Not Equal

The not equal sign (≠) is used to indicate the inequality of two quantities. For example, if A and B have different values, then we can write A ≠ B. This sign provides a concise representation of inequality between two quantities.

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.

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. 

“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.