Signed Addition & Subtraction
- K Redmond
Addition and subtraction with signed numbers tends to be an area where a lot of students get tripped up. Questions frequently include "is this a negative sign or a minus sign?", and "am I adding or subtracting here?" These are all very valid questions that can be boiled down to a few rules. First, forget the idea of "plus and minus". What we really want to look at is the sign of the two numbers involved. Remember that the sign of any given number is what is immediately to the left of that number. For instance, with 4 - 6, the two numbers given are positive 4 and negative 6. Forget the idea of minus! If the signs of the numbers are the same, meaning both positive or both negative, we add the absolute value of the two numbers (essentially ignoring the signs at first), and always keep the sign. If the signs of the two numbers are different, meaning one is positive and one is negative, we subtract the absolute value of the smaller from the absolute value of the larger (essentially ignoring signs: larger - smaller) and keep the sign of the larger number. It can be helpful to remember that in either case, we always keep the sign of the larger number. In the case of signs being the same, whichever number's sign is kept will be correct, but to keep it simpler we'll just take the sign of the larger. The last big rule. If there are two negative signs next to each other with no number between, they become a single plus sign. For example, 4 - (-6) can be instead thought of as 4 + 6. One last thing. 0 is considered neither positive or negative. When adding or subtracting 0, the other number involved will not change. The app below shows more detail. Click the check boxes to show different problems.
Below is an applet to practice on your own. For every incorrect answer, a new hint will appear to help guide you on your way. Try and get 5 in a row correct!