Let’s say we want to figure out what negative 8 minus negative 2 is. There’s a lot of ways to approach this, but we’ll focus on building the intuition with something called number chips. We can represent negative 8 with eight negative number chips: 1, 2, 3, 4, 5, 6, 7, 8.
If we subtract a negative number, we can take away two of these negative number chips. How many negative number chips are we left with? We have 1, 2, 3, 4, 5, 6, so this is going to be negative 6. so this is five minus negative one is equal to positive six
Now let’s up it a little bit and let’s start with something that might seem a little bit intuitive. There are many ways to approach this, but maybe the number chip technique will help build some intuition.
Let’s say we want to figure out 4 minus 7. 4 is a positive number, so I think I’m going to use some positive number chips to represent four. I could represent that as 1, 1, 2, 3, and 4 positive number chips. Now, if I’m taking away seven, I could say I’m taking away a positive 7, which would be equivalent to taking away seven positive number chips. But I don’t have seven positive number chips here, so what could I do?
Well, I talked before that if I have one positive and one negative, they cancel out, so I can add these pairs of positive and negative number chips until I get to seven, so I can then take them away. So I’m going to add a positive and I’m going to add a negative. This is still four because these two cancel out, and I can do that again. My goal is to have seven positive number chips so I can take away a positive seven. I can take away seven positive number chips and I have seven now. So I’m taking away one, two, three, four, five, six, seven. Now, all the positive number chips are gone and all I have left are three negative number chips, so this is going to be negative three.
Let’s do another example. Let’s say that I want to do positive 5 minus negative one. Well, let’s first represent that positive five with five positive number chips, so that’s one, two, three, four, and then five. We’re not taking away a positive number, so we need to have negative number chips in order to take them away. Let’s add one of those pairs, and this is still five because these last two cancel out. Now I can take away a negative one, which is represented by this negative number chip. So if I take that away, I’m now left with one, two, three, four, five, six positive number chips, or that’s just a positive six. So this is 5 minus negative one is equal to positive six.