Which of the following interchanges of signs would make the given equation correct?
40 + 45 × 5 – 12 ÷ 4 = 1

The correct option is ÷ and ×.

Let us verify this interchange step-by-step to see if it makes the given equation correct.

The original equation is:
$40\; +\; 45\; \times \; 5\; -\; 12\; ÷\; 4\; =\; 1$

By interchanging the signs ÷ and ×, the new equation becomes:
$40\; +\; 45\; ÷\; 5\; -\; 12\; \times \; 4\; =\; 1$

Now, we simplify the left-hand side (LHS) of the equation using the BODMAS rule (Bracket, Of, Division, Multiplication, Addition, Subtraction):

Step 1: Perform the Division
Divide 45 by 5:
$45\; ÷\; 5\; =\; 9$
Substituting this back into the equation, we get:
$40\; +\; 9\; -\; 12\; \times \; 4$

Step 2: Perform the Multiplication
Multiply 12 by 4:
$12\; \times \; 4\; =\; 48$
Substituting this back, we get:
$40\; +\; 9\; -\; 48$

Step 3: Perform the Addition
Add 40 and 9:
$40\; +\; 9\; =\; 49$
Substituting this back, we get:
$49\; -\; 48$

Step 4: Perform the Subtraction
Subtract 48 from 49:
$49\; -\; 48\; =\; 1$

Since the LHS equals the RHS (1 = 1), the equation is correct. Therefore, the correct sign interchange is indeed ÷ and ×.