Q:

Fraction Problem

The product of two fractions is 1/9. The larger fraction divided by the smaller fraction is 4. What is the sum of the two fractions?
$\frac{a}{b}\frac{c}{d}=\frac{1}{9}$
I will assume that $\frac{a}{b}>\frac{c}{d}$
I'm trying to find $\frac{a}{b}+\frac{c}{d}=?$
I keep getting stuck. Any help would be great!

A:

Just call them $x,y$. Then $xy=\frac 19,x/y=4$

A:

$ab = \frac{1}{9}, a/b=4, a>b$.
We can obtain $a = \frac{2}{3}, b = \frac{1}{6}$ or $a = -\frac{2}{3}, b = -\frac{1}{6}$.
$a>b$, therefore, $a+ b = \frac{5}{6}$.

A:

There's a thing called computational algebra? Isn't all algebra computational?
And as for this problem,
$$ \frac{a}{b} \cdot \frac{c}{d} = 1/9.$$ 
$$ \frac{ad}{bc} = 4.$$
$ad=4bc$; $a=\dfrac{4bc}{d}$
$\dfrac{4c}{d} \cdot \dfrac{c}{d} = 1/9$
$\dfrac{c}{d} = \sqrt{1/36} = 1/6$
$bc=\dfrac{ad}{4}; c=\dfrac{ad}{4b}$
$\dfrac{a}{b} \cdot \dfrac{a}{4b} = 1/9; \dfrac{a}{b}=\sqrt{4/9}=2/3$
$\text{Sum} = 2/3 + 1/6 = 5/6$.
$%I'm new to MathJax so I don't know how to put that in a nice mathematical format.$

