Question

express 0.6+0.7 bar+0.47bar in the form p/q where p,q are co-prime integers and q is not equal to 0.

Answer 1

0.6=$\frac{6}{10}$=$\frac{3}{5}$

Let x = 0.77...
∴10x = 7.77..
    - x = 0.77..
⇒ 9x =  7
⇒   x = $\frac{7}{9}$

Let x = 0.4747...
∴100x = 47.47...
        x =  0.47...
⇒ 99x = 47
⇒     x = $\frac{47}{99}$

∴addition
= $\frac{3}{5}$ + $\frac{7}{9}$ + $\frac{47}{99}$
= [Do simple lcm and addition of fractions]
= $\frac{385+235+297}{495}$
=$\frac{917}{495}$
I think this is the answer.