Each question Sandra answers incorrectly changes her overall score by
points. Sandra’s overall score was
points, and then she answered the last question incorrectly. What was Sandra’s final score
The Correct Answer and Explanation is:
📘 Explanation
This question tests your understanding of adding and subtracting rational numbers (fractions and mixed numbers), especially negative numbers.
🔢 Step 1: Understand the given values
- Sandra’s current score is −4½ points.
- Each incorrect answer changes the score by −¾ points.
- She just answered a question incorrectly, so we subtract ¾ from her current score.
This becomes a problem of adding two negative numbers: Final Score=−412+(−34)\text{Final Score} = -4\frac{1}{2} + (-\frac{3}{4})
✍️ Step 2: Convert to improper fractions
- −412=−92-4\frac{1}{2} = -\frac{9}{2}
- −34-\frac{3}{4} stays the same
To add them, they need a common denominator.
- The least common denominator of 2 and 4 is 4.
- So, −92=−184-\frac{9}{2} = -\frac{18}{4}
Now add: −184+(−34)=−214-\frac{18}{4} + (-\frac{3}{4}) = -\frac{21}{4}
🧮 Step 3: Convert back to mixed number
−214=−514-\frac{21}{4} = -5\frac{1}{4}
So, Sandra’s final score is: −514\boxed{-5\frac{1}{4}}
💡 Why is the answer negative?
Since Sandra already had a negative score, and she lost more points for answering incorrectly, her score became even more negative. That’s why we’re adding two negative numbers—you’re moving further left on the number line.
✅ Summary
- Started with −4½
- Lost ¾ for a wrong answer
- Final score: −5¼
Correct choice: A. −5¼
This problem helps build your confidence with fractions, mixed numbers, and negative values—essential skills for middle school and high school math.
