Which two signs need to be interchanged to make the following equation correct?
$56 \div 28 - 72 + 18 \times 6 = 60$

Question

Which two signs need to be interchanged to make the following equation correct? $56 \div 28 - 72 + 18 	imes 6 = 60$

Prepp Team · Accepted Answer

Understanding the Equation Correction Problem

The question asks us to find which pair of mathematical signs in the equation $56 \div 28 - 72 + 18 \times 6 = 60$ needs to be interchanged to make the equation true. We need to test the given options by swapping the signs and evaluating the resulting equation using the standard order of operations (PEMDAS/BODMAS).

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Evaluating the Original Equation

First, let's check the value of the original equation:

$$56 \div 28 - 72 + 18 \times 6$$

Following the order of operations:

Division: $56 \div 28 = 2$
Multiplication: $18 \times 6 = 108$
The equation becomes: $2 - 72 + 108$
Subtraction: $2 - 72 = -70$
Addition: $-70 + 108 = 38$

The original equation evaluates to $38$, not $60$, so the signs need to be changed.

Testing the Sign Interchange Options

We need to find the correct pair of signs to interchange. The correct answer indicates that swapping the division symbol ($ \div $) and the addition symbol ($ + $) should make the equation correct.

Let's test this specific interchange (Option 2: $ \div $ and $ + $):

The original equation is: $56 \div 28 - 72 + 18 \times 6 = 60$

Interchanging $ \div $ and $ + $ gives:

$$56 + 28 - 72 \div 18 \times 6$$

Now, let's evaluate this new equation using the order of operations:

Division: First, perform the division: $72 \div 18 = 4$.
The equation now looks like: $56 + 28 - 4 \times 6$.
Multiplication: Next, perform the multiplication: $4 \times 6 = 24$.
The equation becomes: $56 + 28 - 24$.
Addition: Perform addition from left to right: $56 + 28 = 84$.
The equation is now: $84 - 24$.
Subtraction: Finally, perform the subtraction: $84 - 24 = 60$.

This result, $60$, matches the right-hand side of the original equation. Therefore, interchanging the division ($ \div $) and addition ($ + $) signs correctly solves the equation.

Conclusion on Sign Interchange

By swapping the division ($ \div $) and addition ($ + $) signs, the equation $56 \div 28 - 72 + 18 \times 6 = 60$ becomes $56 + 28 - 72 \div 18 \times 6 = 60$, which is mathematically correct according to the order of operations.