We want to determine what we can conclude about two integers whose quotient is positive. To do so, let's divide any two integers, for example 8 by 2.
8 ÷ 2 = 4We can see that the quotient is positive. Now, let's divide - 6 by 3.
- 6 ÷ 3 = -2
The quotient of -6 and 2 is is negative. This is because the integers have different signs. Now, let's divide -10 by -5.
-10 ÷ (-5) = -2
This time, because both integers are negative, their quotient is positive. We can see that when the quotient of two integers is positive, the integers have the same sign.
Now we are asked what we can say about two integers if their quotient is negative. From Part A we already know that the quotient of two integers that have the same sign is positive. However, the quotient of two integers that have different signs is negative. For example, consider the quotient of 12 and -6.
12 ÷ (-6) = 2
We can conclude that when the quotient of two integers is negative, the integers have different signs.
Finally, we are asked what we can conclude about two integers whose quotient is zero. Let's consider the division of any two integers p and q.
p ÷ q
Remember that we cannot divide by zero. This means that the divisor q cannot be equal to zero. From Part A and Part B we know that if the integers have the same sign, then the quotient is positive and if the integers have different signs then the quotient is negative. For the quotient to be equal to zero, we need the dividend to be equal to zero.
0 ÷ q =0
When the quotient of two integers is zero, we know that the dividend is zero.
