Not Equal
2026-02-21 20:41 Diff
https://brightchamps.com/en-us/math/numbers/not-equal

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Last updated on December 12, 2025

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?

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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:

  1. 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.
     
  2. 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
     
  3. 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.
     
  4. Always check for negative signs. For example,
     
  5. Use real life items to express numbers and visualize not equal signs. For example, 10 orange candies are not equal to 5 strawberry candies. 
     
  6. Use real objects to show the differences, so children can easily understand when two quantities are not equal.
     
  7. Show the number cards and use daily examples to compare the values, including cases that use the less-than-or-equal-to sign.
     
  8. 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:

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.

Problem 1

Jerry scored 65 marks in Math, and Annie scored 76 marks. Can we say their scores are not equal?

Okay, lets begin

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.

Well explained 👍

Problem 2

Is a ≠ b? Given: a = 11 and b = 2.5

Okay, lets begin

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.

Well explained 👍

Problem 3

Is 32 not equal to -56?

Okay, lets begin

No

Explanation

Yes, 32 and -56 are different numbers.

So, 
32 ≠ -56

Well explained 👍

Problem 4

A child writes: 6 + 2/3 ≠ 8 Is this correct?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

Yes, the number of chocolates in both boxes is not equal.

Explanation

Yes, 40 ≠ 35


So, the number of chocolates is not equal.

Well explained 👍

FAQs on Not Equal

1.How to explain “not equal” symbol (≠) to my child?

The "not equal" symbol indicates a difference between two values or quantities. It shows that the values on either side of the symbol are not the same.
Give your child 2 chocolate cookies and 3 Oreo cookies. 

Here, 2 ≠ 3.

2.How to explain that 5 is not equal to 8 to my child?

Use real life objects like toys, food or money to help visualize numbers. Give your child $5 and ask to buy an $8 item. Now, explain why they were not able to buy the item, because $5 ≠ $8.

3.Can my child use "≠" in equations?

Yes, ≠ symbol can be used to show that the two sides of an equation differ. For example, 10 + 5 ≠ 2 + 5

4.Is it necessary for my child to understand not equal?

Yes, learning not equal helps children to develop relational understandings in mathematics.

5.How can my child write that 10 is not equal to 18 using the symbol.

Children can write 10 is not equal to 18 using the not equal to sign as 10 ≠ 18.

6.What does the does not equal sign (≠) mean for parents helping their children at home?

The does not equal sign is shows that the two values being compared are different. When children use the not equal sign, they mean the number on the left is not equal to the one on the right.
 

7.How can parents easily explain the not equal sign to children?

Parents can use real objects to make the idea clear. For example, “3 apples ≠ 1 apple” or “2 toys ≠ 5 toys.” When children see the difference between real things, they understand the concept faster.
 

8.Can parents show the difference between the not equal sign (≠) and the less than or equal to sign (≤)?

Yes, parents can explain that the less-than-or-equal-to sign means the value is smaller or the same, while the does-not-equal sign shows that two values are different and cannot be equal.
 

9.How can parents help children practice the not equal sign at home?

Parents can give simple true-or-false statements in a style like “6 + 1 = 10” and ask children to correct them using the does not equal sign. This may help children to learn in a fun and easy way.

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.