When a positive integer is divided by a negative integer, what sign does the quotient have?(1 point)
Responses
always negative
always negative
positive if the sum of the dividend and the divisor is greater than 0, negative otherwise
positive if the sum of the dividend and the divisor is greater than 0, negative otherwise
always positive
always positive
negative if the sum of the dividend and the divisor is less than 0, positive otherwise
negative if the sum of the dividend and the divisor is less than 0, positive otherwise
When a positive integer is divided by a negative integer, the quotient has the sign "negative if the sum of the dividend and the divisor is less than 0, positive otherwise".
The correct response is: positive if the sum of the dividend and the divisor is greater than 0, negative otherwise.
To understand why, let's consider the basic rule of division:
When dividing two numbers, the quotient represents how many times the divisor can be subtracted from the dividend.
When we divide a positive integer by a negative integer, the divisor is negative.
If the dividend is also positive, and the sum of the dividend and divisor is greater than 0, then the quotient will be positive. This is because we can repeatedly subtract the negative divisor from the positive dividend to get a positive result.
On the other hand, if the sum of the dividend and divisor is less than 0, then the quotient will be negative. This is because if we continue subtracting the negative divisor from the positive dividend, we would eventually reach a negative result.
Therefore, the sign of the quotient when dividing a positive integer by a negative integer is positive if the sum of the dividend and divisor is greater than 0, and negative otherwise.