Consider the problem.

Question

−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.

Answer 1

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

1. Identify the Dividend: \(-1 \frac{3}{4}\) can be converted to an improper fraction: \(-1 \frac{3}{4} = -\frac{7}{4}\).

2. Identify the Divisor: \(\frac{2}{5}\) is positive.

Now, we have:

• Dividend: \(-\frac{7}{4}\) (negative)
• Divisor: \(\frac{2}{5}\) (positive)

According to the rules of division:

• The quotient is negative when the dividend is negative and the divisor is positive.

Therefore, the sign of the quotient in this case will be negative, as the dividend and divisor have different signs.

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