To determine which quotient lies between -4 and -5 on the number line, we can calculate each option one by one.
A. \(-9 \frac{1}{3} \div 2\)
First, convert \(-9 \frac{1}{3}\) to an improper fraction: \[ -9 \frac{1}{3} = -\frac{28}{3} \]
Now, divide by 2: \[ -\frac{28}{3} \div 2 = -\frac{28}{3} \times \frac{1}{2} = -\frac{28}{6} = -\frac{14}{3} \approx -4.67 \]
B. \(-5 \frac{1}{2} \div (-1 \frac{1}{2})\)
Convert both to improper fractions: \[ -5 \frac{1}{2} = -\frac{11}{2}, \quad -1 \frac{1}{2} = -\frac{3}{2} \]
Now, divide: \[ -\frac{11}{2} \div -\frac{3}{2} = -\frac{11}{2} \times -\frac{2}{3} = \frac{11}{3} \approx 3.67 \]
C. \(2 \frac{5}{6} \div (-\frac{1}{2})\)
Convert to improper fraction: \[ 2 \frac{5}{6} = \frac{17}{6} \]
Now, divide: \[ \frac{17}{6} \div -\frac{1}{2} = \frac{17}{6} \times -2 = -\frac{34}{6} = -\frac{17}{3} \approx -5.67 \]
D. \(1 \frac{2}{3} \div (-\frac{1}{2})\)
Convert to improper fraction: \[ 1 \frac{2}{3} = \frac{5}{3} \]
Now, divide: \[ \frac{5}{3} \div -\frac{1}{2} = \frac{5}{3} \times -2 = -\frac{10}{3} \approx -3.33 \]
Summary of Results:
- A: \(-\frac{14}{3} \approx -4.67\)
- B: \(\frac{11}{3} \approx 3.67\)
- C: \(-\frac{17}{3} \approx -5.67\)
- D: \(-\frac{10}{3} \approx -3.33\)
The quotient that falls between -4 and -5 is C: \(-\frac{17}{3}\) (approximately -5.67).
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