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Q: What fraction is larger than a half?

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a half

1/2 is larger than 2/5

A proper fraction is a fraction who's numerator is smaller than the denominator. An improper fraction is a fraction who's numerator is larger than or equal to the denominator. 1/2 is a proper fraction. 3/2 is an improper fraction. Now to understand why the improper fraction is larger than the proper fraction, lets split them up. The proper fraction is one half of a whole, whereas the improper fraction is one whole and one half. Basically the proper is one half, and the improper is three halves. In theory, a proper fraction is always less than the whole number under consideration. On the other hand, an improper fraction is either equal to or larger than the whole number under consideration.

A fraction can be larger than 1, for example, 4/2 is a fraction (which can be simplified to 2). Only a fraction that is larger than 1, multiplied by another number gives you a larger number.

Three fifths is larger.

A kilogram is larger than a pound, so half a kilogram is larger than half a pound.

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.

an improper fraction

if the number above the bottom number is smaller than half of the bottom number, the fraction is less than half. For example, say the fraction is 3/8, half of the bottom number is 4. 3 is smaller than 4 therefore the fraction is less than half.

The quotient is larger than the original fraction.

Proper fraction

An improper fraction.

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