Question

Efectuiaza: 3,(3)×0,6= 4,(6)÷1,1(6)= [3,(6)+0,(3)]×0,25=

Answer 1

$3.(3) \times 0.6 = 3 \frac{3}{9} \times \frac{6}{10} \\ = \frac{3 \times 9 + 3}{9} \times \frac{6}{10} = \frac{30}{9} \times \frac{6}{10} =$
$\frac{3}{9} \times 6 = \frac{18}{9} \div 9 = 2$


$4.(6) \div 1.1(6) = \frac{46}{9} \div 1 \frac{1 6 - 1}{90} \\ = \frac{46}{9} \div \frac{1 \times 90 + 15}{90}$
$\frac{46}{9} \div \frac{105}{ 90 } = \frac{46}{9} \times \frac{90}{105} \\ = \frac{46 \times 10}{1 \times 105} = \frac{460}{105} \div 5 = \frac{92}{21}$
$= 4.38....$

$(3.(6) + 0.(3)) \times 0.25 = \\ (3 \frac{6}{9} + \frac{3}{9} ) \times \frac{25}{100}$

$= ( \frac{33}{9} + \frac{3}{9} ) \times \frac{25}{100} = \\ \frac{36}{9} \times \frac{25}{100} = \frac{18 \times 25}{9 \times 50} = \frac{450}{450} = 1$