Pros and Cons
If p is a positive integer and q is a negative integer, which of these expressions is the greatest?
Age
14 to 16
Challenge level
Problem
If $p$ is a positive integer and $q$ is a negative integer, which of the following is the greatest?
$p-q$ $q-p$ $p+q$ $-p-q$
Student Solutions
Answer: $p-q$
Trying out numbers
Imagine $p = 5$ and $q = -2$
$p - q = 5 - -2 = 7$
$q - p = -2 - 5 = -7$
$p + q = 5 + -2 = 3$
$-p - q = -5 - -2 = -3$
Using positives and negatives
$p$ is positive so use $+p$ (not $-p$)
$q$ is negative so subtract $q$
$p-q$ will be the greatest.