Which two signs should be interchanged to make the following equation correct? 18 − 23 × 455 ÷ 7 + 28 = 377

Correct — D.

Rule: interchange the minus and the times, rewrite the whole line, then read it under BODMAS.

18 − 23 × 455 ÷ 7 + 28 becomes 18 × 23 − 455 ÷ 7 + 28.

455 ÷ 7 = 65
18 × 23 = 414
414 − 65 = 349
349 + 28 = 377

The line balances, so option (d) is the pair that works.

Why the others are wrong

• (a)
  ÷ and − — Swapping the divide and the minus gives 18 ÷ 23 × 455 − 7 + 28. That opens with 18 ÷ 23, which is not a whole number, and the line lands near 377.09 rather than on 377.
• (b)
  − and + — Swapping the minus and the plus gives 18 + 23 × 455 ÷ 7 − 28. Times and divide run first, so 23 × 65 = 1495 and the line reaches 1485, not 377.
• (c)
  + and × — Swapping the plus and the times gives 18 − 23 + 455 ÷ 7 × 28. Here 65 × 28 = 1820 before any addition happens, and the line ends at 1815.

Sign-interchange items are settled by substitution, not by inspection. Swap the named pair, rewrite the line in full, and only then evaluate strictly by BODMAS.

The arithmetic tells you where to start. 455 ÷ 7 = 65 is exact, and the target 377 sits close to 414 = 18 × 23, so the pair that makes 18 and 23 multiply is the one to test first.

Four options mean at most four evaluations, and each is short once the division is done.

Key facts

• Substituting a swap means rewriting the whole equation, not re-reading it in place.
• BODMAS is unaffected by the swap: times and divide still run before plus and minus.
• 455 ÷ 7 = 65 and 18 × 23 = 414 are the two anchors that make this line quick.

Common traps

• Evaluating left to right instead of doing times and divide first
• Testing the options in printed order rather than starting with the one the arithmetic suggests
• Accepting an option because the running total is near 377 without finishing the working

No directly related past PYQ was found.