Which two numbers should be interchanged to make the given equation correct?
$14\times5+36-27\div3=85$
Equation Analysis
The problem asks us to identify two numbers within the given equation that need to be interchanged to make the equation mathematically correct. The equation provided is:
$14\times5+36-27\div3=85$
To solve this, we first need to understand the standard order of operations, commonly remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
Checking Original Equation
Let's evaluate the original equation as it is, following the PEMDAS/BODMAS rules:
- Multiplication: Calculate $14 \times 5$. $14 \times 5 = 70$
- Division: Calculate $27 \div 3$. $27 \div 3 = 9$
- Substitute results: The equation now looks like $70 + 36 - 9$.
- Addition: Calculate $70 + 36$. $70 + 36 = 106$
- Subtraction: Calculate $106 - 9$. $106 - 9 = 97$
The calculation yields 97. However, the equation states the result should be 85. Since $97 \neq 85$, the original equation is incorrect as written.
Interchanging Numbers Verification
We are given options for which numbers to interchange. The correct option suggests swapping 27 and 36. Let's see if this swap makes the equation true.
Replace 36 with 27 and 27 with 36 in the original equation:
New Equation: $14\times5+27-36\div3=85$
Now, let's evaluate this modified equation using the order of operations:
- Multiplication: $14 \times 5 = 70$.
- Division: $36 \div 3 = 12$.
- Substitute results: The equation becomes $70 + 27 - 12$.
- Addition: $70 + 27 = 97$.
- Subtraction: $97 - 12 = 85$.
The result of the calculation is 85. This matches the right-hand side of the equation ($85 = 85$).
Conclusion
By interchanging the numbers 27 and 36, the equation $14\times5+36-27\div3=85$ becomes 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.)
