Class 4 Exam > Class 4 Questions > Which operation(s) is/are neither commutative...
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Which operation(s) is/are neither commutative nor associative?
- a)Addition
- b)Subtraction
- c)Multiplication
- d)Division
Correct answer is option 'B'. Can you explain this answer?
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Which operation(s) is/are neither commutative nor associative?a)Additi...
Subtraction is neither commutative nor associative. The order and grouping of numbers being subtracted affect the result.
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Which operation(s) is/are neither commutative nor associative?a)Additi...
Understanding Commutative and Associative Properties
Commutative and associative properties are fundamental concepts in mathematics that help us understand how certain operations behave.
Commutative Property
- An operation is commutative if changing the order of the numbers does not change the result.
- For example:
- Addition: \( a + b = b + a \)
- Multiplication: \( a \times b = b \times a \)
Associative Property
- An operation is associative if the way numbers are grouped does not change the result.
- For example:
- Addition: \( (a + b) + c = a + (b + c) \)
- Multiplication: \( (a \times b) \times c = a \times (b \times c) \)
Analyzing Subtraction
- Subtraction is not commutative:
- For example, \( 5 - 3 \neq 3 - 5 \)
- The results are different (2 and -2, respectively).
- Subtraction is also not associative:
- For example, \( (5 - 3) - 1 \neq 5 - (3 - 1) \)
- The first calculation gives 1, while the second gives 3.
Why Subtraction is Unique
- Since both properties fail for subtraction, it is deemed neither commutative nor associative.
- This distinguishes subtraction from addition and multiplication, which exhibit both properties.
Conclusion
In summary, subtraction is the operation that is neither commutative nor associative, making option 'B' the correct answer. Understanding these properties enhances your mathematical skills and problem-solving abilities!
Commutative and associative properties are fundamental concepts in mathematics that help us understand how certain operations behave.
Commutative Property
- An operation is commutative if changing the order of the numbers does not change the result.
- For example:
- Addition: \( a + b = b + a \)
- Multiplication: \( a \times b = b \times a \)
Associative Property
- An operation is associative if the way numbers are grouped does not change the result.
- For example:
- Addition: \( (a + b) + c = a + (b + c) \)
- Multiplication: \( (a \times b) \times c = a \times (b \times c) \)
Analyzing Subtraction
- Subtraction is not commutative:
- For example, \( 5 - 3 \neq 3 - 5 \)
- The results are different (2 and -2, respectively).
- Subtraction is also not associative:
- For example, \( (5 - 3) - 1 \neq 5 - (3 - 1) \)
- The first calculation gives 1, while the second gives 3.
Why Subtraction is Unique
- Since both properties fail for subtraction, it is deemed neither commutative nor associative.
- This distinguishes subtraction from addition and multiplication, which exhibit both properties.
Conclusion
In summary, subtraction is the operation that is neither commutative nor associative, making option 'B' the correct answer. Understanding these properties enhances your mathematical skills and problem-solving abilities!
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Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer?
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Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer? for Class 4 2024 is part of Class 4 preparation. The Question and answers have been prepared according to the Class 4 exam syllabus. Information about Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 4 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer?.
Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer? for Class 4 2024 is part of Class 4 preparation. The Question and answers have been prepared according to the Class 4 exam syllabus. Information about Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 4 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which operation(s) is/are neither commutative nor associative?a)Additionb)Subtractionc)Multiplicationd)DivisionCorrect answer is option 'B'. Can you explain this answer?.
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