$25 \times 2 - 10 \div 5 + 3 = 49$
To solve the equation and determine which two signs need to be interchanged to make it correct, we'll start by analyzing the provided equation:
The initial equation is:
$$25 \times 2 - 10 \div 5 + 3 = 49$$
Let's evaluate it with the given operators without any interchanges:
- First, address the \(\times\) (multiplication):
$$25 \times 2 = 50$$ - The equation now looks like:
$$50 - 10 \div 5 + 3$$ - Next, address the \(\div\) (division):
$$10 \div 5 = 2$$ - The equation simplifies to:
$$50 - 2 + 3$$ - Perform subtraction and addition from left to right:
$$50 - 2 = 48$$ - Then add 3:
$$48 + 3 = 51$$
The result is 51, which does not equal the right-hand side of the equation (49). Therefore, the given equation is incorrect with the current arrangement of operators.
Now, let's find which pair of operators should be interchanged:
- Try interchanging \(+\) and \(-\):
- The equation becomes:
$$25 \times 2 + 10 \div 5 - 3$$ - Calculate as follows:
- Multiplication: $$25 \times 2 = 50$$
- Division: $$10 \div 5 = 2$$
- Substitute back into the equation:
$$50 + 2 - 3$$ - Perform the arithmetic operations from left to right:
$$50 + 2 = 52$$
$$52 - 3 = 49$$
The result matches the right-hand side of the equation (49). Thus, by interchanging the \(+\) and \(-\) signs, the equation becomes correct.
Conclusion: The correct answer is to interchange the \(+\) (plus) and \(−\) (minus) signs to make the equation correct.
Similar Questions
- Which two signs should be interchanged to make the following equation CORRECT?
$[(15 \div 3) - (4 \times 2)] + [4 - 6] = 5 \times 10$ - If "+" means "$\div$", "-" means "+", "$\times$" means "-" and "$\div$" means "$\times$", which of the following options is CORRECT?
- If 5 @ 2 = 17 and 6 @ 3 = 27, what is 7 @ 4?
- If 9 @ 1 = 82 and 6 @ 2 = 38, what is the value of 7 @ 3?
- You are given a mathematical expression with basic operations. However, the symbols used are not their usual meaning.
You must follow these symbol substitution rules:
'+' means '-'
'-' means 'x'
'x' means '÷'
'÷' means '+'
$120 \div 6 \times 3 - 10 + 4 = ?$ - If $\times$ stands for addition, $\div$ stands for subtraction, + stands for multiplication, and - stands for division, then $12 \times 6 \div 3 - 2 + 5 = ?$
- Which two signs need to be interchanged?
$22 - 4 \times 2 \div 2 + 6 = 20$ - Which interchanges of numbers and signs will make the equation correct? $8 \times 3 + 4 = 28$
- Select the CORRECT sequence of mathematical signs to sequentially replace the A and B to balance the given equation.
15 A 5 B 4 = 35 - The following equation is incorrect. Which two signs should be interchanged to correct the equation?
$14 - 7 \times 30 \div 10 + 4 = 54$
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.)
