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In order to compare two fractions, you have to convert them so that they have the same denominator, which is to say, they are the same kind of fraction, whether that is thirds, quarters, fifths, etc. Let's say that I want to compare 2/9 with 1/5. I can make them both into 45ths. Multiply the 2/9 by 5/5 and you get 10/45. Multiply the 1/5 by 9/9 and you get 9/45. Now you can compare, because 10/45 is obvious 1/45 larger than 9/45. In the example given, since both fractions are less than a half, the larger one is closer to a half. If I had two fractions that were both larger than a half, then the smaller one is closer to a half. What if I have a fraction that is larger than a half and another fraction that is smaller than a half, and I want to know which is closer to a half? I would have to convert all 3 fractions (half is also a fraction) so that they have common denominators, then I can easily subtract a candidate fraction from a half, or subtract a half from it, and see which gives the biggest difference.

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Q: How do you know that a fraction is closest to one half?

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