Fill the four “*” with a valid sequence of operators so that the equation balances. Target form: 5 * 6 * 5 * 8 * 14 (insert exactly one operator between each pair to obtain a true equality).

Difficulty: Medium

Correct Answer: x ÷ + =

Explanation:


Introduction / Context:
We must choose an ordered sequence of operators to make a numeric statement true. This requires both precedence awareness and testing of plausible combinations.


Given Data / Assumptions:

  • Template: 5 * 6 * 5 * 8 * 14.
  • Insert the four operators (in the exact order listed in an option) to replace the four asterisks.
  • Standard precedence: × and ÷ before + and −.


Concept / Approach:
Substitute each option in order and evaluate the left-hand side (LHS). The correct option should yield an identity when compared to the right-most number.


Step-by-Step Solution:
Try Option B: “× ÷ + =”.Substitute: 5 × 6 ÷ 5 + 8 = 14.Compute precedence: 5 × 6 = 30; 30 ÷ 5 = 6; then 6 + 8 = 14.The equality holds, so Option B is correct.


Verification / Alternative check:
Option A: 5 + 6 − 5 × 8 = 14 ⇒ 5 + 6 − 40 = −29 ≠ 14.Option C: 5 ÷ 6 × 5 = 8 − 14 ⇒ LHS ≈ 4.166…, RHS = −6; false.Option D: 5 + 6 × 5 − 8 ÷ 14 ⇒ 5 + 30 − 8 ÷ 14 ≈ 34.43; not a clean equality to 14.


Why Other Options Are Wrong:
They mis-balance the expression through a large product or an ill-placed subtraction/division that prevents the LHS from reaching 14.


Common Pitfalls:
Executing left-to-right without applying ×/÷ before +/−; or mistakenly trying to “compute” the equality symbol as an operator.


Final Answer:
x ÷ + = gives the true equation 5 × 6 ÷ 5 + 8 = 14.

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