The sum of two fractions is $\frac{11}{12}$ and their product is $\frac{1}{6}$. What is the lesser of the two fractions? Express your answer

Sum  = 11/12

Product  =1/6 =  2/12

a*b =  2/12      (1)

a + b =  11/12      b = 11/12 - a     (2) 

Sub (2)  into (1)

a ( 11/12 - a)  = 2/12     

(11/12)a  - a^2  = 2/12       multiply through by 12 and rearrange  as

12a^2 - 11a + 2a  =   0       factor

(4a - 1 )  ( 3a  - 2)  = 0          set each factor to 0  and solve  for  a

4a - 1  =  0                3a - 2   = 0

4a  = 1                       3a  =  2

a = 1/4                         a  = 2/3

Lesser of two  fractions is   1/4