Select the correct combination of mathematical signs to sequentially place from left to right in the blanks below to balance the given equation. 8 _ 27 _ 9 _ 6 _ 5 = 0

Correct — C.

Rule: substitute each option into the blanks, then evaluate under BODMAS — division before addition and subtraction, whatever the printed order looks like.

Putting in +, ÷, −, − gives 8 + 27 ÷ 9 − 6 − 5.
Division first: 27 ÷ 9 = 3
8 + 3 − 6 − 5 = 11 − 11 = 0

The equation balances, so the combination is option (c).

Why the others are wrong

• (a)
  −, ÷, +, + — −, ÷, +, + gives 8 − 27 ÷ 9 + 6 + 5 = 8 − 3 + 6 + 5 = 16. The two plus signs at the tail push the total up, away from zero.
• (b)
  ÷, +, −, + — ÷, +, −, + gives 8 ÷ 27 + 9 − 6 + 5. The opening division is not exact, and the total comes to about 8.30.
• (d)
  −, +, ÷, + — −, +, ÷, + gives 8 − 27 + 9 ÷ 6 + 5 = 8 − 27 + 1.5 + 5 = −12.5. Dividing 9 by 6 instead of 27 by 9 is the misstep.

Sign-substitution items are arithmetic rather than reasoning: four options are offered and testing them is the method. What decides the question is BODMAS, applied to the substituted line and not left to right.

A quick filter saves time. Two of the options divide 27 by 9, which is exact; the other two divide 8 by 27 and 9 by 6, which are not, and no later whole-number step clears a fraction here.

So start with an option whose division comes out exact, evaluate it in full, and stop the moment the line balances.

Key facts

• Under BODMAS, 8 + 27 ÷ 9 − 6 − 5 = 8 + 3 − 6 − 5 = 0.
• Signs are placed into the blanks from left to right, but evaluation still follows BODMAS.
• Of the divisions the four options create, only 27 ÷ 9 comes out whole.

Common traps

• Evaluating left to right and computing (8 + 27) ÷ 9 instead of 8 + (27 ÷ 9)
• Committing to an option before checking that its division comes out whole

No directly related past PYQ was found.