Subtracting a negative integer from a positive integer

The addition algorithm from 3a: Adding and subtracting with positive integers gives us a way to subtract a negative integer from a positive integer. For example, to solve 83 – (–47), write 83 – (–47) = 83 + 47 and use the addition algorithm to obtain the answer 130. More generally, A – (–B) = A + B.

Adding a negative integer to a positive integer

The subtraction algorithm from 3a: Adding and subtracting with positive integers gives us a way to add a negative integer to a positive integer. For example, to solve 83 + (–47), write 83 + (–47) = 83 – 47 and use the subtraction algorithm to obtain the answer 36. More generally, A + (–B) = A – B.

Adding a positive integer to a negative integer

The subtraction algorithm from 3a: Adding and subtracting with positive integers gives us a way to add a positive integer to a negative integer. For example, to solve –47 + 83, write –47 + 83 = 83 – 47 and use the subtraction algorithm to obtain the answer 36. More generally, –A + B = B – A.

Subtracting a larger integer from a smaller integer

What if we’re subtracting a larger integer from a smaller integer, for example, 47 – 83? In this case, write 47 – 83 = –(–47 + 83) = –(83 – 47) and use the subtraction algorithm to calculate 83 – 47 = 36. Then –(83 – 47) must be –36, so 47 – 83 = –36. More generally, A – B = – (B – A).

Adding and subtracting with positive and negative integers

The following two tables summarize the various possibilities for adding and subtracting with positive and negative integers.

The video below works through some examples of adding and subtracting with negative integers.