Not Equal
In this minilesson, we will explore the unequal sign, unequal synonym, and inequality while discovering the interesting facts around them.
Did you know, the equal sign was first given by an English mathematician named Robert Recorde to avoid repetition of the words "is equal to".
In this chapter, we will learn about an unequal synonym which is "not equal".
Joey received two packets of chocolates from his friends. Is the quantity of chocolates in them equal?
No, one bag contains 2 chocolates while the other bag contains 6 chocolates.
Hence, the quantities of chocolates in bags are not equal.
Let's have a look at this simulation below.
Click on the green buttons to increase or decrease the number of apples on either side and see whether your guess for them being equal or unequal is right.
Lesson Plan
What Do You Mean by Not Equal?
The not equal sign is an unequal synonym. The not equal symbol is a sign of "inequality". It is meant to show a comparison between the two quantities which are unequal hence, representing inequality among them.
It is represented by two parallel horizontal lines cut by an inclined vertical line as (\(\neq\)).
 The symbol used to show the not equal to sign is "\(\neq\)".
 There are different symbols for each comparison aspect, not equal sign being one of them.
Where Do We Use Not Equal in Maths?
In mathematics, not equal is used to show two quantities are unequal. The unequal sign for two quantities is shown in the following way:
Let's see a few examples from a mathematical perspective:
Example 1: Oliver's teacher asked him to solve the equation \( 3a + 51 = 60\) and conclude whether a = 2 or not? Help him find the answer.
Solution:
Oliver will first solve the equation to conclude whether a = 2 or not.
In the equation \( 3a + 51 = 60\), "\(a\)" is a variable.
The solution of linear equation is given as:
\( \begin{align}3a+51&= 60 \\ 3a& = 60  51 \\ 3a& = 9\\ a& = 3 \end{align} \)
Hence, he will conclude that \(a\) is not equal to \(2\) i.e. \(a \neq 2 \)
Example 2: Lisa has to find out the area of squares having lengths of sides 2 inches and 2.2 inches. Can you help her find whether their areas are equal?
Solution:
Area of square having length of side 2 inches is,
Area of square = \((2)^2\) = \(4\) sq. inches
\(\therefore\) Area of square = 4 inch^{2}.
Area of square having length of side 2.2 inches is,
Area of square = \((2.2)^2\) = \(4.84\) sq. inches
\(\therefore\) Area of square = 4.84 inch^{2}.
Hence, area of both squares is not equal i.e. \(4 \neq 4.84 \)
Where Do We Use Not Equal in Real Life?
Example 1: John went to a fruit seller to buy two pounds of oranges. The fruit seller weighed it on his weighing scale, to check their weight. Is the weight of oranges equal to two pounds?
No, the weight of oranges is three pounds.
The weight of oranges is three pounds which are not equal to two pounds, i.e. \(2 \neq 3 \)
Example 2: Jenny and Jessica scored 78 and 82 respectively in French. They seem confused. Help them determine whether they scored equal marks or not?
Solution: Marks scored by Jenny are 78 while those scored by Jessica are 82
They did not score equal marks.
Hence, marks scored by Jenny and Jessica are unequal, i.e. \(78 \neq 82 \)
Solved Examples
Example 1 
Jake went to buy fruits for his home. In the list of fruits purchased, he got one watermelon and one pumpkin. Check the bill and tell, did he pay equal money for both?
Solution
He got one watermelon for \($5\)
However, he got one pumpkin in \($10\)
As, \(5 \neq 10\)
Hence, as per the bill, it can be told that he did not pay equal money for both.
\(\therefore\) He paid unequal money. 
Example 2 
William and Jill got their height's checked. This is how it looks.
Do the heights of William and Jill look equal?
Solution
As per their heights visible in the scales, the height of William is more than the height of Jill.
Hence, we can conclude that the heights of William and Jill are not equal.
\(\therefore\) Their heights are unequal. 
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.

If the price of 4 watermelons is exactly the same as the price of 5 apples, can Jane say that price of 6 watermelons is equal to the price of 10 apples?

Mike and his sister are in the same class. He scored 5 marks more than what his sister scored. If the sum of marks scored by Mike and his sister is 25. Is Mike's score equal to 20?
Let's Summarize!
We hope you enjoyed learning about unequal with the practice questions. Now you will have a better understanding of unequal, unequal sign, unequal synonym, inequality, and equal.
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Frequently Asked Questions (FAQs)
1. Which comparison operator means “not equal to”?
The comparison operator which means "not equal to" is (\(\neq\)).
2. How to type does not equal sign?
The not equal sign can be typed as "\(\neq\)".
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