Question

how is the sign of the quotient determined

Answer 1

The sign of a quotient (i.e., the result of dividing one number by another) is determined by the signs of the numerator and the denominator. Here are the basic rules:

1. **Positive divided by Positive**:
- If both the numerator and the denominator are positive, the quotient is positive.
- Example: \(6 \div 3 = 2\) (positive)

2. **Positive divided by Negative**:
- If the numerator is positive and the denominator is negative, the quotient is negative.
- Example: \(6 \div -3 = -2\) (negative)

3. **Negative divided by Positive**:
- If the numerator is negative and the denominator is positive, the quotient is negative.
- Example: \(-6 \div 3 = -2\) (negative)

4. **Negative divided by Negative**:
- If both the numerator and the denominator are negative, the quotient is positive.
- Example: \(-6 \div -3 = 2\) (positive)

In summary:
- If the signs of the numerator and denominator are the same (both positive or both negative), the quotient is positive.
- If the signs are different (one positive and one negative), the quotient is negative.