Decimal multiplication with grids

- [Instructor] So we're told the entire figure is one whole. So that is this entire square right over there. And then they ask us which multiplication equation best represents the figure. And so we're supposed to choose one of these four right over here. So pause this video, try it on your own before we work through it together. All right, now let's work through it together. So this whole square is a whole, and now let's first think about what's going on with this 3/10. So they've labeled the 3/10 as three of these vertical bars right over here. We could view the 3/10 as these three vertical bars. And then they also have this 7/10, which are seven of these horizontal bars. And notice each of those bars are 1/10 of the whole. So we have seven of these horizontal bars. If that doesn't look like seven bars, let me just draw it this way. So that's one, two, three, four, five, six, and seven. And of course we see something similar with these vertical bars. That's one, two, and three. Now what's going on here is we're looking at where these bars overlap. And one way to think about that is the overlap is going to be 3/10 times 7/10. You could view this overlap... Let me do this in another color right over here. This overlap right over here. You could view that as 7/10 of the 3/10 or 3/10 of the 7/10 or 7/10 times 3/10. So we immediately know it's going to be either this choice that has 0.3 times 0.7 or this choice that has 0.3 times 0.7. But let's see what this should be. Well, when we look at that overlap, we get 21 of these squares, because we have seven in this direction, three in this direction. I could count them, but we have 21 squares here. And each of those squares are what fraction of the whole? Well, each of those squares are now 1/100 of the whole because this is now a 10 by 10 grid, each of those is 1/100. So in the overlap we have 21 of these squares, that's 21/100. So 21/100 is 0.21. That's the same thing as 21/100, which is this choice right there. And we're done.