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Greater Than
Greater than is a symbol used to compare values and indicate the larger value. For e.g., 5>3. Here, the symbol is used to indicate that 5 is greater than 3. The symbol is widely used in basic arithmetic and advanced mathematics.
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What is “Greater Than” in Math?
In math, the greater than symbol is used for comparison. It might be the comparison between numbers, data, or ranking. 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.
History of “Greater Than” Symbol
Thomas Harriot, an English mathematician, introduced the “greater than” symbol (>) in the 17th century. In 1631, he published his book Artis Analyticae Praxis, where he used the greater than (>) and lesser than (<) symbols to denote the relationship between values.
These symbols simplified mathematical notation and gave a clearer understanding of inequalities. The symbol resembles an arrowhead that points to the lower number, signifying the inequality. Now, it is a fundamental part of mathematics which is used in equations, logic, and data analysis.
Properties of “Greater Than”
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 the number 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 the 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 x c > b x 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 either 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.
Importance of “Greater than” in Math
An important mathematical concept, the “greater than” symbol (>), is used in calculus, algebra, and data analysis. Its simplicity makes it a very significant concept in mathematics communication and problem-solving.
Tips and Tricks to Understand “Greater than”
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 want 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. A left pointing L looks like < (less than), and a right pointing L looks like > (greater 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. Which will help the students grasp more of the topic.
Real-World Applications of “Greater than”
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 ingredients 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.
Common Mistakes and How to Avoid them in “Greater Than”
While students use greater than in problems and equations, they tend to make small mistakes. Here is a list of the most common mistakes the students tend to make while solving concerns using greater than. The list contains the mistake and the solution to said mistake.
Mistake 1
Confusing the direction of the symbols, for example: writing 5 < 3 instead of 5 > 3.
Students can use the alligator trick to imagine and compare an alligator’s open mouth with the symbol. The open mouth will always face the larger number.
Solved Examples on “Greater than”
Problem 1
John is 12 years old. His sister, Mary, is 8 years old. Compare their ages using greater than symbol.
12 > 8
Explanation
Identify the ages: John = 12 years and Mary = 8 years old.
Determine the greater age: John’s age is greater than Mary
Write the inequality: 12 > 8.
Problem 2
The temperature in New York City is 75°F. The temperature in Miami is 88°F. Write an inequality to compare the temperatures.
88 degrees > 75 degrees
Explanation
Identify the temperatures: New York = 75°F, and Miami = 88°F.
Determine which temperature is higher: Miami’s temperature is greater than New York City’s.
Write the inequality: 88 degrees > 75 degrees.
Problem 3
A giraffe is 18 feet tall, and a horse is 6 feet tall. Write an inequality to compare their heights.
18 feet > 6 feet.
Explanation
Identify the heights: Giraffe = 18 ft and Horse = 6 ft.
Determine which animal is taller: the giraffe is taller than the horse.
Write the inequality: 18 ft > 6 ft.
Problem 4
In a basketball game, Team A scored 98 points, and Team B scored 85 points. Write an inequality to compare their score.
98 points > 85 points.
Explanation
Identify the scores: Team A = 98 points, and Team B = 85 points.
Determine the higher score: Team A scored more than Team B.
Write the inequality: 98 > 85.
Problem 5
A toy car costs $15. A board game costs $22. Write an inequality to compare the prices.
$22 > $15.
Explanation
Identify the prices: toy car = $15, and board game = $22.
Determine the greater price: the board game is more expensive than the toy car.
Write the inequality: $22 > $15.
FAQs on “Greater than”
1.What does “greater than” mean?
2.What is the symbol for “greater than”?
3.How do you use the greater than symbol in a sentence?
4.Can you use greater than symbol for decimals?
5.What are some real-world applications of the “greater than” concept?
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.
