# Pros and Cons

If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

## 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.