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Must a mixed number be converted to improper fraction to get reciprocal?


Kezia
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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? 

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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. 

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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!

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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. 

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