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