By interchanging the given two signs which of the following equation will not be correct?
+ and ÷
I. 27 ÷ 3 - 18 × 3 + 9 = 24
II. 12 ÷ 8 × 12 + 16 - 7 = 19

Question

By interchanging the given two signs which of the following equation will not be correct?+ and &divide;I. 27 &divide; 3 - 18 &times; 3 + 9 = 24II. 12 &divide; 8 &times; 12 + 16 - 7 = 19

Prepp Team · Accepted Answer

Solving the Sign Interchange Puzzle

The problem asks us to identify which of the given equations will not be correct after interchanging the '+' and '÷' signs. We need to perform the sign swap in each equation and then evaluate if the resulting equation holds true.

Analyzing Equation I

The original Equation I is:

\(27 \div 3 - 18 \times 3 + 9 = 24\)

Now, we interchange '+' and '÷'. The new equation becomes:

\(27 + 3 - 18 \times 3 \div 9\)

Let's evaluate the left side using the BODMAS/PEMDAS rule (Division, Multiplication, Addition, Subtraction):

First, perform the division: \(3 \div 9 = \frac{3}{9} = \frac{1}{3}\)
The equation becomes: \(27 + 3 - 18 \times \frac{1}{3}\)
Next, perform the multiplication: \(18 \times \frac{1}{3} = 6\)
The equation becomes: \(27 + 3 - 6\)
Finally, perform addition and subtraction from left to right: \(27 + 3 = 30\)
Then: \(30 - 6 = 24\)

The left side evaluates to 24. The original right side was also 24.

\(24 = 24\)

So, Equation I is correct after interchanging the signs.

Analyzing Equation II

The original Equation II is:

\(12 \div 8 \times 12 + 16 - 7 = 19\)

Now, we interchange '+' and '÷'. The new equation becomes:

\(12 + 8 \times 12 \div 16 - 7\)

Let's evaluate the left side using the BODMAS/PEMDAS rule (Division, Multiplication, Addition, Subtraction):

First, perform the division: \(12 \div 16 = \frac{12}{16} = \frac{3}{4}\)
The equation becomes: \(12 + 8 \times \frac{3}{4} - 7\)
Next, perform the multiplication: \(8 \times \frac{3}{4} = \frac{8 \times 3}{4} = \frac{24}{4} = 6\)
The equation becomes: \(12 + 6 - 7\)
Finally, perform addition and subtraction from left to right: \(12 + 6 = 18\)
Then: \(18 - 7 = 11\)

The left side evaluates to 11. The original right side was 19.

\(11 \neq 19\)

So, Equation II is not correct after interchanging the signs.

Summary of Results

Equation	Original	Signs Swapped (+ <-> ÷)	Evaluated Result	Original Right Side	Correct After Swap?
I	\(27 \div 3 - 18 \times 3 + 9 = 24\)	\(27 + 3 - 18 \times 3 \div 9\)	24	24	Yes
II	\(12 \div 8 \times 12 + 16 - 7 = 19\)	\(12 + 8 \times 12 \div 16 - 7\)	11	19	No

Based on our analysis, only Equation II is not correct after interchanging the '+' and '÷' signs.

Revision Table: Sign Interchange Concepts

Concept	Description	Importance
Sign Interchange	Replacing one mathematical operator with another throughout an equation.	Tests understanding of operator properties and order of operations.
Order of Operations	Rules governing the sequence in which mathematical operations are performed (BODMAS/PEMDAS).	Crucial for correctly evaluating expressions after sign changes.
Equation Verification	Checking if the left side of an equation equals the right side after modifications.	Determines if the modified equation is valid.

Additional Information: BODMAS/PEMDAS Explained

When solving mathematical expressions, especially after changing signs, it's vital to follow the correct order of operations. The BODMAS or PEMDAS rules help us remember this order.

BODMAS: Brackets, Orders (powers, square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Both acronyms represent the same order. Division and Multiplication have equal priority and are done from left to right as they appear. Similarly, Addition and Subtraction have equal priority and are done from left to right.