Balancing Mathematical Equations with Operators

The problem asks us to find the correct combination of mathematical signs (+, −, ×, ÷, =) that will balance the given equation structure: 12__4__2__2__5__3.

To solve this, we need to test each option provided. Each option offers a sequence of five signs to fill the five blank spaces. The correct combination is the one that makes the left side of the equation equal to the right side when evaluated according to the order of operations (BODMAS/PEMDAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction).

Testing Option 2: ÷, ×, +, =, +

Let's substitute the signs from Option 2 into the equation structure:

12 ÷ 4 × 2 + 2 = 5 + 3

Evaluating the Left Side of the Equation

The left side is: 12 ÷ 4 × 2 + 2

Following the order of operations:

1. Perform division and multiplication from left to right.
   • First, perform the division: 12 ÷ 4
   • $\text{12} \div \text{4} = \text{3}$
2. Substitute the result back into the expression: 3 × 2 + 2
3. Next, perform the multiplication: 3 × 2
4. $\text{3} \times \text{2} = \text{6}$
5. Substitute the result back into the expression: 6 + 2
6. Finally, perform the addition: 6 + 2
7. $\text{6} + \text{2} = \text{8}$

So, the left side of the equation evaluates to 8.

Evaluating the Right Side of the Equation

The right side is: 5 + 3

Following the order of operations:

1. Perform the addition: 5 + 3
2. $\text{5} + \text{3} = \text{8}$

So, the right side of the equation evaluates to 8.

Comparing Both Sides

Left Side = 8

Right Side = 8

Since 8 = 8, the equation is balanced with the signs from Option 2.

12 ÷ 4 × 2 + 2 = 5 + 3 is a true statement.

Conclusion

The combination of mathematical signs ÷, ×, +, =, + successfully balances the given equation structure. Therefore, this is the correct combination.

You could test the other options similarly, substituting the signs and evaluating both sides to see if they balance. If the left side does not equal the right side for an option, that option is incorrect.

Revision Table: Balancing Equations Practice

Additional Information: Mathematical Operator Rules

When solving equations involving different mathematical operators, it is crucial to follow a specific order to ensure you get the correct result. This order is commonly known as the order of operations.

• BODMAS stands for:
  • Brackets
  • Orders (powers, square roots, etc.)
  • Division and Multiplication (from left to right)
  • Addition and Subtraction (from left to right)
• PEMDAS is another acronym for the same order:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Following this order consistently is key to solving complex expressions and balancing equations correctly.