Which of the following is true of the commutative property under subtraction?
A) [tex]$10-9=10+9$
B) [tex]$10-9 \neq 9-10$
C) [tex]$10+9=9+10$
D) [tex]$10-9=10-9$
Answer (2)
Option B is the correct answer as it states that 10 − 9 = 9 − 10 , demonstrating that subtraction is not commutative. The other options either describe addition, are false, or are trivially true without relevance to the question. Thus, subtraction does not maintain the property of changing order without affecting the result.
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The commutative property states that the order of operands does not affect the result.
Evaluate each option to determine if it correctly describes the commutative property under subtraction.
Option A is false because 10 − 9 e q 10 + 9 .
Option B is true because 10 − 9 e q 9 − 10 , showing subtraction is not commutative. The final answer is B .
Explanation
Understanding Commutative Property The question asks us to identify the statement that correctly describes the commutative property under subtraction. The commutative property means that changing the order of the operands does not change the result. For example, addition is commutative because a + b = b + a . We need to determine if a similar property holds for subtraction.
Evaluating Each Option Let's examine each option:
Option A: 10 − 9 = 10 + 9 . We know that 10 − 9 = 1 and 10 + 9 = 19 . Since 1 e q 19 , this statement is false.
Option B: 10 − 9 e q 9 − 10 . We know that 10 − 9 = 1 and 9 − 10 = − 1 . Since 1 e q − 1 , this statement is true. Subtraction is not commutative because changing the order of the numbers changes the result.
Option C: 10 + 9 = 9 + 10 . We know that 10 + 9 = 19 and 9 + 10 = 19 . Since 19 = 19 , this statement is true, but it describes the commutative property of addition, not subtraction.
Option D: 10 − 9 = 10 − 9 . This statement is trivially true since 1 = 1 , but it doesn't tell us anything about the commutative property.
Conclusion Therefore, the correct answer is Option B, which states that 10 − 9 e q 9 − 10 . This accurately reflects that subtraction is not commutative.
Examples
Understanding the commutative property is crucial in various real-life scenarios, such as calculating distances or balancing accounts. For instance, if you walk 5 steps forward and then 2 steps back, the net displacement is different from walking 2 steps forward and then 5 steps back. Similarly, in accounting, subtracting expenses from revenue yields a different result than subtracting revenue from expenses. Recognizing whether an operation is commutative helps in accurately modeling and solving problems in these contexts.
