Mixed number subtraction

Let's say that we want to figure out what is 7 and 11/12 minus 1 and 6/12. Pause this video and see if you can figure that out.

All right, now let's work on this together. So there's a couple of ways that you could approach this. You can view this as the same thing as 7 plus 11/12 and then minus 1. You might be attempting to say minus 1 and then plus 6/12. But remember, you're subtracting not just the 1; you're subtracting 1 and you're subtracting 6/12. So minus 1, minus 6/12.

Now why is that useful to think about it that way? Well, now you can think about the whole number. So you could say this is going to be 7 minus 1 plus 11/12 plus 11/12 minus 6/12 minus 6/12. So 7 minus 1 is 6, so it's going to be 6 plus...

Now, if I have 11 of something, in this case twelfths, and I'm subtracting six of them away, six of the twelfths, I'm going to be left with five of those somethings, five twelfths. So it's going to be 6 plus 5/12, which is the same thing as 6 and 5/12.

Now, as you get more used to this, you could do some of this maybe even in your head. You could say, "Hey, look at the whole number parts. 7 minus 1 is going to give me 6," and then if I say 11/12 minus 6/12 is going to give me 5/12. So that takes up a little bit less base.

Another way that you might see this approached is you could rewrite this as 7 and 11/12 minus 1 and 6/12. Let me do the 6/12 in that blue color that I'm using for the fraction parts: 6/12. Then I would first focus on the fractional parts and I say 11/12 minus 6/12 is 5/12, and 7 minus 1 is 6, and I got 6 and 5/12.

So many different ways to approach the same thing, and at the end of the day, there really are the same underlying idea.