Kezia Posted November 10, 2021 Share Posted November 10, 2021 Reciprocal of 2 and 4/5; well convert to improper fraction 14/5 = 5/14 is the reciprocal. Ok easy but... The kid forgot to convert the mixed number to get the reciprocal. So to muscle his way through he knows the reciprocal is: what number do you multiply this number by to get 1? Since 2 and 4/5 is the same as 2 + 4/5, he took the reciprocal both 2 and 4/5 and added them so 1/2 + 5/4 = 7/4 So obviously that does not work. So if one forgets that the easiest way is to convert the mixed number to an improper fraction, what is the hard way to get the reciprocal? Quote Link to comment Share on other sites More sharing options...
forty-two Posted November 10, 2021 Share Posted November 10, 2021 Basically, the reciprocal of (2+4/5) is 1/(2+4/5), which, as your student discovered, *isn't* the same as 1/2 + 1/(4/5) - your student forgot the distributive law, there. In the process of working through the complex fraction 1/(2+4/5), step one is turning (2+4/5) into an improper fraction anyway. 2 Quote Link to comment Share on other sites More sharing options...
Kezia Posted November 10, 2021 Author Share Posted November 10, 2021 12 minutes ago, forty-two said: your student forgot the distributive law, there. Yeah I figured something needed distributing. I just always remembered to convert it first but I was more of a procedural student. He figured out the required distribution in the multiplication when he refused to convert the fraction. thank you! Quote Link to comment Share on other sites More sharing options...
Not_a_Number Posted November 11, 2021 Share Posted November 11, 2021 10 hours ago, Kezia said: Reciprocal of 2 and 4/5; well convert to improper fraction 14/5 = 5/14 is the reciprocal. Ok easy but... The kid forgot to convert the mixed number to get the reciprocal. So to muscle his way through he knows the reciprocal is: what number do you multiply this number by to get 1? Since 2 and 4/5 is the same as 2 + 4/5, he took the reciprocal both 2 and 4/5 and added them so 1/2 + 5/4 = 7/4 So obviously that does not work. So if one forgets that the easiest way is to convert the mixed number to an improper fraction, what is the hard way to get the reciprocal? Yeah, I'm not sure there's much of a way without converting it to an improper fraction 😄 . I mean, you can estimate it to do a sanity check... like, 1/4.5 is going to be between 1/5 and 1/4... but you can't really calculate it quickly. Quote Link to comment Share on other sites More sharing options...
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