Question

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

Answer 1

\[
\begin{align}
a+b&={11\over12}\\
ab&={1\over6}\\
a\left({11\over12}-a\right)&={1\over6}\\
11a-12a^2&=2\\
12a^2-11a+2&=0\\
12a^2-8a-3a+2&=0\\
(4a-1)(3a-2)&=0\\
\end{align}\\
\boxed{a={1\over4}}\qquad\boxed{b={3\over2}}
\]

Answer 2

x + y = 11/12
xy = 1/6 = 24/144

x = 8/12 = 2/3
y = 3/12 = 1/4

(3/12) or (1/4) is the lesser of the two fractions.

Answer 3

Good work! Thanks to both of you