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

Question

Hint: Use your calculator for this problem.

(1 point)
Responses

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

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

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

−9 1/3÷2

Answer 1

To determine which quotient is between -4 and -5, we need to calculate each of the provided options.

1. \( 1 \frac{2}{3} \div (-\frac{1}{2}) \)

   • Convert \( 1 \frac{2}{3} \) to an improper fraction: \[ 1 \frac{2}{3} = \frac{5}{3} \]
   • Perform the division: \[ \frac{5}{3} \div (-\frac{1}{2}) = \frac{5}{3} \times (-2) = -\frac{10}{3} \approx -3.33 \]

2. \( -5 \frac{1}{2} \div (-1 \frac{1}{2}) \)

   • Convert both to improper fractions: \[ -5 \frac{1}{2} = -\frac{11}{2}, \quad -1 \frac{1}{2} = -\frac{3}{2} \]
   • Perform the division: \[ -\frac{11}{2} \div -\frac{3}{2} = \frac{11}{2} \times \frac{2}{3} = \frac{11}{3} \approx 3.67 \]

3. \( 2 \frac{5}{6} \div (-\frac{1}{2}) \)

   • Convert \( 2 \frac{5}{6} \) to an improper fraction: \[ 2 \frac{5}{6} = \frac{17}{6} \]
   • Perform the division: \[ \frac{17}{6} \div (-\frac{1}{2}) = \frac{17}{6} \times (-2) = -\frac{34}{6} = -\frac{17}{3} \approx -5.67 \]

4. \( -9 \frac{1}{3} \div 2 \)

   • Convert \( -9 \frac{1}{3} \) to an improper fraction: \[ -9 \frac{1}{3} = -\frac{28}{3} \]
   • Perform the division: \[ -\frac{28}{3} \div 2 = -\frac{28}{3} \times \frac{1}{2} = -\frac{28}{6} = -\frac{14}{3} \approx -4.67 \]

Now, let's summarize the results:

1. \( \approx -3.33 \)
2. \( \approx 3.67 \)
3. \( \approx -5.67 \) (not between -4 and -5)
4. \( \approx -4.67 \) (between -4 and -5)

The answer is \( -9 \frac{1}{3} \div 2 \), which is approximately -4.67 and falls between -4 and -5.