Video: Determining the Improper Fraction/Mixed Number That Is Closest to a Certain Whole Number

Victoria jogged for 21/8 miles on Monday, 21/10 miles on Tuesday, and 2 4/5 miles on Wednesday. Determine the day on which she jogged for a distance that is the closest to 2 miles.

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Video Transcript

Victoria jogged for twenty-one eighths miles on Monday, twenty-one tenths miles on Tuesday, and two and four-fifth miles on Wednesday. Determine the day on which she jogged for a distance that is closest to two miles.

Let’s break down our days: Monday twenty-one eighth miles, Tuesday twenty-one tenths miles, and Wednesday two and four-fifths miles. Let’s take each of these values and round them to the nearest whole number, starting with Monday.

We want to take this fraction and break it into two pieces. twenty-one eighths can become sixteen-eighths and five-eighths. We now take these two pieces, sixteen-eighths plus five-eighths, and convert them to a mixed number. 16 over eight is equal to two. Five-eighths is already in its most simplified form. A mixed number for how far Victoria jogged on Monday is two and five-eighths.

We can follow the same process for Tuesday. twenty-one tenths can be broken into twenty tenths plus one tenth. 20 over 10 is equal to two, and one tenth is already in its most simplified form. On Tuesday, Victoria jogged two and one tenth miles. The distance Victoria ran on Wednesday is already given to us as a mixed number, two and four-fifths.

We now need to take each of these mixed numbers and round them to the nearest whole number. Two and five-eighths is larger than two and a half. And that means the nearest whole number to two and five-eighths is three. Two and one tenth is less than two and a half. Two and one tenth rounds down to two. Two and four-fifths is more than two and a half, rounded to the nearest whole number would be three. Two and four-fifths is closer to three than it is to two. Only one of these values rounded to the nearest whole number was equal to two miles. On Tuesday, Victoria jogged for a distance that is closest to two miles.

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