$25 \times 2 - 10 \div 5 + 3 = 49$
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.
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Important Questions from Mathematical Operations
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