When adding positive integers, the process is straightforward: 1 + 1 = 2. But subtracting two positive integers where the larger is being subtracted from the smaller will yield a negative result. It is sometimes hard for kids to grasp the concept of negatives, especially subtracting a negative. When you subtract a negative, you add, and this doesn't seem like it should work. Suppose you have a six-pack of soda, and only three slots are full. If you fill the three empty spaces, you are subtracting -3 -- that is, filling the empty space by adding three sodas.
Another way to remind students that they add when subtracting a negative integer is to say two minuses make a plus. A plus sign (+) is formed when you put two negative signs (-) together, so 3 - (-3) = 6. Adding a negative is simpler to grasp. 3 + (-2) = 1. You subtract the two from the three. In the soda example, you have three sodas, and you are adding two empty spaces, so that means you will only have one soda left when two of the slots are emptied. When the negative is higher than the positive number, the result will be negative. 3 - 4 = -1. You had three sodas, you took them all away, but you still have one empty space left over.
Absolute value is always positive. The number in the absolute value brackets, or pipes, whether it is a positive or negative number, will have a positive absolute value. An example of an absolute value equation is I-4I + 3 = 7. So even though the 4 is negative, you are taking the absolute value of -4, which is positive. If there is a negative sign outside the brackets, you find the absolute value first, and add the negative sign second. So -I-4I would be -4.
Once the basics of adding and subtracting positive and negative integers are understood, students can use these concepts to determine the missing number in an equation. If the equation is 45 + ? = 80, the principles of addition and subtraction can lead students to the missing number. If 45 plus a number is 80, then 80 minus the number should be 45. Subtract 45 from 80, and the missing number is shown to be 35. The 35 can be plugged into the original equation to check: 45 + 35 = 80.