Question

Which of the following interchanges of signs would make the given equation correct ?

$5\times4\div10-8+2=8$

• A. + , ÷
• B. x , ÷
• C. + , x
• D. + , -

Answer 1

Answer:

D. + , -

Interchanging the mathematical signs $-$ and $+$ will make the given equation correct.

1. Analyze the original equation

First, evaluate the given expression using the standard BODMAS/PEMDAS rule (Division and Multiplication first from left to right, then Addition and Subtraction):
$5 \times 4 \div 10 - 8 + 2 = 8$

Evaluate the multiplication and division first:
$5 \times 4 = 20$
$20 \div 10 = 2$

Substitute this back into the expression:

$2 - 8 + 2 = -4$

Since $-4 \neq 8$, the original equation is incorrect.

2. Interchange minus and plus signs

Now, swap every minus sign ($-$) with a plus sign ($+$) and vice versa. The updated mathematical expression becomes:
$5 \times 4 \div 10 + 8 - 2 = 8$

3. Verify the new equation

Apply the order of operations to solve the new expression:

• Step A (Multiplication): $5 \times 4 = 20$

• Step B (Division): $20 \div 10 = 2$

• Step C (Addition): $2 + 8 = 10$

• Step D (Subtraction): $10 - 2 = 8$

Both sides match perfectly ($8 = 8$), proving the interchange is correct.

Correct Sign Interchange

The interchange of the $-$ and $+$ signs makes the equation $5 \times 4 \div 10 - 8 + 2 = 8$ correct.