Estimate five-sixths divided by seven-eighths by rounding each fraction to the nearest half.
So if we were to round a fraction to the nearest half, that will either be zero, one-half, or one. And we know that these fractions are less than one because five-sixths is less than six-sixths, which is one, and seven-eighths is less than eight-eighths, which is one. So these fractions are indeed between zero and one.
So we wanna know, if we’re going to round these, are they gonna round to zero, one-half, or one. Let’s begin with five-sixths. If we were to take our number line and cut it into six pieces, we would create sixths.
So we would begin at zero with zero-sixths, then one-sixths, two-sixths, three-sixths, which reduces to one-half, four-sixths, five-sixths, and six-sixths. And we care about the five-sixths. So is five-sixths closer to one-half or one? Well, it’s two spaces away from one-half and it’s only one space away from one. So we will round five-sixths to be one. So we will replace five-sixths with one.
Now we need to look at seven-eighths. So let’s cut our number line into eighths. So here we’ve labeled our eighths. And we care about seven-eighths. So is seven-eighths closer to one-half or one? Well, seven-eighths is three spaces away from one-half and only one space away from one. So it’s closer to one. So we will round seven-eighths up to one. So now we can estimate by rounding, since we rounded each fraction up to one, and one divided by one is one. Therefore, our estimate is one.