Three digit subtraction word problems

There are 461 homes in the part of town where Samir lives. He counted that 352 of those homes are apartments. How many of the homes are not apartments?

So, like always, pause this video and see if you can work through it on your own.

All right, now let's do this together. So we're starting with 461 homes. So we have 461, and we want to know how many are not apartments.

So what we want to do is take out the number that are apartments, and they tell us that 352 of those homes are apartments. So, we'll take out the number that are apartments, and what we're left with is going to be the number that are not apartments.

So we really just have to evaluate 461 minus 352. As we've talked about in other videos, there are many techniques for doing this. We could break apart 352 into the various place values.

So we could say that this is the same thing as 461 minus—let's use different colors—minus three hundreds, or three hundred, minus five tens, or fifty, and then minus 2, and then minus 2 right over there.

Then you might be able to figure out that 461 minus 300, that is going to be—I'm just taking three hundreds from this—so that's going to be 161.

Then if I subtract 50 from that, well what's 61 minus 50? Well, that would be 11. So, 161 minus 50 would be 111.

Another way of thinking about it is if you take these five tens away from these six tens, you'll be left with one ten. So that would be one hundred, one ten, and one one, so you have a hundred eleven.

Then you want to subtract that two. Last but not least, 11 minus 2 would be 9. So, 111 minus 2 would be equal to 109.

But I mentioned there's many other ways that you might try to approach something like this. You could say, "Hey, maybe it's easier to subtract 350, or I should say 50, than 352."

So you could subtract 2 from both of these numbers. If you subtract 2 from 461—if you subtract 1, you get to 460; you subtract 2, you get to 459. 459 minus—you subtract 2 from this, you get to 350.

This is all about the idea that the difference doesn't change as long as you add or subtract the same number to both.

So here, we might say that 400s minus 300s is 100, and then 59 minus 50 is 9. So, we would get the same result. The thing to appreciate is that this is all about subtracting 352 from 461, and that there's multiple ways of calculating this.