Which two signs should be interchanged to make the given equation correct? 171 ÷ 3 - 16 + 72 × 412 = 572

Question

Which two signs should be interchanged to make the given equation correct?

171 ÷ 3 - 16 + 72 × 412 = 572

1. A. × and - (Correct answer)
2. B. ÷ and -
3. C. ÷ and +
4. D. - and +

Correct Answer

Option A — × and -

Detailed Solution & Explanation

The correct answer is × and −.

Key Points

• The equation as printed is 171 ÷ 3 − 16 + 72 × 412 = 572, which is false.
• Interchanging the × and − signs gives 171 ÷ 3 × 16 + 72 − 412.
• Applying BODMAS, division and multiplication are resolved left to right first:
  • 171 ÷ 3 = 57
  • 57 × 16 = 912
• The expression becomes 912 + 72 − 412 = 572, which matches the right-hand side.

Note

• Always resolve division and multiplication left to right before addition and subtraction; working strictly left to right across all operators gives a different, incorrect result.

Additional Information

• Every such question is governed by BODMAS — Brackets, Orders (powers and roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).
• The practical method is to test each option rather than reason forwards: there are only four possible swaps, and evaluating each is faster than deducing which one must work.
• Verifying the chosen swap: 171 ÷ 3 = 57, then 57 × 16 = 912, then 912 + 72 = 984, and 984 − 412 = 572.