When a positive integer is divided by a negative integer, what sign does department have?
When a positive integer is divided by a negative integer, the quotient will have a negative sign.
When a positive integer is divided by a negative integer, the quotient will always be negative.
When a positive integer is divided by a negative integer, the quotient will be negative.
To understand why, let's consider the basic rules of division. When we divide two numbers, we are essentially finding how many times the divisor can be subtracted from the dividend.
For example, if we have 10 divided by 2, we keep subtracting 2 from 10 until we cannot subtract anymore. In this case, 10 divided by 2 equals 5.
Now, let's consider the case of dividing a positive integer by a negative integer. Since the divisor is negative, we still have to subtract it from the dividend to find the quotient.
For example, if we have 10 divided by -2, we still keep subtracting -2 from 10 until we cannot subtract anymore. In this case, we perform the subtraction as follows:
10 - (-2) = 10 + 2 = 12
12 - (-2) = 12 + 2 = 14
14 - (-2) = 14 + 2 = 16
We see that we need to subtract -2 three times to reach a final quotient of 16. Therefore, 10 divided by -2 equals -5.
In general, when a positive integer is divided by a negative integer, the quotient will be negative. This is because subtracting a negative number is the same as adding a positive number.