Question

five students are playing a video game where they can spend and earn points. point values are represented as positive and negative numbers. the scores for round 1 are shown in the table.

student	1	2	3	4	5

which student number had the lowest score? enter your answer in the box provided.
student \boxed{1} had the lowest score.

Explanation:

Step1: Convert mixed numbers to decimals

• Student 1: \(-1\frac{3}{4} = -1.75\)
• Student 2: \(-2\frac{1}{8} = -2.125\)
• Student 3: \(-1.10\)
• Student 4: \(2\frac{1}{4} = 2.25\)
• Student 5: \(-2\frac{1}{5} = -2.2\)

Step2: Compare the decimal values

Negative numbers with larger absolute values are smaller. Comparing the negative decimals: \(-2.25\) (wait, no, Student 2 is -2.125, Student 5 is -2.2, Student 1 is -1.75, Student 3 is -1.10. Wait, let's list all:

Student 1: -1.75

Student 2: -2.125

Student 3: -1.10

Student 4: 2.25 (positive, so larger than negatives)

Student 5: -2.2

Now, order the negative numbers from smallest (most negative) to largest:

-2.2 (Student 5) is more negative than -2.125 (Student 2)? Wait, no: \(-2.2 = -2.200\), \(-2.125\) is greater than \(-2.2\) because \(-2.200 < -2.125\) (since on the number line, left is smaller). Wait, let's check:

\(-2.2\) is -2.20, \(-2.125\) is -2.125. So \(-2.20 < -2.125\), so Student 5's score (-2.2) is less than Student 2's (-2.125). Then Student 1 is -1.75, Student 3 is -1.10. So the order from smallest to largest (for negatives) is: -2.2 (Student 5), -2.125 (Student 2), -1.75 (Student 1), -1.10 (Student 3). And Student 4 is positive. So the lowest score is Student 5? Wait, wait, maybe I made a mistake earlier. Wait, let's recalculate:

Student 5: \(-2\frac{1}{5} = -2.2\)

Student 2: \(-2\frac{1}{8} = -2.125\)

So -2.2 is less than -2.125, because -2.2 is to the left of -2.125 on the number line. Then Student 5's score is -2.2, Student 2's is -2.125, so Student 5 has a lower score than Student 2. Then Student 1 is -1.75, Student 3 is -1.10. So the lowest score is Student 5? Wait, but the initial answer was Student 1, which is wrong. Let's check again.

Wait, the scores:

Student 1: \(-1\frac{3}{4} = -1.75\)

Student 2: \(-2\frac{1}{8} = -2.125\)

Student 3: \(-1.10\)

Student 4: \(2\frac{1}{4} = 2.25\)

Student 5: \(-2\frac{1}{5} = -2.2\)

Now, let's list all scores: -1.75, -2.125, -1.10, 2.25, -2.2.

Now, arrange them in ascending order (smallest to largest):

-2.2 (Student 5), -2.125 (Student 2), -1.75 (Student 1), -1.10 (Student 3), 2.25 (Student 4).

So the smallest (lowest) score is -2.2, which is Student 5. Wait, but the original answer was Student 1, which is incorrect. So the correct answer should be Student 5? Wait, maybe I messed up the conversion. Wait, \(-2\frac{1}{5}\) is -2.2, correct. \(-2\frac{1}{8}\) is -2.125, correct. So -2.2 is less than -2.125, so Student 5 has the lowest score.

Wait, maybe the initial problem's table was misread. Let me check the table again:

Student 1: \(-1\frac{3}{4}\)

Student 2: \(-2\frac{1}{8}\)

Student 3: \(-1.10\)

Student 4: \(2\frac{1}{4}\)

Student 5: \(-2\frac{1}{5}\)

Yes. So converting to decimals:

Student 1: -1.75

Student 2: -2.125

Student 3: -1.10

Student 4: 2.25

Student 5: -2.2

So the lowest score is Student 5, because -2.2 is less than -2.125, -1.75, -1.10, and 2.25.

Wait, maybe the original answer was wrong. Let's confirm:

On the number line, numbers to the left are smaller. So -2.2 is to the left of -2.125, which is to the left of -1.75, which is to the left of -1.10, and 2.25 is to the right. So the leftmost (smallest) is -2.2, which is Student 5.

So the correct answer is Student 5.

Answer:

5