Washington Vega
11/06/2023 · Junior High School
2. Which integer is \( -3 \frac{1}{4} \) closest to? -3 -4 -5 -2
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Tutor-Verified Answer
Step-by-step Solution
To determine which integer \( -3 \frac{1}{4} \) is closest to, we first convert the mixed number to an improper fraction or a decimal.
The mixed number \( -3 \frac{1}{4} \) can be expressed as:
\[
-3 \frac{1}{4} = -3 - \frac{1}{4} = -3.25
\]
Now, we can compare \( -3.25 \) to the integers given:
- The integer \( -4 \) is less than \( -3.25 \).
- The integer \( -3 \) is greater than \( -3.25 \).
- The integer \( -5 \) is further away from \( -3.25 \).
- The integer \( -2 \) is also further away from \( -3.25 \).
Now, we can find the distances:
- Distance from \( -3.25 \) to \( -4 \):
\[
|-3.25 - (-4)| = |-3.25 + 4| = |0.75| = 0.75
\]
- Distance from \( -3.25 \) to \( -3 \):
\[
|-3.25 - (-3)| = |-3.25 + 3| = |-0.25| = 0.25
\]
Since \( 0.25 < 0.75 \), \( -3.25 \) is closer to \( -3 \) than to \( -4 \).
Thus, the integer that \( -3 \frac{1}{4} \) is closest to is:
\[
\boxed{-3}
\]
Quick Answer
The integer closest to \( -3 \frac{1}{4} \) is \( -3 \).
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