The sum of two fractions is 11/12 and their product is 1/6. What is the lesser of the two fractions? Express your answer as a common fraction.
+128407 We have this system
a + b = 11/12 ⇒ b = 11/12 - a (1)
ab = 1/6 (2)
Sub (1) into (2)
a ( 11/12 - a) = 1/6 simplify
(11/12)a - a^2 = 1/6 rearrange as
a^2 - (11/12) a + 1/6 = 0 multiply through by 12
12a^2 - 11a + 2 = 0 factor as
(4a - 1) (3a - 2) = 0
Set each factor to 0 and solve for a and we have that
a =1/4 b = 2/3
So the lesser fraction is 1/4 and the greater is 2/3
