Bài 1 :
a) $\frac{2}{7}$ + $\frac{5}{7}$ : $\frac{2}{21}$ + $\frac{19}{21}$
= $\frac{2}{7}$ + $\frac{5}{7}$ . $\frac{21}{2}$ + $\frac{19}{21}$
= $\frac{2}{7}$ + $\frac{15}{2}$ + $\frac{19}{21}$
= ($\frac{2}{7}$ + $\frac{19}{21}$) + $\frac{15}{2}$
= $\frac{25}{21}$ + $\frac{15}{2}$
= $\frac{365}{42}$
b) $\frac{14^{1005}.5^{1006} }{2^{1007}.35^{1004} }$
= $\frac{2^{1005}.7^{1005}.5^{1006} }{2^{1007}.7^{1004}.5^{1004} }$
= $\frac{7.5^{2}}{2^{2}}$
= $\frac{7.25}{4}$
= $\frac{175}{4}$
c) /-2,5/ + /$\frac{1}{3}$/ . /6/ - /$\frac{2}{3}$/
= 2,5 + $\frac{1}{3}$ . 6 - $\frac{2}{3}$
= 2,5 + 2 - $\frac{2}{3}$
= $\frac{9}{2}$ - $\frac{2}{3}$
= $\frac{23}{6}$
d) $\sqrt{32.18}$ + 2$\sqrt{25}$ + /$\frac{-1}{3}$/ . /6/ - 2²
= 24 + 10 + $\frac{1}{3}$ . 6 - 4
= 24 + 10 + 2 - 4
= 34 + 2 - 4
= 36 - 4
= 32
Bài 2 :
a) $x^{10}$ : $x^{7}$ = $\frac{1}{27}$
$x^{3}$ = $\frac{1}{3^{3}}$
⇒ x = $\frac{1}{3}$
b) $\frac{1}{8}$x - 1 = 0,25
$\frac{1}{8}$x = 0,25 + 1
$\frac{1}{8}$x = 1,25
x = 1,25 : $\frac{1}{8}$
x = 10
c) /2$\frac{1}{2}$ - x/ = 4
/$\frac{5}{2}$ - x/ = 4
⇒ $\left \{ {{\frac{5}{2} - x=4} \atop {\frac{5}{2} - x=-4}} \right.$
⇒ $\left \{ {{x=\frac{5}{2}-4= \frac{-3}{2}} \atop {x=\frac{5}{2}-(-4) =\frac{13}{2} }} \right.$
d) $\frac{x}{6}$ = $\frac{y}{7}$ và x + y = -39
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
$\frac{x}{6}$ = $\frac{y}{7}$ =$\frac{x+y}{6+7}$ = $\frac{-39}{13}$ = -3
⇒$\left \{ {{x=-3.6=-18} \atop {y=-3.7=-21}} \right.$
