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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.

 Mar 27, 2020
 #1
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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

 

 

cool cool cool

 Mar 27, 2020

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