The Purplemath Forums

http://www.purplemath.com/modules/setnotn.htm I think the definition of a 'fraction' raises some ambiguity: what is a fraction in terms of what can be defined by \mathbb{Q} ? All integers can be placed in a fraction, 2\over1 . \mathbb{Z} = \mathbb{Q} ? Decimals can convert to fractions, are they de...

Thanks for your responses, Any value which can be expressed as a ratio of integers will belong in \mathbb{Q} . This clarifies it for the most part, just one thing: recurring non-repeating decimals can't accurately be placed in a fraction, would these be exceptions or would they be included in \mathb...

I see, thanks!

hmm, I saw a button on here to mark the thread as "solved" before but it seems to have disappeared...

I understand the numerical ones, but am having trouble with the variable ones... It works in theory, and I can see how it would work, but when I substitute numbers for the variables, it doesn't work: x = 2, y = 3 This was the expression: x 2 y 3 +xy 4*27+6 = 114 This was the answer: xy(xy 2 + 1) 6(2...

I understand the numerical ones, but am having trouble with the variable ones... It works in theory, and I can see how it would work, but when I substitute numbers for the variables, it doesn't work: x = 2, y = 3 This was the expression: x 2 y 3 +xy 4*27+6 = 114 This was the answer: xy(xy 2 + 1) 6(...

To find the least common denominator of {2 \over 3a}+{4 \over a^2} the book I'm reading says to multiply them to get a common denominator of 3a^2: {2a \over 3a^2}+{12 \over 3a^2} = {2a+12 \over 3a^2} But wouldn't it be more efficient to find the square roots of the second fraction before multiplying...

Oh, I see now... Thought I could cheat my way through and remove the exponent by squaring, guess not! Thanks for your help, and the link, although my problem wasn't LCM/GCF here :P Edit: I just noticed you moved this thread, sorry for posting in the wrong area, arithmetic's description listed fracti...