Matthew and Daniel were comparing
their elevations. Matthew’s position was 15.5 metres
below sea level, while Daniel’s position was 30 metres above sea level. Which of the following expressions
represents the difference in elevation between Matthew and Daniel? A) Negative 15.5 plus 30, B) 15.5
minus 30, C) 30 minus 15.5, D) the absolute value of 30 minus 15.5, or E) the
absolute value of 30 minus negative 15.5. And the second part, calculate the
difference in elevation.
First, we’ll need to figure out the
expression for the difference in elevation and then we’ll calculate. We could visualise the difference
in elevation. If this base is the sea level, we
know that Matthew is 15.5 metres below sea level and Daniel is 30 metres above sea
level. The difference between the
elevations of Matthew and Daniel will be this space. But how do we write that as an
We know that when we use the word
difference, it means subtraction. If we were going to take Daniel’s
elevation and subtract Matthew’s elevation, we know that Daniel’s elevation is 30
metres above sea level. But because Matthew is located
below sea level, we need to list his elevation with a negative value. We need to say that he is located
at negative 15.5 metres of elevation.
We know that when we’re dealing
with distances, we need a positive result, which means we want the absolute value of
this difference. One expression to find the
difference in elevation between Matthew and Daniel would be the absolute value of 30
minus negative 15.5, which is option E.
We now want to try and solve this
expression. The absolute value of 30 minus
negative 15.5. That’s going to be equal to the
absolute value of 30 plus 15.5 because to subtract a negative is to add. 30 plus 15.5 is 45.5. And the absolute value of 45.5 is
We can use our diagram to check and
see if this makes sense. To get from Daniel to Matthew, you
would travel from Daniel’s elevation to sea level, which is 30 metres. And then, you would travel from sea
level to Matthew’s elevation, which is 15.5 metres for a total change in elevation
of 30 metres plus 15.5 metres, which is 45.5.