Which quotient is between -4 and -5 on a number line?

Question

Hint:  Use your calculator for this problem.

(1 point)
Responses

2/5/6÷(−1/2)
2 and 5 sixths divided by open paren negative 1 half close paren

1/2/3÷(−1/2)
1 and 2 thirds divided by open paren negative 1 half close paren

−9/1/3÷2
negative 9 and 1 third divided by 2

−5/1/2÷(−1/1/2)
negative 5 and 1 half divided by open paren negative 1 and 1 half close paren

GPT-4o mini · Answer

To find the quotient that is between -4 and -5, we need to evaluate each of the given expressions. Let's calculate them one by one:

\( \frac{2 \frac{5}{6}}{-\frac{1}{2}} \):
- Convert \(2 \frac{5}{6}\) to an improper fraction: \(2 \times 6 + 5 = 12 + 5 = \frac{17}{6}\).
- Now divide by \(-\frac{1}{2}\): \[ \frac{17}{6} \div -\frac{1}{2} = \frac{17}{6} \times -2 = -\frac{34}{6} = -\frac{17}{3} \approx -5.67 \]
\( \frac{1 \frac{2}{3}}{-\frac{1}{2}} \):
- Convert \(1 \frac{2}{3}\) to an improper fraction: \(1 \times 3 + 2 = 3 + 2 = \frac{5}{3}\).
- Divide by \(-\frac{1}{2}\): \[ \frac{5}{3} \div -\frac{1}{2} = \frac{5}{3} \times -2 = -\frac{10}{3} \approx -3.33 \]
\( -9 \frac{1}{3} \div 2 \):
- Convert \(-9 \frac{1}{3}\) to an improper fraction: \(-9 \times 3 - 1 = -27 - 1 = -\frac{28}{3}\).
- Divide by \(2\): \[ -\frac{28}{3} \div 2 = -\frac{28}{6} = -\frac{14}{3} \approx -4.67 \]
\( -5 \frac{1}{2} \div -1 \frac{1}{2} \):
- Convert \(-5 \frac{1}{2}\) and \(-1 \frac{1}{2}\):
  - \(-5 \frac{1}{2} = -\frac{11}{2}\)
  - \(-1 \frac{1}{2} = -\frac{3}{2}\)
- Divide: \[ -\frac{11}{2} \div -\frac{3}{2} = -\frac{11}{2} \times -\frac{2}{3} = \frac{11}{3} \approx 3.67 \]

Now, let's summarize our results:

The only quotient that falls between -4 and -5 is:

Final Answer: \( -9 \frac{1}{3} \div 2 \) is the quotient between -4 and -5.