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 as a common fraction.
Please include an explanation. Thanks so much!
+421 Let the fractions be x and y. Then, we have that x + y = 11/12 and xy = 1/6. We also have that y = 11/12-x, so x(11/12-x) = 1/6. Thus, 6x(11/12-x) = 1, and 66x/12 - 6x^2 = 1. Simplifying, 11x/2 - 6x^2 = 1, and we have a quadratic that we can solve with the quadratic formula, getting x = 1/4 or 2/3. Thus, the lesser fraction is 1/4.
+421 Let the fractions be x and y. Then, we have that x + y = 11/12 and xy = 1/6. We also have that y = 11/12-x, so x(11/12-x) = 1/6. Thus, 6x(11/12-x) = 1, and 66x/12 - 6x^2 = 1. Simplifying, 11x/2 - 6x^2 = 1, and we have a quadratic that we can solve with the quadratic formula, getting x = 1/4 or 2/3. Thus, the lesser fraction is 1/4.
