Equation Sign Interchange Solution

The problem asks us to find which pair of mathematical signs, when swapped in the given equation, will make the equation correct. The given equation is: \(286 \div 13 \times 2 + 50 - 6 = 0\).

First, let's evaluate the original equation using the standard order of operations (BODMAS/PEMDAS - Brackets, Orders, Division/Multiplication, Addition/Subtraction):

• Division: \(286 \div 13 = 22\)
• Multiplication: \(22 \times 2 = 44\)
• Addition: \(44 + 50 = 94\)
• Subtraction: \(94 - 6 = 88\)

So, the original equation evaluates to \(88 = 0\), which is incorrect. Now, we will test each option by interchanging the specified signs.

Testing Option 1: Interchanging + and ×

If we interchange the '+' and '×' signs, the new equation becomes: \(286 \div 13 + 2 \times 50 - 6 = 0\).

Let's evaluate this new equation:

• Division: \(286 \div 13 = 22\)
• Multiplication: \(2 \times 50 = 100\)
• Addition: \(22 + 100 = 122\)
• Subtraction: \(122 - 6 = 116\)

The result is \(116 = 0\), which is incorrect. So, interchanging '+' and '×' does not make the equation correct.

Testing Option 2: Interchanging + and -

If we interchange the '+' and '-' signs, the new equation becomes: \(286 \div 13 \times 2 - 50 + 6 = 0\).

Let's evaluate this new equation:

• Division: \(286 \div 13 = 22\)
• Multiplication: \(22 \times 2 = 44\)
• Subtraction: \(44 - 50 = -6\)
• Addition: \(-6 + 6 = 0\)

The result is \(0 = 0\), which is correct. So, interchanging '+' and '-' makes the equation correct.

Testing Option 3: Interchanging ÷ and ×

If we interchange the '÷' and '×' signs, the new equation becomes: \(286 \times 13 \div 2 + 50 - 6 = 0\).

Let's evaluate this new equation:

• Multiplication: \(286 \times 13 = 3718\)
• Division: \(3718 \div 2 = 1859\)
• Addition: \(1859 + 50 = 1909\)
• Subtraction: \(1909 - 6 = 1903\)

The result is \(1903 = 0\), which is incorrect. So, interchanging '÷' and '×' does not make the equation correct.

Note: Option 4 is identical to Option 3, so testing it would yield the same incorrect result.

Conclusion: Finding the Correct Interchange

Based on our testing, interchanging the '+' and '-' signs is the only option that makes the given equation \(286 \div 13 \times 2 + 50 - 6 = 0\) correct.

Revision Table: Summary of Sign Changes

Additional Information: The BODMAS/PEMDAS Rule for Equations

When solving mathematical equations or expressions, we follow a specific order to ensure consistency. This order is commonly remembered using mnemonics like BODMAS or PEMDAS.

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

In the problems above, we strictly followed this order, performing division and multiplication before addition and subtraction, after making the specified sign interchanges.