Difference Between Positive and Negative Numbers

Want to know more about positive and negative numbers and the difference between them. This article will help your to clear all your doubts.

In mathematics, numbers are the basic building blocks of all mathematical concepts. In the previous articles, we have discussed rational, irrational, natural and whole numbers. All these numbers are either positive numbers or negative numbers. So, in this article, we will discuss all about positive and negative numbers.

Before starting the article, let’s discuss the number line.

Number Line: A number line is a horizontal line on which the numbers (especially integers) are placed at equal intervals. On the number line, zero is the middle point. All the positive numbers are arranged at the right of zero, and all the negative numbers are at the left.

Must Check: A Beginner Guide to Learn Math’s for Data Science

Now, without further delay, let’s explore the difference between positive and negative numbers.

Table of Content

• Difference Between Positive and Negative Numbers
• What is a Positive Number?
• What is a Negative Number?
• Real-Life Application of Positive and Negative Numbers

Difference Between Positive and Negative Numbers

What are Positive Numbers?

Positive numbers are numbers greater than zero. It can be a natural number, whole number, positive integer, or fractions and are represented by plus (+) sign

Examples: 1, 22, 0.34, 3.14, 22/7

Properties of Positive Number

• Greater than zero: Positive numbers are number that is always greater than zero.

• Closed under addition

The sum of two positive numbers is always a positive number.

Example – 1: 2 + 2 = 4 

• Closed under multiplication

The product of two positive numbers is always a positive number.

Example – 1: 2 * 2 = 4 

Note: The product of two negative numbers is also a positive number.

Example: (-2) * (-2) = 4

• Additive Identity: When 0 is added to any number, it will return the same number.

Example: 2 + 0 = 0 + 2 = 2

• Commutative Property: Positive numbers are commutative in nature i.e., a + b = b + a

Example: 2 + 3 = 5 = 2 + 3

• Order Property: Every positive number can be ordered from least to greatest, i.e., if a and b are two number such that a is less than b then it is given by a < b.

Example: 2 < 3

• Existence of additive and multiplicative inverse

Every positive number has additive as well as multiplicative inverse.

• Additive Inverse: -a is the additive inverse of a.
• Multiplicative Inverse: 1/a is the multiplicative inverse of a.

What are Negative Numbers?

Any number that is less than zero is called negative number. In simple terms all real number that are not positive numbers (except zero) are negative numbers.

Example: -0.24, -22/7, -3

Properties of Negative Number

• Less than zero: Negative numbers are numbers that are always less than zero.
• Closed under addition: The sum of two negative numbers is always a negative number.

Example: -2 + (-2) = -4

• Commutative Property: Negative numbers are commutative in nature, i.e., if a and b are two negative numbers, then a + b = b + a

Example: -2 + (-3) = -5 = -3 + (-2)

• Existence of Additive inverse and multiplicative inverse: Every negative number has additive as well as multiplicative inverse.

• Additive Inverse: -a is the additive inverse of a.
• Multiplicative Inverse: 1/a is the multiplicative inverse of a.

Application of Positive and Negative Numbers

• Temperature: Positive numbers represent high temperature (high temperature represents high fever), whereas negative numbers represent negative temperature (when storing food in the freezer).
• Coordinates: Positive and negative numbers represent the co-ordinate in 2D and 3D.
• Physics: Positive and negative numbers represent force, velocity, and acceleration.
• Accounting: Positive and negative numbers represent credits and debits, respectively.
• Stock Market: Positive and negative numbers represent gain and loss in the stock market.

Conclusion

In this article, we have briefly discussed the positive and negative numbers, difference between them and their properties with the help of examples.

Hope you will like the article.

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