Which two signs should be interchanged to make the given equation correct? 306 ÷ 17 + 4 - 50 × 8 = 30
Equation Sign Swap Puzzle
The task is to determine which pair of mathematical signs in the given equation, 306 ÷ 17 + 4 - 50 × 8 = 30, should be interchanged to make the equation true. We will solve this by systematically testing each option and applying the standard order of operations (BODMAS/PEMDAS).
The order of operations ensures calculations are done correctly: Brackets first, then Orders (like powers), followed by Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right).
Sign Interchange Accuracy Check
Let's examine each option to see which sign swap makes the equation correct.
Swap 1: ÷ and × Check
Interchanging the division (÷) and multiplication (×) signs.
The equation becomes: 306 × 17 + 4 - 50 ÷ 8 = 30
Result Analysis for Swap 1
- First, perform the multiplication:
306 \times 17 = 5202 - Next, perform the division:
50 \div 8 = 6.25 - The equation now is:
5202 + 4 - 6.25 - Perform addition:
5202 + 4 = 5206 - Perform subtraction:
5206 - 6.25 = 5199.75
The result 5199.75 is not equal to 30. This swap is incorrect.
Swap 2: + and × Check
Interchanging the addition (+) and multiplication (×) signs.
The equation becomes: 306 ÷ 17 × 4 - 50 + 8 = 30
Result Analysis for Swap 2
- Perform division:
306 \div 17 = 18 - Perform multiplication:
18 \times 4 = 72 - The equation now is:
72 - 50 + 8 - Perform subtraction (left to right):
72 - 50 = 22 - Perform addition:
22 + 8 = 30
The result is 30. This matches the target value, so this swap is correct.
Swap 3: × and - Check
Interchanging the multiplication (×) and subtraction (-) signs.
The equation becomes: 306 ÷ 17 + 4 × 50 - 8 = 30
Result Analysis for Swap 3
- Perform division:
306 \div 17 = 18 - Perform multiplication:
4 \times 50 = 200 - The equation now is:
18 + 200 - 8 - Perform addition:
18 + 200 = 218 - Perform subtraction:
218 - 8 = 210
The result 210 is not equal to 30. This swap is incorrect.
Swap 4: + and - Check
Interchanging the addition (+) and subtraction (-) signs.
The equation becomes: 306 ÷ 17 - 4 + 50 × 8 = 30
Result Analysis for Swap 4
- Perform division:
306 \div 17 = 18 - Perform multiplication:
50 \times 8 = 400 - The equation now is:
18 - 4 + 400 - Perform subtraction (left to right):
18 - 4 = 14 - Perform addition:
14 + 400 = 414
The result 414 is not equal to 30. This swap is incorrect.
Conclusion on Sign Interchange
After evaluating all the options, we confirmed that swapping the addition sign (+) with the multiplication sign (×) results in the correct equation: 306 ÷ 17 × 4 - 50 + 8 = 30.
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