[tex]\frac{34}{52} : \frac{18}{144} =[/tex]
[tex]\frac{\frac{34}{52}}{\frac{18}{144}} =[/tex]
[tex]=\frac{34\cdot \:144}{52\cdot \:18}[/tex]
[tex]=\frac{34\cdot \:8}{52}[/tex]
[tex]=\frac{2\cdot \:17\cdot \:8}{52}[/tex]
[tex]=\frac{2\cdot \:17\cdot \:8}{2\cdot \:26}[/tex]
[tex]=\frac{17\cdot \:8}{26}[/tex]
[tex]=\frac{136}{26}[/tex]
[tex]=\frac{2\cdot \:68}{26}[/tex]
[tex]=\frac{2\cdot \:68}{2\cdot \:13}[/tex]
[tex]=\frac{68}{13}[/tex]