Question

Which shows the best use of the associative and commutative properties to make simplifying −10+7+5 easier?

A. [−(10)+(−7)]+[5+(− 1/4)]
B. [5+(−3)+(−10)]+(−7)
C. Both a and b
D. None of the above

Answer 1

The best use of the associative and commutative properties to simplify the expression -10+7+5 is shown in option B, which groups the positive and negative numbers to allow for easier simplification. The correct sequence using these properties results in (5) + (-10 + 7), which simplifies to 2.

Step-by-step explanation:

The question is asking which option best demonstrates the use of the associative and commutative properties to simplify the expression −10+7+5. The associative property allows us to group numbers in any way when adding, and the commutative property allows us to change the order of numbers when adding. The end result will remain the same due to these properties. Option B, [5+(−3)+(−10)]+(−7), is the correct one because it demonstrates the application of both properties. By rearranging the numbers to group the positive number 5 with the negative numbers, we simplify the process of adding a positive number to a set of negative numbers. Here's how to simplify it step-by-step:

1. First, by commutative property, change the order to group the like terms: (5) + (−10 + 7).
2. Next, use the associative property to group −10 and 7: 5 + (−10 + 7).
3. Add the numbers within the parentheses: 5 + (−3).
4. Finally, combine the remaining terms: 2.

Option A introduces an irrelevant fraction and does not make the simplification easier. Consequently, answer B is correct and answer A and D are incorrect. Answer C is also incorrect because it states that both options are correct, which is not the case.