Decimal multiplication with grids | Multiply Decimals | 5th grade | Khan Academy

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. 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. This whole square is a whole. Now, let's first think about what's going on with this three tenths. They've labeled the three tenths as three of these vertical bars right over here. We could view the three tenths as these three vertical bars, and then they also have this seven tenths, which are seven of these horizontal bars.

Notice each of those bars are a tenth 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, six, and seven. 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. One way to think about that is the overlap is going to be three tenths times seven tenths. You could view this overlap, let me just in another color right over here, this overlap right over here, you could view that as seven tenths of the three tenths or three tenths of the seven tenths or seven tenths times three tenths.

So we immediately know it's going to be either this choice that has three tenths times seven tenths or this choice that has three times three tenths times seven tenths. 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 and three in this direction.

I could count them, but we have 21 squares here. Each of those squares are what fraction of the whole? Well, each of those squares are now one hundredth of the whole because this is now a 10 by 10 grid. Each of those is one hundredth.

So in the overlap, we have 21 of these squares. That's 21 hundredths. So 21 hundredths is 0.21. That's the same thing as 21 over 100, which is this choice right there, and we're done.