Missing numbers in three digit subtraction

Let's say that we are told that 495 is equal to 621 minus blank. What would blank be? Pause this video and see if you can figure that out.

Okay, now let's do this together. One technique is to try to visualize this on a number line. 495 is what you get when you subtract something from 621. So let me put those two numbers on a number line. So let me do the number line like this. We're going to start at 621 and subtract blank to get to 495.

So if this is 621, we're going to subtract some amount to get to 495. So let's say this right over here is 495. Now, what amount did we subtract? Here we are subtracting blank—that's my blank over there—and so we need to figure out what that is.

So how do you go from 621 to 495? Well, one way that my brain does it, first we can subtract 21 to get to 600. So let me do minus 21, which would get us to 600. Then we could subtract another 100 to get to 500. So then we could subtract another 100, so minus 100 to get us to 500.

Then to go from 500 to 495, we would subtract another 5. So to go from 621 to 495—and I picked these numbers intentionally—I picked 21 to subtract to get to 600, I picked 100 to get to 500, and then I picked 5 to get to 495.

I subtracted a total of 21, then I subtracted 100, and then I subtracted 5. So I subtracted 100, I subtracted 21, and I subtracted 5. So how much did I subtract in total?

Let me put it this way: this is the same thing as 621 minus these things that's equal to 495. So in total, let's see, if I subtract 21 and I subtract 5, that is subtracting 26. And so I subtracted 126.

So I subtracted a total of 126. So 495 is equal to 621 minus 126.

Let's do another example. Let's say we want to figure out if someone tells us blank minus 435 is equal to 210. What is blank in this situation? Well, this is a little bit different now because now we're not trying to figure out what to subtract from the larger number. In this situation, we're trying to figure out the larger number— the larger number minus something is equal to 210.

But as always, it's useful to draw this on a number line just to make sure we're thinking about things in a reasonable way. So we're going to start at blank, take out 435, and then we're going to get to 210.

So we're starting here—maybe I'll put a question mark there so we know that point we're starting there. We are subtracting 435, so that's minus 435, and we are getting to 210.

So to figure out blank, we could go the other way around. We could start at 210 and then just add 435. So what's 210 plus 435? Well, there's many ways of doing it, but I encourage you to pause this video and see if you can work that out.

One way to do it is first we can add 400—I'll do this in another color just for a little bit of a variety. So first I'll add 400. If I add 400 to that, that would get us—let's see—if you had 400 to that, that would get you to 610.

Then if I add 30 to that, so if I add plus 30—and I haven't drawn it exact but this is just to help us think about things—that's three more tens. I already have one ten, so 10 plus 30 is 40, so that gets us to 640.

Then I'm going to add the 5. So this right over here, if I add 5 to it, is 645. So there you have it—645 minus 435 is equal to 210.