
Which property is illustrated by the following statement?
Answer
492k+ views
Hint:
Here, we need to find the property illustrated in the given equation. We will use the definitions of the commutative and associative property to see which of the two is illustrated in the given statement.
Complete step by step solution:
We can observe that the given statement contains the addition operation.
First, we will define the two properties – commutative property of addition, and associative property of addition.
The commutative property of addition states that the sum of two numbers remains the same even if the numbers are swapped and their order is changed. This is true for all real numbers.
The associative property of addition states that the sum of three or more numbers remains the same even if the numbers are grouped in a different way. This is true for all real numbers.
Now, we can observe that in the statement , the numbers grouped in the parentheses are the same.
Therefore, this does not illustrate the associative property of addition.
From the commutative property of addition, we have .
Substituting in the expression , we get
Therefore, we can conclude that the given statement illustrates the commutative property of addition.
Note:
Commutative property can be represented by the equation .
For example: the sum of 2 and 3 is 5. The sum of 3 and 2 is also 5. Therefore, .
Associative property can be represented by the equation .
For example: The sum of 2 and 3 is 5. The sum of 5 and 4 is 9.
Also, the sum of 3 and 4 is 7, and the sum of 2 and 7 is 9. Therefore, .
Here, we need to find the property illustrated in the given equation. We will use the definitions of the commutative and associative property to see which of the two is illustrated in the given statement.
Complete step by step solution:
We can observe that the given statement contains the addition operation.
First, we will define the two properties – commutative property of addition, and associative property of addition.
The commutative property of addition states that the sum of two numbers remains the same even if the numbers are swapped and their order is changed. This is true for all real numbers.
The associative property of addition states that the sum of three or more numbers remains the same even if the numbers are grouped in a different way. This is true for all real numbers.
Now, we can observe that in the statement
Therefore, this does not illustrate the associative property of addition.
From the commutative property of addition, we have
Substituting
Therefore, we can conclude that the given statement illustrates the commutative property of addition.
Note:
Commutative property can be represented by the equation
For example: the sum of 2 and 3 is 5. The sum of 3 and 2 is also 5. Therefore,
Associative property can be represented by the equation
For example: The sum of 2 and 3 is 5. The sum of 5 and 4 is 9.
Also, the sum of 3 and 4 is 7, and the sum of 2 and 7 is 9. Therefore,
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Chemistry: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Trending doubts
Full Form of IASDMIPSIFSIRSPOLICE class 7 social science CBSE

The southernmost point of the Indian mainland is known class 7 social studies CBSE

Convert 200 Million dollars in rupees class 7 maths CBSE

How many crores make 10 million class 7 maths CBSE

One lakh eight thousand how can we write it in num class 7 maths CBSE

What is meant by Indian Standard Time Why do we need class 7 social science CBSE
