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________ is not associative for rational numbers.
- a)Subtraction or Division
- b)Addition or Multiplication
- c)Addition or Division
- d)Multiplication or Division
Correct answer is option 'A'. Can you explain this answer?
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________ is not associative for rational numbers.a)Subtraction or Divi...
This is how associative property works. It states that you can add or multiply numbers regardless of how they are grouped. Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.
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________ is not associative for rational numbers.a)Subtraction or Divi...
Introduction:
Associativity is a property of operations where the grouping of elements does not affect the result. In other words, for an operation to be associative, regardless of how we group the elements, the result should remain the same. In this context, we will explore whether subtraction or division is associative for rational numbers.
Explanation:
To determine whether an operation is associative, we need to check if the following condition holds for all rational numbers a, b, and c:
(a - b) - c = a - (b - c)
Subtraction:
Let's consider the operation of subtraction. If we take three rational numbers a, b, and c, and evaluate the left-hand side of the equation, we have:
(a - b) - c
Now, let's evaluate the right-hand side of the equation:
a - (b - c)
Counterexample:
To show that subtraction is not associative for rational numbers, we need to find an example where the left-hand side of the equation is not equal to the right-hand side.
Let's take a = 2/3, b = 1/4, and c = 1/6:
(a - b) - c = (2/3 - 1/4) - 1/6 = (8/12 - 3/12) - 2/12 = 5/12 - 2/12 = 3/12 = 1/4
a - (b - c) = 2/3 - (1/4 - 1/6) = 2/3 - (3/12 - 2/12) = 2/3 - 1/12 = 8/12 - 1/12 = 7/12
As we can see, (a - b) - c is not equal to a - (b - c). Therefore, subtraction is not associative for rational numbers.
Conclusion:
In conclusion, subtraction is not associative for rational numbers. This means that regardless of how we group the elements, the result of subtraction can change. Therefore, option A is the correct answer.
Associativity is a property of operations where the grouping of elements does not affect the result. In other words, for an operation to be associative, regardless of how we group the elements, the result should remain the same. In this context, we will explore whether subtraction or division is associative for rational numbers.
Explanation:
To determine whether an operation is associative, we need to check if the following condition holds for all rational numbers a, b, and c:
(a - b) - c = a - (b - c)
Subtraction:
Let's consider the operation of subtraction. If we take three rational numbers a, b, and c, and evaluate the left-hand side of the equation, we have:
(a - b) - c
Now, let's evaluate the right-hand side of the equation:
a - (b - c)
Counterexample:
To show that subtraction is not associative for rational numbers, we need to find an example where the left-hand side of the equation is not equal to the right-hand side.
Let's take a = 2/3, b = 1/4, and c = 1/6:
(a - b) - c = (2/3 - 1/4) - 1/6 = (8/12 - 3/12) - 2/12 = 5/12 - 2/12 = 3/12 = 1/4
a - (b - c) = 2/3 - (1/4 - 1/6) = 2/3 - (3/12 - 2/12) = 2/3 - 1/12 = 8/12 - 1/12 = 7/12
As we can see, (a - b) - c is not equal to a - (b - c). Therefore, subtraction is not associative for rational numbers.
Conclusion:
In conclusion, subtraction is not associative for rational numbers. This means that regardless of how we group the elements, the result of subtraction can change. Therefore, option A is the correct answer.
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