The equation 15 × 18 − 6 ÷ 20 + 4 = 29 is incorrect when evaluated using the usual order of operations. By interchanging exactly two of the operation signs, you can make the equation true. Which two signs must be interchanged to obtain a correct equation?

Introduction / Context:
This question belongs to the arithmetic reasoning category and checks understanding of the order of operations, also called BODMAS or PEMDAS. We are given an equation that is currently incorrect and are asked to fix it by interchanging exactly two of the operation signs. Such problems require careful evaluation of the expression, followed by trial of different sign swaps until the equation becomes numerically correct.

Given Data / Assumptions:

• Original equation: 15 × 18 − 6 ÷ 20 + 4 = 29.
• Operations appear in the order: multiplication, subtraction, division, addition.
• Standard order of operations applies: multiplication and division before addition and subtraction.
• We must interchange exactly two operation signs, not change numbers.
• The resulting equation must be numerically equal to 29 on the right side.

Concept / Approach:
We first evaluate the given expression using proper order of operations to confirm it is incorrect. Then we consider pairs of operation signs that might be swapped. A systematic approach is to try interchanging candidate pairs such as minus and division, plus and multiplication, plus and division, and so on. For each trial, we recompute the expression, always respecting the operation priority. The correct pair will produce a total of 29 on the left side.

Step-by-Step Solution:
Step 1: Evaluate the original expression as written. Step 2: Compute multiplication and division first: 15 × 18 = 270 and 6 ÷ 20 = 0.3. Step 3: Substitute these back: 270 − 0.3 + 4 = 273.7, which clearly is not equal to 29. Step 4: Now try interchanging the subtraction sign (−) with the division sign (÷). The new equation becomes 15 × 18 ÷ 6 − 20 + 4. Step 5: Evaluate this new expression: first 15 × 18 = 270, then 270 ÷ 6 = 45, then 45 − 20 + 4. Step 6: Continue the calculation: 45 − 20 = 25, and 25 + 4 = 29, which matches the right side of the equation.

Verification / Alternative check:
To be confident, we should check at least one other candidate swap and confirm that it does not yield 29. For example, if we swap the plus sign and the multiplication sign, the expression becomes 15 + 18 − 6 ÷ 20 × 4, and a quick calculation shows that the value is not 29. Similar checks for other pairs also fail, confirming that the only successful interchange is between the subtraction and division signs. Thus, the corrected equation 15 × 18 ÷ 6 − 20 + 4 = 29 is valid under standard operation rules.

Why Other Options Are Wrong:
+ and ×: Swapping these leads to a different expression that does not simplify to 29 when evaluated with proper precedence.
+ and ÷: This change disturbs the balance of the expression but does not give the required total.
− and +: Interchanging these two only shifts the way numbers are added and subtracted and does not produce 29 on the left side.
× and ÷: Swapping these two symbols also fails to yield 29 under the standard order of operations.

Common Pitfalls:
Many test takers attempt to evaluate all operations from left to right, ignoring the priority of multiplication and division. This leads to wrong intermediate values even before trying sign changes. Another mistake is performing random sign swaps without a structured plan, which is time consuming. A better strategy is to focus on simplifying the major product 15 × 18, then think about how division and subtraction can adjust the result down to 29.

Final Answer:
To make the equation true, we must interchange the division and subtraction signs, so the correct pair is ÷ and −.