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Brian ran three and three-eighths miles along the river.
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Determine the number of miles that he ran rounded to the nearest half mile.
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Well to start off, we can see that he ran three and a bits mile, so somewhere between three miles and four miles.
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Now we’ve gotta round to the nearest half mile; so we gotta split this into halves.
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So the option we’ve got is three and a half miles in between.
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Now let’s think about it.
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Brian ran three whole miles plus some fraction of a mile — three-eighths of a mile.
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So we’ve got to fit three and three-eighths on that scale; but we’ve got three, three and a half, four.
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Does it go to the left of three and a half?
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Or does it go to the right of three and a half?
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Is it nearer to three, three and a half, or four?
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Well, our job will be made a lot easier if this number instead of saying three and a half it was three and a certain number of eighths.
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So what is a half in terms of eighths?
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Well, if I multiply the denominator by four and I multiply the numerator by four, a half is equivalent to four-eighths.
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So another way of writing three and a half is three and four-eighths; now that makes life a little bit easier.
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Three and three-eighths is clearly to the left of three and four-eighths.
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So we just need to determine now is it closer to three and no eighths or just three or three and four-eighths.
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Well, the distance between three and three-eighths and three and four-eighths is one-eighth, and the distance between three and three-eighths and three is three-eighths.
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So that means it’s nearer to three and four-eighths or three and a half then it is to just three.
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So our options were three and no half miles, three and one half miles, or four and no half miles.
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And we’ve discovered that three and three-eighths is closer to three and a half than it is to three and no halves or to four and no halves.
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So our answer is three and a half miles.