Which two numbers(not digits) and two signs should be interchanged to make the given equation correct? 100 $\times$ 5 - 110 $\div$ 2 + 12 = 210
5 and 2; + and -
The problem requires us to find which two numbers and two signs need to be interchanged in the given equation to make it mathematically correct.
Equation Analysis
The given equation is:
$100 $\times$ 5 - 110 $\div$ 2 + 12 = 210$
We must follow the order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Original Equation Evaluation
Let's evaluate the original equation:
- Division: $110 \div 2 = 55$
- Multiplication: $100 \times 5 = 500$
- The equation becomes: $500 - 55 + 12$
- Subtraction: $500 - 55 = 445$
- Addition: $445 + 12 = 457$
The result is 457, which is not equal to the right side (210). Therefore, the original equation is incorrect.
Testing Interchange Option A
The proposed correct answer involves interchanging numbers 5 and 2, and signs + and -.
Let's apply these interchanges to the original equation:
- Original: $100 $\times$ 5 - 110 $\div$ 2 + 12 = 210$
- Interchange 5 with 2 and 2 with 5.
- Interchange - with + and + with -.
- New Equation: $100 $\times$ 2 + 110 $\div$ 5 - 12 = 210$
New Equation Evaluation
Now, let's evaluate the modified equation using BODMAS/PEMDAS:
- Division: $110 \div 5 = 22$
- Multiplication: $100 \times 2 = 200$
- The equation becomes: $200 + 22 - 12$
- Addition: $200 + 22 = 222$
- Subtraction: $222 - 12 = 210$
The result is 210, which correctly matches the right side of the equation.
Conclusion
Interchanging the numbers 5 and 2, and the signs + and - makes the equation correct.
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.)
