Fourth Edition, Guide 3 Inequalities, pg 101, Q9

[saurabhbanerjeeiimk]

The questions reads as " If a2b >1 and b<2, which of the following could be the value of a?

A 1/2
B 1/4
C -1/2
D -2
E 2/3

I went through the explanation and it reads that "1 divided by a positive number less than 2 is greater than 1/2"

Can we take this as a general rule?

Example

1/LT3 = GT 1/3
Similarly 1/LT13 = GT 1/13

[zdgura]

This seems to be echoing the rule that as we decrease denominators proper fraction increase. So I would say so. Take your example 1/13 less than 1/12, 1/11 and so forth....

[NMencia09]

Yes this is a general rule as long as the denominator is positive.

If the numerator stays the same and the denominator decreases to a smaller positive number, then the value of the fraction will increase.

a=2, b=3

a/b: If you decrease b, the fraction increases as long as b is positive. If b turns negative, then the more negative it gets, the larger it gets, assuming b is an integer.

a=2, b= -1 vs. a=2, b= -3
a/b = -2 a/b = 2/-3 ===> -2/3 > -2

Here, the fraction increases as b gets smaller.

[jnelson0612]

Great answers--thanks for your help!