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