SOLUTION: When 0 is less than a and a is less than b, is it correct that a over b is less than b over a? Why? 0<a<b a/b < b/a

Algebra ->  Real-numbers -> SOLUTION: When 0 is less than a and a is less than b, is it correct that a over b is less than b over a? Why? 0<a<b a/b < b/a       Log On


   

Question 1120380: When 0 is less than a and a is less than b, is it correct that a over b is less than b over a? Why?
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Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
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When 0 is less than a and a is less than b, is it correct that a over b is less than b over a? Why?
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system%280%3Ca%2Cand%2Ca%3Cb%29

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a%2Fb versus b%2Fa
%28a%2Fb%29%28a%2Fa%29 versus %28b%2Fa%29%28b%2Fb%29
system%28a%5E2%2F%28ab%29%2Ccomparedto%2C+b%5E2%2Fab%29

Both denominators are now the same so you can look at the order for a%5E2 and b%5E2.

Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
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Simply notice that under given conditions  a%2Fb  is less than  1,  while  b%2Fa  is greater than 1.


Hence,  a%2Fb < b%2Fa.


Nothing more and nothing else.