SOLUTION: If a and b are any real numbers such that 0 < a < 1 < b, which of the following must be true of the value of ab ? F. 0 < ab < a G. 0 < ab < 1 H. a < ab < 1 J. a < ab < b K.

Algebra ->  Real-numbers -> SOLUTION: If a and b are any real numbers such that 0 < a < 1 < b, which of the following must be true of the value of ab ? F. 0 < ab < a G. 0 < ab < 1 H. a < ab < 1 J. a < ab < b K.      Log On


   

Question 324930: If a and b are any real numbers such that 0 < a < 1 < b, which of the following must be true of the value of ab ?

F. 0 < ab < a
G. 0 < ab < 1
H. a < ab < 1
J. a < ab < b
K. b < ab


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
0+%3C+a+%3C+1+%3C+b
Multiply all terms by b since b%3E1
0+%3C+ab+%3C+b+%3C+b%5E2
Since b%3E1, then ab%3Ea so then,
0+%3C+a+%3C+ab+%3C+b+%3C+b%5E2
Given that,
F. 0+%3C+ab+%3C+a, Never true
G. 0+%3C+ab+%3C+1, Not always true
H. a+%3C+ab+%3C+1, Not always true
J. a+%3C+ab+%3C+b, True
K. b+%3C+ab, Never true