Question

Calcule a fração geratriz para:
a) 1,333… b) 0,078 c) 12,3484848…
d) 4,4444….

Answer 1

$a) \: \frac{3}{9} + \frac{1}{1} \\ mmc = 9 \\ \frac{3}{9} + \frac{9}{9} = \frac{12}{9} ^{ \div 3} = \frac{4}{3}$

$b) \: \frac{078 - 0}{990} = \frac{78}{990} ^{ \div 6} = \frac{13}{165}$

$c) \: \frac{3484 - 34}{9900} = \frac{3450}{9900} \\ \\ \frac{3450}{9900} + \frac{12}{1} \\ mmc = 9900 \\ \frac{3450}{9900} + \frac{118800}{9900} = \frac{122250}{9900} ^{ \div 50} = \frac{2445}{198} \\ \\ \frac{2445}{198} ^{ \div 3} = \frac{815}{66}$

$d) \: \frac{4}{9} + \frac{4}{1} \\ mmc = 9 \\ \frac{4}{9} + \frac{36}{9} = \frac{40}{9}$