The sum of two fractions is 11/12 and their product is 1/6. what is the lesser of the two fractions

X+y=11/12
xy=1/6

x+y=11/12
minus x both sides
y=11/12-x
sub that for y
x(11/12-x)=1/6
11/12x-x^2=1/6
times -1
x^2-11/12x=-1/6
add 1/6 both sides
x^2-11/12x+1/6=0
use quadratic formula
for
ax^2+bx+c=0
x=
a=1
b=-11/12
c=1/6

x=
x=
x=
x=
x=
x=
x=(11/24)+/-(5/24)
x=(11+/-5)/24
x=(16/24) or (6/24)
x=(2/3) or (1/4)
the numbers are 2/3 and 1/4
2/3*1/4=2/12=1/6
2/3+1/4=8/12+3/12=11/12
the smaller number is 3/12 or 1/4

smaller number is 1/4