Properties of fractions 2

Algebra Level 3

Given that, 0< a b \frac{a}{b} <1

and b 0 b \neq 0

what is always true?

b<a a<b 1< b a \frac{b}{a} ab=1

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1 solution

Bar Kam
Jan 16, 2019

This problem doesn't state any limitations on the variables a and b.

There are two scenarios to consider,

Scenario 1: a and b are both positive , in that case a<b

Scenario 2: a and b are both negative , in that case a>b

but the common between those is that no matter the sign b a \frac{b}{a} <1 will always be true.

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