Understanding the Mathematical Signs Puzzle

The question asks us to find the correct sequence of mathematical signs that, when placed sequentially in the equation 11 * 13 * 238 * 17 * 34 = 123 in place of the asterisks (*), makes the equation true or balanced.

We are given four options, each containing a sequence of four signs. We need to test each sequence by substituting the signs into the equation and performing the calculations according to the standard order of operations (BODMAS/PEMDAS).

Testing the Options: Finding the Correct Sequence

Let's test the options provided. The correct combination of signs will result in the left side of the equation evaluating to 123.

One of the options provides the sequence: multiplication (×), addition (+), division (÷), and subtraction (-).

Let's substitute these signs into the equation:

11 × 13 + 238 ÷ 17 - 34 = 123

Applying the Order of Operations (BODMAS/PEMDAS)

To evaluate this expression, we must follow the order of operations:

• B/P: Brackets/Parentheses (None in this case)
• O/E: Orders/Exponents (None in this case)
• DM: Division and Multiplication (from left to right)
• AS: Addition and Subtraction (from left to right)

Let's perform the calculations step-by-step:

1. First, perform the multiplication: $$11 \times 13 = 143$$
2. Next, perform the division: $$238 \div 17$$ To calculate this, we can perform long division or recognize that $17 \times 10 = 170$ and $238 - 170 = 68$. Since $17 \times 4 = 68$, $17 \times (10+4) = 17 \times 14 = 170 + 68 = 238$. So, $$238 \div 17 = 14$$
3. Substitute these results back into the equation: $$143 + 14 - 34$$
4. Now, perform the addition: $$143 + 14 = 157$$
5. Finally, perform the subtraction: $$157 - 34 = 123$$

The result of the calculation is 123, which matches the right side of the original equation.

Conclusion: Balancing the Equation

The sequence of mathematical signs ×, +, ÷, - successfully balances the given equation 11 * 13 * 238 * 17 * 34 = 123.

Thus, the correct combination is multiplication, addition, division, and subtraction in that specific order.

Revision Table: Key Mathematical Operations

Additional Information: Order of Operations

The order of operations is a crucial concept in mathematics to ensure consistent results when evaluating expressions involving multiple operations. BODMAS or PEMDAS provides the widely accepted sequence:

• BODMAS: Brackets, Orders (powers, square roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).
• PEMDAS: Parentheses, Exponents (powers, square roots), Multiplication and Division (left to right), Addition and Subtraction (left to right).

Following this order is essential for solving mathematical puzzles and equations accurately.