Calculations with Negative Numbers

The introduction of negative numbers can become a very confusing concept for some people. The thought of something less than zero or nothing is hard to see in real terms.  For those that find it hard to understand, lets take a look at this in a manner that may be easier to understand. Consider a question such as -5 ? -12.  What is ?.  The basic math is not hard but for some, the answer would appear to be 7. Others may come up with 17 and sometimes even -17.  All these answers have indications of a slight understanding of the concept, but they are incorrect.   We can look at a few of the practices that are used to help with this concept. The first example comes from the financial view.   Consider This Scenario You have 20 dollars but choose to purchase an item for 30 dollars and agree to hand over your 20 dollars and owe 10 more.  Thus in terms of negative numbers,  your cash flow has gone from 20 to -10.  Thus  20 - 30 -10.  This was displayed on a line, but for financial math, the line was usually a timeline, which added complexity above the nature of negative numbers.   The advent of technology and programming languages has added another way to view this concept that may be helpful for many beginners.  In some languages, the act of modifying a current value by adding 2 to the value is shown as   Step 2.  This works nicely with a number line.  So lets say we are currently sitting at -6.  To step 2, you simply move 2 numbers to the right and arrive at -4.  Just the same a move of Step -4 from -6 would be 4 moves to the left ( signified by the (-) minus sign.One more interesting way to view this concept is to use the idea of incremental movements on the number line.  Using the two terms,  increment- to move to the right and decrement- to move to the left,  one can find the answer to negative number issues.  An example:  the act of adding 5 to any number is the same as increment 5.  So should you start at 13,  increment 5 is the same as moving up 5 units on the timeline to arrive at 18. Starting at 8,  to handle -15,  you w ould decrement 15 or move 15 units to the left and arrive at -7.   Try these ideas in conjunction with a number line and you can get over the less than zero issue, a step in the right direction.