are equal.
- Always check for negative signs. For example,
- Use real life items to express numbers and visualize not equal signs. For example, 10 orange candies are not equal to 5 strawberry candies.
- Use real objects to show the differences, so children can easily understand when two quantities are not equal.
- Show the number cards and use daily examples to compare the values, including cases that use the less-than-or-equal-to sign.
- Draw a balance scale to help children to see the equal and unequal quantities clearly.
Ask students to explain their reasoning to strengthen understanding and confidence.
Common Mistakes and How to Avoid Them in Not Equal
Not equal is an important sign that shows two quantities are different. However, students often make mistakes when using this sign. Here are a few common mistakes and tips to avoid them:
Mistake 1
Confusion Between ≠ and =
Students get confused with the equal (=) and not equal (≠) signs. For example, they might mistakenly write 5 ≠ 5 instead of writing 5 = 5.
Before using the symbol, compare the values and check if they are equal or not.
Mistake 2
Using ≠ instead of > or <
Mixing up symbols can cause confusion and incorrect results. Sometimes, students may use the not equal sign instead of using other symbols like > or <.
For example, writing 20 ≠ 7 instead of writing 20 > 7.
To make the comparisons, always use signs like > or <.
Mistake 3
Solving Both Sides Without Comparing
In some cases, students may evaluate both expressions without comparing values.
Always compare the values and then decide whether to use the equal symbol or the not equal symbol.
Mistake 4
Considering ≠ Sign as Opposites
Students might mistakenly interpret the ≠ sign as denoting that the values are opposite. For example, they may think one is positive and the other negative.
Keep in mind that ≠ only implies "not equal." The two numbers might have opposite signs or the same signs. The only important thing is that their values are different.
Mistake 5
Ignoring the Complete Equation
Students may not look at both sides of the equation while solving problems. To avoid this error, always compare both sides and then decide on what symbol to use.
Real-Life Applications of Not Equal
“Not equal to” has several practical applications from our daily to daily life activities to advanced mathematical concepts. Let’s see how “not equal to” applies to real-life scenarios:
- Comparing quantities: Using the concept of “not equal,” we can compare items of different prices.
For example:
The price of a scrapbook = $15
The price of a pencil = $5
Since 15 ≠ 5, the prices are not equal.
- Comparing weather: We can also represent varying weather conditions using the not equal sign.
For example: 16°C ≠ 22 °C.
- Academics: The not equal sign can be used to express different marks obtained by students, and can be compared to obtain ranks.
For example, if the top marks achieved by a student is 97 out of 100, then by using not equal sign we can find if there are other students as well who have also achieved the same marks,
- Sports: To compare goals and scores acquired by a player or team to decide the winner can be done by not equal sign.
For example, a team has scored 4 goals and another has 7. Since 4 ≠ 7, the match isn't a tie, and the team with greater scores wins.
- Construction: To find the right size of a material for construction or carpentry purpose, not equal signs are used.
For example, if a table has a top surface area of 12cm2, then the marble to build the table-top is 7 cm2. Since, 12 ≠ 7, the marble is not of the right size.
Solved Examples of Not Equal
Problem 1
Jerry scored 65 marks in Math, and Annie scored 76 marks. Can we say their scores are not equal?
Yes, we can say that their scores are not equal.
Explanation
Jerry scored 65 marks and Annie scored 76 marks. 65 and 76 are different.
So we conclude that 65 ≠ 76.
Problem 2
Is a ≠ b? Given: a = 11 and b = 2.5
a ≠ b
Explanation
The value of a is 11, which is a whole number and b has a value of 2.5 (decimal number)
Since 11 is not equal to 2.5, a ≠ b.
Problem 3
Is 32 not equal to -56?
No
Explanation
Yes, 32 and -56 are different numbers.
So,
32 ≠ -56
Problem 4
A child writes: 6 + 2/3 ≠ 8 Is this correct?
Yes
Explanation
6 can be written as: 6/1.
- Taking LCM of 1 and 3 is 3
6/1 = 6 × 3 / 1 × 3 = 18/3
- Adding 18/3 and 2/3
18/3 + 2/3 = 20/3
- Since, 20/3 ≠ 8
6 + 2/3 ≠ 8 is correct.
Problem 5
There are 40 and 35 chocolates in each of the two boxes. Can we say the number of chocolates in both boxes is not the same?
Yes, the number of chocolates in both boxes is not equal.
Explanation
Yes, 40 ≠ 35
So, the number of chocolates is not equal.
FAQs on Not Equal
1.How to explain “not equal” symbol (≠) to my child?
2.How to explain that 5 is not equal to 8 to my child?
3.Can my child use "≠" in equations?
4.Is it necessary for my child to understand not equal?
5.How can my child write that 10 is not equal to 18 using the symbol.
6.What does the does not equal sign (≠) mean for parents helping their children at home?
7.How can parents easily explain the not equal sign to children?
8.Can parents show the difference between the not equal sign (≠) and the less than or equal to sign (≤)?
9.How can parents help children practice the not equal sign at home?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
