In the following equation, two of the arithmetic signs are interchanged so that the equation becomes correct: 6 + 8 ÷ 4 – 4 = 8. Which two signs must be interchanged?

Introduction / Context:
This question gives an equation that is not true as it stands. You are allowed to interchange exactly two operation signs in order to turn the equation into a correct statement. This type of problem checks your understanding of how each sign affects the value of an expression and how the order of operations influences the final result.

Given Data / Assumptions:

• The original equation is 6 + 8 ÷ 4 – 4 = 8.
• All numbers remain fixed; only two signs can swap positions.
• We must apply standard precedence rules during evaluation.
• The main signs that can be interchanged are "+", "÷" and "–".

Concept / Approach:
We first evaluate the original left side to see how far it is from 8. Then, for each candidate pair of signs, we swap their positions in the expression and re-evaluate. The correct answer is the pair whose interchange produces a left hand side equal to 8. It is important to respect the precedence of division over addition and subtraction in each case.

Step-by-Step Solution:
Step 1: Evaluate the original left side: 6 + 8 ÷ 4 – 4. Compute 8 ÷ 4 = 2, so the expression is 6 + 2 – 4 = 8 – 4 = 4, which is not 8. Step 2: Consider interchanging "+" and "–". The expression becomes 6 – 8 ÷ 4 + 4. Step 3: Evaluate 8 ÷ 4 = 2. Step 4: Now the left side is 6 – 2 + 4. Step 5: Perform subtraction and addition from left to right: 6 – 2 = 4, then 4 + 4 = 8. Step 6: Now the left side equals the right side, 8, so this interchange works.

Verification / Alternative check:
We can briefly test the other possible swaps. Swapping "÷" and "+" or "÷" and "–" yields expressions whose left sides do not evaluate to 8. Swapping "divide and equal to" or introducing multiplication instead of plus also fails to balance the equation. Therefore, only the swap of plus and minus gives a valid equality.

Why Other Options Are Wrong:
"Divide and equal to" would move the equality sign into the arithmetic part, which does not make sense in standard algebra. "Divide and plus" or "divide and minus" change the structure so that the left side becomes either too large or too small compared with 8. "Multiply and plus" introduces multiplication where it was not intended and again fails to produce 8.

Common Pitfalls:
A common mistake is to ignore the order of operations and simply compute the expression strictly left to right after the swap. Another is to think that numbers can also be rearranged, which the question does not allow. Only the positions of two operation signs may be interchanged, and all other parts must be left untouched.

Final Answer:
So, by interchanging the plus and minus signs, the equation becomes correct. The required pair is plus and minus.