If a and b are integers when is 1/ab positive?
Please help me, I don't know what to do.
In order for 1/ab to be positive meaning it is greater the zero the denominator must be positive since the numerator is positive.
Since both a and b are in the denominator to get a positive number a&b both have to be positive or they both have to be negative.
Did I explain clearly?
Well, it's "positively" amusing that you're puzzled by this question!
To determine when 1/ab is positive, we need to consider the signs of a and b.
If both a and b are positive, then their product (ab) is also positive. So, 1/ab will be positive when a and b are both positive integers.
If both a and b are negative, then their product (ab) is positive as well. So, 1/ab will also be positive in this case.
However, if one of the integers (a or b) is positive and the other is negative, their product (ab) will be negative. So, 1/ab will not be positive when a and b have opposite signs.
Therefore, the answer is: 1/ab is positive when both a and b are positive, or when both a and b are negative.
To determine when the quantity 1/ab is positive, we need to consider the possible cases for the values of a and b.
Case 1: Both a and b are positive integers:
If both a and b are positive integers, then ab will be positive. Since the reciprocal of a positive number is also positive, 1/ab will be positive in this case.
Case 2: Both a and b are negative integers:
If both a and b are negative integers, then ab will also be positive (since a negative multiplied by a negative gives a positive result). Therefore, 1/ab will still be positive.
Case 3: One of the integers, either a or b, is positive and the other is negative:
If one integer is positive and the other is negative, then ab will be negative (since a positive multiplied by a negative gives a negative result). In this case, the reciprocal of ab will be negative, not positive.
In summary, 1/ab is positive when both a and b are either positive or negative integers.
To determine when 1/ab is positive, we need to consider the signs of a, b, and the product ab.
Let's break it down step by step:
1. If both a and b are positive, then the product ab is positive. In this case, 1/ab will be positive.
2. If both a and b are negative, then the product ab is also positive. Again, 1/ab will be positive.
3. If one of a or b is positive and the other is negative, then the product ab is negative. In this case, 1/ab will be negative.
Therefore, 1/ab will be positive only when either both a and b are positive, or both a and b are negative.