Greater Than

In math, the greater than symbol is used for comparison. It is used for the comparison between numbers, data, or rankings. The greater than indicates that one number is greater than another. It is commonly used in inequalities, arranging and organizing numbers, and problem-solving to compare values and understand their relationships.

Thomas Harriot, an English mathematician, introduced the “greater than” (>) symbol in the 17th century. In 1631, he published an Artis Analyticae Praxis, in which he introduced the greater-than (>) and less-than (<) symbols. These symbols simplified mathematical notation and made it easier to understand. The symbol’s arrowhead points toward the smaller number, showing inequality. Today, these symbols are widely used in equations, logic, and data analysis.
 

There are many important properties that help students learn the ‘Greater than’ concept. The students must understand these properties to make the concept of greater than much simpler. The list of properties is mentioned below:

• Comparison property:  
  a > b means that a is greater than b.

• Transitive property: 
  If a > b and b > c, then a > c.

• Non-symmetric property: 
  If a > b, then b is not greater than a.

• Non-reflexive property: 
  A number can never be greater than itself, so this property is always false; for example, a > a is never true.

• Asymmetry property: 
  If a > b, then b < a.
  
   

• Additive property: 
  The inequality is preserved if the same number is added to both sides:
  If a > b, then a + c > b + c.

• Multiplicative property: 
  If c > 0, multiplying both sides by c preserves the inequality: 
  If a > b, then a × c > b × c.  If c is negative, the inequality reverses: If a > b and c < 0, then a × c < b × c.

• Subtractive property: 
  The inequality is preserved if the same number is subtracted from both sides:
  If a > b, then a - c > b - c.

• Division property: 
  If c > 0, dividing both sides by c preserves the inequality: 
  If a > b, then a/c > b/c. If c is negative, then the inequality reverses.    

• Compatibility with zero: 
  A number greater than zero is always positive. A number less than zero is always negative.

• The greater than sign ( > ) is an important concept used in algebra, calculus, and data analysis.

• The greater than sign helps in clear communication and easy problem-solving in mathematics.
  
  
   
• Tools like a greater than less than calculator can also help students easily compare numbers and understand relationships between quantities.

• In programming, the greater than symbol is used in conditions like if x > 10 to make decisions.

• In statistics, the greater than sign ( > ) is used in hypothesis testing to represent an alternative hypothesis, such as Hₐ: μ > 0.

While students use greater than in problems, they tend to confuse it with another symbol, i.e., the less than symbol. So to avoid confusion, here are some tips and tricks I can use to understand how and where to use the symbol.
 

The alligator method: Imagine the symbol as an open mouth of alligators, and imagine the alligator always wants to eat the bigger number. For example, 5 > 3. The alligator eats the 5, as 5 is the bigger number.
 

The number line: You can visualize the number line. Just remember that the number on the right-hand side is greater than its left counterpart. This is how a number line works.
 

The “L” trick: Students can use the L trick. The letter ‘L’ can help you understand the direction of the symbol. The symbol that looks like a crooked 'L' (<) means 'Less than'. 
 

Use real-world examples: Students can understand the concepts better when they use real-world examples. They can use examples like comparing heights, comparing ages, or comparing weights.
 

Positive reinforcement: Remember to make the concept of greater than fun and engaging. This will help the students grasp more of the topic.


Use Real-Life Examples:
Show two sets of items, like apples or toys. Ask, “Which has more?” And let them know that the set that has more items is the one that is greater than the one with fewer items. If both are the same, it means greater than or equal to (≥).


The Alligator Rule:
Say to children that the alligator ( > ) always eats the bigger number because it’s hungry for more. Later, show that when the alligator eats the smaller number, it means less than (<), and when both are equal, it means greater than or equal to (≥).


 Use a Number Line:
Show the number line and explain to the children that numbers to the right side represent greater values while numbers on the left side represent smaller ones. This helps children easily grasp the concepts of greater than and less than.


Play Comparison Games:
Use either cards or dice to visually show two different numbers. Ask them to place the correct sign — >, <, or ≥ — between them. This makes learning greater than or less than fun.


 Relate to Daily Life:
Ask simple questions such as “Who has more crayons?” or “Which bottle has more water?” These kinds of questions help children use greater than, less than, and greater than or equal to in real-life situations.

We use the concept of greater than in our day-to-day applications like cooking, shopping, comparing ages, temperature. Let us now see what kind of applications we use greater than:

Shopping: We use greater than while purchasing things from the shopping mart. For example, this pen costs Rs. 15, which is greater than Rs. 10.

Cooking: We use greater than in measuring ingredients while cooking. For example, we use it to decide the quantity of each ingredient to cook said amount of servings.

Age and heights:  We use greater than to compare the age and heights of people. For example, I am taller than you, or I am the older kid in the group of siblings.

Temperatures: We use greater than in measuring temperatures, like which is hotter or colder. 

Decision-making: We use greater than in everyday choices like making decisions on what causes greater risks and the least risks.