Finding the Correct Mathematical Signs to Balance an Equation

The question asks us to find the correct sequence of mathematical signs (operators) that, when substituted into the place of the asterisks (*) in the expression 25 * 2 * 220 * 11 * 43, will make the equation balance. This means the value of the expression on the left side must equal the value on the right side (43 in this case).

We are given four options, each providing a sequence of four signs. Assuming the equation structure is number operator number operator number operator number = number, we will test each option by replacing the asterisks sequentially from left to right and checking if the resulting equation holds true. Remember to follow the order of operations (like BODMAS/PEMDAS) while calculating.

Testing Option 1: +, -, ×, =

Substituting these signs gives the equation:

\(25 + 2 - 220 \times 11 = 43\)

Let's evaluate the left side following the order of operations (multiplication first, then addition and subtraction from left to right):

• Multiplication: \(220 \times 11 = 2420\)
• Now the equation becomes: \(25 + 2 - 2420\)
• Addition: \(25 + 2 = 27\)
• Now the equation becomes: \(27 - 2420\)
• Subtraction: \(27 - 2420 = -2393\)

So, the equation becomes \(-2393 = 43\). This is incorrect.

Testing Option 2: +, -, ÷, =

Substituting these signs gives the equation:

\(25 + 2 - 220 \div 11 = 43\)

Let's evaluate the left side following the order of operations (division first, then addition and subtraction from left to right):

• Division: \(220 \div 11 = 20\)
• Now the equation becomes: \(25 + 2 - 20\)
• Addition: \(25 + 2 = 27\)
• Now the equation becomes: \(27 - 20\)
• Subtraction: \(27 - 20 = 7\)

So, the equation becomes \(7 = 43\). This is incorrect.

Testing Option 3: +, +, ÷, =

Substituting these signs gives the equation:

\(25 + 2 + 220 \div 11 = 43\)

Let's evaluate the left side following the order of operations (division first, then addition from left to right):

• Division: \(220 \div 11 = 20\)
• Now the equation becomes: \(25 + 2 + 20\)
• Addition: \(25 + 2 = 27\)
• Now the equation becomes: \(27 + 20\)
• Addition: \(27 + 20 = 47\)

So, the equation becomes \(47 = 43\). This is incorrect.

Testing Option 4: -, +, ÷, =

Substituting these signs gives the equation:

\(25 - 2 + 220 \div 11 = 43\)

Let's evaluate the left side following the order of operations (division first, then subtraction and addition from left to right):

• Division: \(220 \div 11 = 20\)
• Now the equation becomes: \(25 - 2 + 20\)
• Subtraction: \(25 - 2 = 23\)
• Now the equation becomes: \(23 + 20\)
• Addition: \(23 + 20 = 43\)

So, the equation becomes \(43 = 43\). This is correct. The equation is balanced with this sequence of signs.

Conclusion on Balancing the Equation

The combination of mathematical signs -, +, ÷, = correctly balances the given equation 25 * 2 * 220 * 11 * 43.

Revision Table: Order of Operations (BODMAS/PEMDAS)

Additional Information: Balancing Equations

Balancing equations involves ensuring that the expression on one side of the equals sign represents the same value as the expression on the other side. In problems like this, where we need to insert arithmetic operators, it's crucial to apply the correct order of operations to evaluate the expression accurately. If the question involved variables, balancing would involve isolating the variable while maintaining equality on both sides of the equation.

The order of operations is a fundamental concept in mathematics that ensures consistent results when evaluating expressions with multiple operations. Division and Multiplication have equal priority and are performed from left to right. Similarly, Addition and Subtraction have equal priority and are performed from left to right after Division and Multiplication.