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Q: What are all the fractions less than one half?

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a quarter or one fourth or 0.25 are all the same thing and are thess than one half. But many other nuumbers and fractions are also less than one half.

nothing is less than one third

No, improper fractions (ex: 3/2) are greater than one.

Such a list cannot exist, because there are an infinite number of such fractions.

If you're trying to ask a multiple choice question, you must include the choices in the question so we can help you.

the median is a value of which half of all the values are less than, and half of all the values are greater than.

There are an infinite number of fractions with a value less than 1/2. Some examples are 1/3 1/4 1/5 2/5 1/6 1/7 2/7 3/7 3/8 11212/22425 1/10000090067856 and countless more. Any positive fraction, where the denominator is more than twice the numerator, and all negative fractions as well.

No particular name would encompass 1/2, -1/2, -5/2 all of which are fractions with a less than 1.

Fractions that are less than one are known as proper fractions. Their denominators are greater than their numerators. Their reciprocals would have numerators greater than their denominators, making them improper. Improper fractions are greater than one.

No. There are infinitely many equivalent fractions for any given fraction.

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.

A proper fraction is less than 1. Whenever you multiply something by a number < 1, the result (product) is less than the original number. So when you multiply a proper fraction by a number less one (such as another proper fraction, the product is less than the original proper fraction. The only time a product involving a given number is larger than the given number is when you multiply the given number by a number that is > 1. Since all proper fractions are < 1, products involving them are always less than the original given number.

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