Regrouping whole numbers
We have 4,5000 equals 3 thousands plus how many hundreds, question mark hundreds? So let's write this left-hand side, but I'm going to write it out in terms of thousands and hundreds. So I'll write the thousands in orange. So this is equal to 4 thousands, which is the same thing as just 4,000, plus 500, which you could also view as 5 hundreds. So this is the left-hand side. Now let's look at the right-hand side. We have 3 thousands. So it's 3 thousands. Now let's not even look at this right now. Let's just think about what do we have to add to this right-hand side in order to get the same thing that we have on the left-hand side? Well, if you compare the 3,000 and the 4,000, you see you have an extra 1,000 over here. So let's add an extra 1,000 on the right. So we're going to add one extra 1,000. And now we just have 3,000 plus 1,000. This makes it the 4,000. But then, of course, we also need another 500. So we're going to need plus a 500 right over here. So in order for these two things to be equal, we need to say 4,000 plus 500 is equal to 3,000 plus 1,500. Now, the way they've set this up, we need to express-- so it almost looks the same. On the left-hand side, this is 4,500. So this right over here, this is the same thing as 4,500. This is this right over here. And on the right-hand side, we have 3 thousands. So that's this right over here. That's the 3 thousands. And then we just need to express this as hundreds. So 1,500, this is the same thing as 15 hundreds. So let's rewrite everything. We can rewrite this as saying 4,500, just to get the exact same form that they wrote it over there. So we could write 4,500 is equal to 3 thousands plus-- now we have to just write this in terms of hundreds. Well, This is 15 hundreds. Literally, if you took 15 times 100, it's going to be equal to 1,500. So this could be viewed as 15 hundreds, so plus 15 hundreds. So in this situation, the question mark is equal to 15.