Effectuer des opérations entre des fractions simples.☘

$a = \frac{\ \ \frac{4}{3}\ \ }{12} = \frac{\ \ \frac{4}{3}\ \ }{\frac{12}{1}} = \frac{4}{3}\times \frac{1}{12}= \frac{4\times 1}{3\times (4\times 3)}$, soit $a = \frac{1}{9}$.

$b = \frac{4}{\ \frac{3}{12}\ } = \frac{4}{\ \frac{1}{4}\ } = 4\times \frac{4}{1} = 16$

$c = \frac{\ \ \frac{5}{8}\ \ }{\frac{3}{4}} = \frac{5}{8}\times \frac{4}{3} = \frac{5\times 4}{(2\times 4)\times 3}$, soit $c = \frac{5}{6}$.

$d = \frac{2}{5} \times \left( \frac{-1}{2} +7 \times \frac{3}{14}\right) = \frac{2}{5} \times \left( \frac{-1}{2} + \frac{7}{1}\times\frac{3}{2\times 7}\right)$, soit $d = \frac{2}{5} \times \left( \frac{-1}{2} + \frac{7\times 3}{1\times 2\times 7}\right)$,
$d = \frac{2}{5} \times \left( \frac{-1}{2} + \frac{3}{2}\right)$
$d = \frac{2}{5} \times \left( \frac{2}{2} \right)$
$d = \frac{2}{5} \times \left( 1 \right)$
$d = \frac{2}{5}$

$k = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4} =\frac{2}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4} = \frac{3}{2}+\frac{1}{3}+\frac{1}{4}$
$k = \frac{6}{4}+\frac{1}{3}+\frac{1}{4}$
$k = \frac{7}{4}+\frac{1}{3}$ (en regroupant le premier terme et le dernier)
$k = \frac{7\times 3}{4\times 3}+\frac{1\times 4}{3\times 4}$
$k = \frac{21}{12}+\frac{4}{12}$
$k = \frac{25}{12}$

$j = \left(\frac{2}{3}-1\right)-\left(2+\frac{1}{3}\right)$
$j = \frac{2}{3}-1-2-\frac{1}{3}$
$j = \frac{1}{3}-3$
$j = \frac{1}{3}-\frac{9}{3}$
$j = \frac{-8}{3}$