\(6 - 2 \times 4 \div 10 + 5 = 6\)
Solving Equation by Sign Interchange
The goal is to find which pair of signs, when interchanged in the equation \(6 - 2 \times 4 \div 10 + 5 = 6\), makes it correct.
We will use the order of operations (PEMDAS/BODMAS): Division/Multiplication before Addition/Subtraction, evaluated from left to right.
Original Equation Evaluation
The given equation is \(6 - 2 \times 4 \div 10 + 5 = 6\).
- Calculate multiplication: \(2 \times 4 = 8\). Equation becomes \(6 - 8 \div 10 + 5 = 6\).
- Calculate division: \(8 \div 10 = 0.8\). Equation becomes \(6 - 0.8 + 5 = 6\).
- Calculate subtraction: \(6 - 0.8 = 5.2\). Equation becomes \(5.2 + 5 = 6\).
- Calculate addition: \(5.2 + 5 = 10.2\).
The result \(10.2 = 6\) is false. The original equation is incorrect.
Testing Sign Interchange: Option D (\(\div\) and \(\times\))
Interchange the multiplication (\(\times\)) sign and the division (\(\div\)) sign.
The equation transforms to \(6 - 2 \div 4 \times 10 + 5 = 6\).
- Calculate division: \(2 \div 4 = 0.5\). Equation becomes \(6 - 0.5 \times 10 + 5 = 6\).
- Calculate multiplication: \(0.5 \times 10 = 5\). Equation becomes \(6 - 5 + 5 = 6\).
- Calculate subtraction: \(6 - 5 = 1\). Equation becomes \(1 + 5 = 6\).
- Calculate addition: \(1 + 5 = 6\).
The result \(6 = 6\) is true.
Conclusion
Interchanging the division (\(\div\)) and multiplication (\(\times\)) signs correctly solves the equation.
Similar Questions
If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’ and ‘D’ stands for ‘−’, what will come in place of the question mark ‘?’ in the following equation?
14 A 30 B 45 C 15 D 9 = ?
If ‘A’ stands for ‘+’, ‘B’ stands for ‘−’, ‘C’ stands for ‘×’ and ‘D’ stands for ‘÷’, then what will come in place of the question mark (?) in the following equation?
28 A 16 C 3 B 12 D 4 = ?
If ‘A’ stands for ‘+’, ‘B’ stands for ‘−’, ‘C’ stands for ‘×’ and ‘D’ stands for ‘÷’, then what will come in place of the question mark (?) in the following equation?
31 B 35 D 7 A 9 C 2 = ?
What will come in place of the question mark (?) in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
42 × 6 ÷ 7 − 35 + 19 = ?
What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘−’ are interchanged and ‘x’ and ‘÷’ are interchanged?
5 ÷ 3 + 15 x 5 − 3 = ?
- What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘-‘ are interchanged and ‘×’ and ‘÷’ are interchanged?
29 - 6 + 19 × 19 ÷ 8 = ?
Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
