Video Transcript
Select the expression that has an undefined answer. Option (A) three minus three all over two. Option (B) zero over two. Option (C) two minus two all over three. Option (D) negative zero over three. Or is it option (E) two over three minus three?
In this question, we are given five numerical expressions and asked to select the expression that has an undefined answer, that is, the expression that we cannot evaluate.
There are many ways that we can answer this question. One way is to recall that the quotient of two integers is well defined so long as we are not dividing by zero. In fact, 𝑎 over 𝑏 is the unique number that when multiplied by 𝑏 gives us 𝑎. This only works if 𝑏 is nonzero. We can use this idea to check if any of the expressions is dividing by zero.
We see that options (A), (B), (C), and (D) do not have zero in the denominator. However, the denominator in option (E) is three minus three, which evaluates to give zero. So, option (E) shows two divided by zero. We know that we cannot divide by zero, so this is undefined. Hence, the expression in option (E), two over three minus three, is undefined since it includes division by zero.
For due diligence, we can check the other four options to make sure that they are all defined. In expression (A), we have that three minus three is zero. So, we can simplify the expression to be zero divided by two. This is the number which when multiplied by two gives zero. Of course, we know that zero times two is zero. So, expression (A) is equal to zero.
The same reasoning works for expression (B). Zero over two is just equal to zero. Similarly, in expression (C), we have two minus two is zero. And then we divide this by three. This is well defined and is once again equal to zero. Finally, in expression (D), we can note that zero over three is zero. And then multiplying zero by any number gives zero. So, negative zero over three is just zero.
Hence, only the expression in option (E) is undefined, since all the expressions are the quotients of integers. But only expression (E) includes division by zero.
