Which of the following is an arrangement of the four basic arithmetic operation signs so that when the signs are placed in the equation 3 _ (5 _ 4) _ (4 _ 2) = 5 in order from left to right, the equation shown is true?

Rationale

+,-,x,+ is the correct arrangement of the four basic arithmetic operation signs.

When the signs are placed in the equation 3 + (5 - 4) × (4 + 2) = 5, the operations follow the order of operations correctly and yield a true statement.

A (+,-,x,+) CORRECT

This arrangement leads to the equation: 3 + (5 - 4) × (4 + 2). Calculating this: 5 - 4 = 1, and 4 + 2 = 6, so it becomes 3 + 1 × 6. Following the order of operations, we first calculate 1 × 6 = 6, then add 3 + 6 = 9, which does not equal 5. Therefore, this choice is incorrect.

B (x,+,-,+) YOUR ANSWER

This arrangement forms the equation: 3 × (5 + 4) - (4 + 2). Calculating this gives: 5 + 4 = 9, so it becomes 3 × 9 - 6. This evaluates to 27 - 6 = 21, which does not equal 5. Hence, this option is also incorrect.

C (-,x,+,+) YOUR ANSWER

This leads to the equation: 3 - (5 × 4) + (4 + 2). Calculating gives: 5 × 4 = 20, so it becomes 3 - 20 + 6. This evaluates to 3 - 20 = -17, and -17 + 6 = -11, which is not equal to 5. Thus, this choice is also incorrect.

D (+, -, +, x) YOUR ANSWER

This arrangement results in: 3 + (5 - 4) + (4 × 2). Calculating this gives: 5 - 4 = 1, so it becomes 3 + 1 + 8. This evaluates to 3 + 1 = 4, and 4 + 8 = 12, which does not equal 5. Therefore, this option is incorrect as well.

Conclusion

All choices provided lead to incorrect evaluations of the equation, demonstrating the importance of proper operation placement in arithmetic expressions. The only arrangement that satisfied the equation was erroneously indicated as correct, but through careful evaluation, we established that none of the given options yielded the desired result.

Which of the following is an arrangement of the four basic arithmetic operation signs so that when the signs are placed in the equation 3 _ (5 _ 4) _ (4 _ 2) = 5 in order from left to right, the equation shown is true?

+,-,x,+ is the correct arrangement of the four basic arithmetic operation signs.

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