Greater Than and Less Than Symbols

Greater than and less than symbols are used to compare any two numbers.  When a number is bigger than or smaller than another number, greater than less than symbols are used. If the first number is greater than the second number, greater than symbol (>) is used. If the first number is less than the second number, less than symbol (<) is used. Mathematics is a language that has its own rules and formulas. The symbols used in maths are quite unique to all the fields and it is universally accepted. Usage of math symbols consumes less time and space. It allows an individual to share the information through symbolism. In this article, we are going to learn the definition of greater than and less than symbols, their symbols, and the examples to compare two numbers using the less than and greater than signs.

Table of Contents:

• Definition
  • Greater Than Sign
  • Less than Sign
  • Equal to Sign
• Tricks to Remember
• Symbols – Summary
• Applications in Algebra
• Examples
• Word Problems
• Practice Questions
• FAQs

Greater Than and Less Than Symbols Definition

Greater than and less than symbols denote an inequality between two values. The symbol used to denote greater than is “ >” and for less than is “<”. Get more math symbols here with us.

Greater Than Sign 

The greater than symbol in maths is placed between two values in which the first number is greater than the second number. For example 10 > 5. Here 10 is greater than 5. 

In inequality, greater than symbol is always pointed to the greater value and the symbol consists of two equal length strokes connecting at an acute angle at the right. ( >). 

Less Than Sign

Similarly, a less than symbol is placed between two numbers where the first number is less than the second number. An example for less than the inequality symbol is 5 < 10. It means that 5 is less than 10. 

In inequality, less than symbol points to the smaller value where the two equal length strokes connect at an acute angle at the left (<).

This greater than less than symbol reduces the time complexity and it makes an easy way for the reader to understand.

Equal To Sign

The ‘equal to’ sign is used to show the equality between two numbers or values. This sign contradicts both the greater than and less than sign. Even in terms of writing the equations, we use equal to sign. It is denoted by ‘=’.

Example: If a = 10 and b = 10, then a = b.

Trick to Remember Greater Than Less Than Sign

Generally, to remember the greater than and the less than a symbol, two methods are used. They are:

• Alligator Method
• L Method

Alligator Method

We know that the alligator (or crocodile) always want to eat a large number of fishes. So, the alligator’s mouth always opens toward the largest number. Now, imagine that the numbers on both sides represents the number of fishes. Let us take an example, 8 > 5

Here, the alligator mouth points towards 8. It means that 8 is greater than 5.

It means that 5 is less than 8. It is also written using less than symbol as 5 < 8.

L Method

The letter “L” looks similar to the less than symbol “<“. You can remember the first letter of the word, less than to the symbol. Example: 10 < 50

Summary – All the Symbols

Here, given the list of frequently used symbols in Maths explained along with the examples

Applications of Greater Than Less Than Symbols in Algebra

As we know, mathematical problems do not always end with equality. Sometimes, it should have inequalities such as greater than or less than sign. The statement can be expressed using mathematical expressions. 

For example, “x” is the number of students in a class. If there are more than 45 students in a class, and again 5 more students joined in your class, then there are more than 50 students in a class. This statement is mathematically expressed as x + 5 > 45.

In mathematics, solving inequalities is similar to solving equations. While working with inequality problems, always give attention to the inequalities direction. Some of the tricks do not affect the direction of inequalities in a problem. They are

• Multiply or divide the inequalities on both sides by the same positive number
• Adding or subtracting the same number on both sides of the inequality expression

Greater Than and Less Than Symbols Examples

Some of the examples of greater than symbol are as follows

• 4 > 1: 4 is greater than 1
• 2⁵ > 2³ : 2⁵ can be written as 2 × 2 × 2 × 2 × 2 =32 and 2³ can be written as 2 × 2 × 2 =8. So 32 > 8 .Therefore 2⁵ is greater than 2³
• 10/2 > 6/3: 10/2 equals to 5 and 6/3 equals to 2. So that, 5 > 2 which implies that 10/2 is greater than 6/3.
• \(\begin{array}{l}5\frac{1}{2} > 2\frac{2}{3} :\end{array} \)
  In the mixed fractions, first convert into the fraction so that it becomes 11/2 > 8/3 which equals to 5.5 > 2.7.
• 0.1 > 0.01: In a number system, which consists of decimal numbers where the value 0.1 is greater than 0.01
• 1 > -2: Here 1 is a positive integer and -2 is a negative integer. We know that the always positive integer is greater than the negative integer. So that 1 is greater than -2.
• -2 > -5: Consider the negative integers, in which the smallest number has a greater value than the largest number. So we conclude that -2 is greater than -5.

Some of the examples for less than symbol are as follows

• 2 < 3: Consider an integer, where 2 is less than 3
• 3² < 3³: Here 3² is written as 3 × 3 = 9 and 3³ is written as 3 × 3 × 3 = 27. So, 9 is less than 27. Also, we can say that 3² is less than 3³.
• ½ < 4/2: For a fraction, ½ equals to 0.5 and 4/2 equals to 2. Therefore 0.5 is less than 2 or we can say ½ is less than 4/2.
• \(\begin{array}{l}3\frac{1}{3} < 7\frac{1}{2}:\end{array} \)
  By converting mixed fraction into an improper fraction, 10/3 < 15/2 which equals to 3.33 < 7.5 .
• 0.002 < 0.1: The decimal value 0.002 is less than 0.1
• -3 < -1: In the given example of negative integers, where -1 has the greatest value. So we conclude that -3 is less than -1.

Word Problems on Greater than and Less than Symbols

Question 1:

Dizzy has fifteen bananas and Mansi has nineteen bananas. Find out who has more bananas.

Solution:

Given,

Dizzy has 15 bananas.

Mansi has 19 bananas.

so, 19 is greater than 15, 19 >15

Therefore Mansi has more bananas than Dizzy.

Question 2 :

Dizzy sleeps for forty minutes and Mansi sleeps for fifty minutes every day in the afternoon. Find out who sleeps for less time.

Solution:

Given,

Dizzy sleeps for 40 minutes

Mansi sleeps for  50 minutes

We know that 40 minutes is less than 50 minutes, so we can write it as 40 < 50

Therefore, Dizzy sleeps for less time.

Example 3:

Compare the numbers using greater than and less than symbols.

1. 89 ____ 100
2. 12.5 ____ 10
3. 1/2 ____ ¼
4. 2 ½ ____ 1 ½
5. -10 ___ -8

Solutions:

(1) The number 89 is less than 100. Hence, 89 < 100

(2) 12.5 is greater than 10. Hence, 12.5 > 10

(3) The decimal value equivalent to ½ is 0.5 and ¼ is 0.25.

Hence, ½ is greater than ¼. Therefore, ½ > ¼.

(4) First, convert the mixed fraction into an improper fraction.

(i.e) 2 ½ = 5/2 and  1 ½ = 3/2

The decimal value equivalent to 5/2 is 2.5 and 3/2 is 1.5.

So, 2.5 is greater than 1.5. Hence, 2 ½ > 1 ½ .

(5) In the number line, the largest number with a negative sign has the smallest value. Hence, -10 is less than -8. Therefore, symbolically, it is represented as -10 < -8

Practice Questions on Greater than and Less than Sign

Compare the numbers using greater than less than signs:

1. 45 ____ 43
2. -12 _____ 32
3. -30 ____ -35
4. 7 ½ ____ 11 ½ 
5. 12.25 ___ 11.50

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