Câu 1:
a) $\frac{-5}{9}$. $\frac{-5}{12}$ =$\frac{-5.(-5)}{9.12}$ =$\frac{25}{108}$
b) $\frac{-5}{12}$:$\frac{15}{4}$
$\frac{-5}{12}$ . $\frac{4}{15}$
= $\frac{-5.4}{12.15}$
= $\frac{-5.4}{4.3.(-5).(-3)}$
= $\frac{1}{3.(-3)}$
= $\frac{1}{-9}$
c)$\frac{1}{13}$ . $\frac{8}{13}$ + $\frac{5}{13}$ . $\frac{1}{13}$ - $\frac{14}{13}$
= $\frac{1.8}{13.13}$ + $\frac{5.1}{13.13}$ -$\frac{14}{13}$
= $\frac{1.8+5.1}{13.13}$ - $\frac{14}{13}$
= $\frac{13}{13.13}$ - $\frac{14}{13}$ = $\frac{1}{13}$ - $\frac{14}{13}$
= $\frac{-13}{13}$ = -1
d) A= $\frac{4}{1.5}$ + $\frac{4}{5.9}$ + $\frac{4}{9.13}$ +...+$\frac{4}{41.45}$
=$\frac{1}{1}$ - $\frac{1}{5}$ + $\frac{1}{5}$ - $\frac{1}{9}$ +$\frac{1}{9}$ - $\frac{1}{13}$ +...+$\frac{1}{41}$ - $\frac{1}{45}$
= 1- $\frac{1}{45}$
=$\frac{44}{45}$
Câu 2:
a)x=$\frac{1}{5}$ +$\frac{-3}{7}$
=>x = $\frac{7}{35}$ + $\frac{-15}{35}$
=>x=$\frac{-8}{35}$
b)$\frac{3}{5}$ - $\frac{4}{7}$ : x =$\frac{-9}{10}$
=> $\frac{4}{7}$ : x = $\frac{3}{5}$ - $\frac{-9}{10}$
=> $\frac{4}{7}$ : x = $\frac{6}{10}$ + $\frac{9}{10}$
=> $\frac{4}{7}$ : x = $\frac{3}{2}$
=> x = $\frac{3}{2}$ . $\frac{4}{7}$
=> x=$\frac{6}{7}$
c)x-($\frac{-3}{4}$)=$\frac{-2}{3}$ - $\frac{1}{2}$
=>x-($\frac{-3}{4}$)= $\frac{-4}{6}$ - $\frac{3}{6}$
=>x-($\frac{-3}{4}$)=$\frac{-7}{6}$
=> x=$\frac{-7}{6}$ + ($\frac{-3}{4}$)
=> x= $\frac{-14}{12}$ + $\frac{-9}{12}$
=> x=$\frac{-23}{12}$
