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gamow99

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In summary, the conversation discusses fractions, specifically 2/5 and 4/10, and the concept of irreducible fractions. The speaker explains that 2/5 cannot be simplified further without converting the integers into decimals and expresses uncertainty about the correct term for an irreducible fraction. Another example is given, and the speaker clarifies that "irreducible" is the appropriate term, without the addition of "form." The conversation also touches on the definition of a rational number as an equivalence class of fractions, and the criteria for a fraction to be considered irreducible. The speaker expresses gratitude for the help given.

- #1

gamow99

- 71

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I would just call the fraction 'irreducible', ie I would say 2/5 is an irreducible fraction and 4/10 is not (we could say it is a 'reducible fraction'). I would not bother adding 'form' because in common usage a fraction is a representation of a (rational) number, rather than a number itself. So that 2/5 and 4/10 are different fractions, both of which represent the same rational number.

Set theoretically, it is convenient to define a rational number as an equivalence class of elements of ##\mathbb Z\times\mathbb N##, under the equivalence relation ##=_{\mathbb Q}## such that ##(a,b)=_{\mathbb Q} (c,d)## iff ##a/b=c/d##. The equivalence class is a*rational number*. The elements of the equivalence class are *fractions*, where the fraction ##(a,b)## is formally written as ##\frac ab##, and that fraction is irreducible iff the greatest common factor of ##a## and ##b## is 1.

Set theoretically, it is convenient to define a rational number as an equivalence class of elements of ##\mathbb Z\times\mathbb N##, under the equivalence relation ##=_{\mathbb Q}## such that ##(a,b)=_{\mathbb Q} (c,d)## iff ##a/b=c/d##. The equivalence class is a

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- #3

gamow99

- 71

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Thanks. I appreciate you taking the time to help me out.

A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number). In other words, the value of the fraction is less than one.

An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). In other words, the value of the fraction is equal to or greater than one.

A mixed fraction is a combination of a whole number and a proper fraction. It is written in the form of a whole number and a proper fraction separated by a plus sign, such as 3 1/2.

A unit fraction is a fraction where the numerator is one and the denominator is a positive integer. It represents one part of a whole unit or group.

An equivalent fraction is a fraction that has the same value as another fraction, but has a different numerator and denominator. This can be achieved by multiplying or dividing both the numerator and denominator by the same number.

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