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Consider the problem. −1 3/4÷2/5 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.

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To determine the sign of the quotient for the problem \(-1 \frac{3}{4} \div \frac{2}{5}\), we first need to identify the signs of the dividend and divisor:

  1. The dividend is \(-1 \frac{3}{4}\), which is negative.
  2. The divisor is \(\frac{2}{5}\), which is positive.

When dividing a negative number by a positive number, the result will always be negative. Therefore, regardless of the size of the numbers, since we have a negative dividend and a positive divisor, the quotient will be negative.

Thus, the correct response is: Negative - If the dividend is negative, the quotient is negative.