Question

(0,(3)+1,(3):7/9):(1+1/12)^2=

Answer 1

$(0,(3)+1,(3): \frac{7}{9}) :(1+ \frac{1}{12} )^2=?$

$=( \frac{3}{9} + \frac{13-1}{9} :\frac{7}{9} ): (\frac{12+1}{12} )^2$

$=( \frac{3}{9} + \frac{12}{9} * \frac{9}{7}): \frac{13^2}{12^2} }$

[tex]=( \frac{3}{9}+ \frac{12}{7} )* \frac{144}{169} [/tex]

$=( \frac{1}{3} +\frac{12}{7} )* \frac{144}{169}$

$= \frac{7+36}{21} * \frac{144}{169}$

$= \frac{43}{21} * \frac{144}{169}$

$=\frac{43*48}{7*169}$

$= \frac{2064}{1183}$

Answer 2

Transformam in fractii oridinare.
0.(3)=1/3
1.(3)=4/3

(1/3+4/3)/7/9 / (12/12+1/12)^2=
(5/3*9/7)/(13/12)^2=
(15/7)/ 169/144=
15/7*144/169
2160/1183