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Consider the problem.

−134÷25
Determine the sign of the quotient.

(1 point)
Responses

Positive - If the divisor is larger than the dividend, the quotient has the sign of the divisor.
Positive - If the divisor is larger than the dividend, the quotient has the sign of the divisor.

Negative - If the dividend is negative, the quotient is negative.
Negative - If the dividend is negative, the quotient is negative.

Negative - If the dividend and divisor have different signs, the quotient is negative.
Negative - If the dividend and divisor have different signs, the quotient is negative.
Question 2
Consider the problem.

−134÷25

Determine the quotient in simplest form.

(1 point)
Responses

438
4 and 3 eighths

−438
negative 4 and 3 eighths

−1420
negative 14 over 20

358
35 eighths
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1 answer

Question 1: Determine the Sign of the Quotient

To determine the sign of the quotient when dividing \(-134\) by \(25\):

  • The dividend (\(-134\)) is negative.
  • The divisor (\(25\)) is positive.
  • When dividing a negative number by a positive number, the result is negative.

Response: Negative - If the dividend and divisor have different signs, the quotient is negative.

Question 2: Determine the Quotient in Simplest Form

To find the quotient of \(-134 \div 25\), we can compute the division:

  1. Perform the division: \(-134 \div 25\).
  2. The absolute value of \(-134\) is \(134\), and dividing \(134\) by \(25\) gives \(5\) with a remainder.
  3. To find the remainder: \(134 - (5 \times 25) = 134 - 125 = 9\).
  4. So, we can write it as: \[ -134 \div 25 = -5 \text{ remainder } 9 \]
  5. This can also be expressed as: \[ -5 \frac{9}{25} \]

Thus, the simplest form of the quotient \(−134÷25\) is \(-5\) and \(9/25\).

However, none of the options directly say this, but we can derive from the available responses:

Response: Negative 5 and 9 over 25. (Note: this exact option may not be present in the original choices, but it is the correct interpretation.)