# Rules for Adding and Subtracting Integers

When adding two positive integers together, you will always get a positive result. When adding negative integers, you will always get a negative result. When adding a positive integer to a negative integer, you will need to subtract the number with the smaller absolute value from the number with the larger absolute value, keeping the sign of the number with the larger absolute value in your result. When subtracting a positive integer from a negative integer, you will need to change it to an addition problem and change the positive integer to a negative integer.

## Adding and Subtracting Integers

When adding 2 positive integers together the rules are simple, you add them, and you will always get a positive result. 3 plus 4 is 7. When adding 2 negative integers together, you add them the same as you do when they are positive, but then you change the sign to negative, since they’re both negative.

3 plus 4 is 7. Since both of these numbers are negative, our result is negative. When you’re adding 2 integers with different signs, you’re going to subtract. You’re going to subtract the number with the smaller absolute value, so in this case 5, from the number with the larger absolute value, In this case 7, and then you’ll keep the sign of the number with the larger absolute value.

Let’s try it. 7 minus 5 is 2, and since negative 7 has a larger absolute value and it’s negative, the result is also negative. When you’re subtracting, you can change a subtraction problem to an addition problem, and then follow the same rules you do for addition.

To change this to an addition problem you’re going to first change subtraction to addition, and then we’re going to reverse the sign on the second term, so this 2 becomes a negative 2. Notice that (or note that) minus 2 and negative 2 are the same. Now that we’ve changed subtraction to an addition problem, we’re going to follow the same rules we did when we were adding 2 negative integers together. Since these have the same signs, they’re both negative, we’re going to add them together, 5 plus 2 which is 7, and then since they’re both negative, our result is negative.