Solving Mathematical Equation by Replacing Signs

The question asks us to find the correct sequence of mathematical signs that, when replaced sequentially in the given expression, makes the equation correct. The expression is: 88 * 120 * 42 * 240 * 48 * 2. We need to test the combinations of signs provided in the options.

Understanding the Problem Structure and Options

We are given 5 asterisks (*) and 5 signs in each option. The options provide combinations like =, –, +, ÷, ×. This implies the structure of the equation will be number operator number operator number operator number operator number operator number, or perhaps include the equals sign somewhere to form an equation.

Let's examine the structure based on the signs provided in the correct option: =, –, +, ÷, ×. If we place these signs sequentially, the equation becomes:

\(88 = 120 - 42 + 240 \div 48 \times 2\)

To verify if this equation is correct, we need to evaluate the right-hand side (RHS) using the order of operations (BODMAS/PEMDAS).

Applying the Order of Operations (BODMAS/PEMDAS)

The order of operations tells us the sequence in which mathematical operations should be performed:

• Brackets (Parentheses)
• Orders (Exponents, Roots)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Let's evaluate the RHS of the equation \(120 - 42 + 240 \div 48 \times 2\):

Step 1: Division

First, we perform the division operation:

\(240 \div 48 = 5\)

The equation now becomes:

\(120 - 42 + 5 \times 2\)

Step 2: Multiplication

Next, we perform the multiplication operation:

\(5 \times 2 = 10\)

The equation now becomes:

\(120 - 42 + 10\)

Step 3: Subtraction and Addition (from left to right)

Now we perform the subtraction and addition from left to right:

\(120 - 42 = 78\)

The equation now becomes:

\(78 + 10\)

Finally, perform the addition:

\(78 + 10 = 88\)

Verifying the Equation

After evaluating the right-hand side, we get 88. The equation is:

\(88 = 88\)

Since the left-hand side (LHS) equals the right-hand side (RHS), the equation is correct with this combination of signs.

The sequence of signs used is =, –, +, ÷, ×.

Conclusion

The correct combination of mathematical signs that makes the given equation correct is =, –, +, ÷, ×.

Revision Table: Mathematical Signs and Operations

Additional Information: The Importance of BODMAS/PEMDAS

When solving equations or expressions with multiple operations, following the correct order of operations (BODMAS or PEMDAS) is crucial. Without a standard order, the same expression could yield different results, leading to ambiguity. BODMAS/PEMDAS provides a clear rule set to ensure consistent evaluation of mathematical expressions. Remember to work from Brackets/Parentheses first, then Orders/Exponents, then Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right).