What are the different operations conducted on real numbers?

Real numbers can be considered the backbone of mathematics. Almost every quantity we deal with, in real life, is measured in real numbers. These are the numbers that can be represented in the cartesian plane and the number line. Real numbers can be rational and irrational. Different operations can be performed on these numbers.

Answer: The operations that can be conducted on real numbers are addition, subtraction, multiplication and division.

Let's understand these in detail.

Explanation:

As we know, real numbers can be classified into two categories: Rational and Irrational.

First of all, we look at the operations conducted on two or more rational numbers:

• Addition - Two rational numbers can be added to give another rational number. For example, 4 + 10 = 64.
• Subtraction - Two rational numbers can be subtracted to given another rational number. For example, 20 - 15 = 5.
• Multiplication - Two rational numbers can be multiplied to given another rational number. For example, 9 × 5 = 45.
• Division - Two rational numbers can be divided to given another rational number. For example, 45 ÷ 5 = 9.

Next, we look at the operations on two or more irrational numbers:

• Addition - Two irrational numbers can be added to give either irrational number. For example, 2√2 + 5√2 = 7√2. Note that the radix must be the same for all the numbers to be added.
• Subtraction - Two irrational numbers can be subtracted to give another irrational number. For example, 6√2 - 5√2 = √2. Note that the radix must be the same for all the numbers to be subtracted.
• Multiplication - Two irrational numbers can be multiplied to give a rational or irrational number. For example, 4√3 × 2√2 = 8√6 which is irrational, and 4√5 × 4√5 = 80 which is rational.
• Division - Two irrational numbers can be divided to give a rational or irrational number. For example, 4√10 ÷ 2√2 = 2√5 which is irrational, and 6√5 ÷ √5 = 6 which is rational.

Similarly, we look at the operations conducted on a rational and an irrational number:

• Addition - A rational and an irrational number can't be added to give a single term as a result.
• Subtraction - A rational and an irrational number can't be subtracted to give a single term as a result.
• Multiplication - A rational and an irrational number can be multiplied to give an irrational number. For example, 5√7 × 5 = 25√7.
• Division - A rational and an irrational number can be divided to give an irrational number. For example, 5√7 ÷ 5 = √7.

Hence, the operations that can be conducted on real numbers are addition, subtraction, multiplication and division.