Tính trang 20 vở thực hành Toán 7 Tập 1

Tính:

Giải vở thực hành Toán 7 Bài 5: Bài tập cuối chương 1

Bài 3 trang 20 vở thực hành Toán 7 Tập 1: Tính:

a) $\left(\frac{-2}{5}+\frac{3}{8}\right):\frac{2}{5}+\left(\frac{-1}{5}+\frac{4}{8}\right):\frac{2}{5}$;

b) $\frac{-5}{12}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{-5}{12}:\left(\frac{1}{15}-\frac{2}{3}\right)$.

Lời giải:

a) $\left(\frac{-2}{5}+\frac{3}{8}\right):\frac{2}{5}+\left(\frac{-1}{5}+\frac{4}{8}\right):\frac{2}{5}$

= $\left(\frac{-2}{5}+\frac{3}{8}\right).\frac{5}{2}+\left(\frac{-1}{5}+\frac{4}{8}\right).\frac{5}{2}=\left(\frac{-2}{5}+\frac{3}{8}+\frac{-1}{5}+\frac{4}{8}\right).\frac{5}{2}$

= $\left(\frac{-24}{40}+\frac{35}{40}\right).\frac{5}{2}=\frac{11}{40}.\frac{5}{2}=\frac{55}{80}=\frac{11}{16}$

= $\left(\left(\frac{-2}{5}+\frac{-1}{5}\right)+\left(\frac{3}{8}+\frac{4}{8}\right)\right).\frac{5}{2}=\left(\frac{-3}{5}+\frac{7}{8}\right).\frac{5}{2}$

b) $\frac{-5}{12}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{-5}{12}:\left(\frac{1}{15}-\frac{2}{3}\right)$

= $\frac{-5}{12}:\left(\frac{2}{22}-\frac{5}{22}\right)+\frac{-5}{12}:\left(\frac{1}{15}-\frac{10}{15}\right)$ = $\frac{-5}{12}:\frac{-3}{22}+\frac{-5}{12}:\frac{-9}{15}$

$=\frac{-5}{12}.\frac{-22}{3}+\frac{-5}{12}.\frac{-15}{9}$ = $\frac{-5}{12}.\left(\frac{-22}{3}+\frac{-15}{9}\right)=\frac{-5}{12}.\left(\frac{-22}{3}+\frac{-5}{3}\right)$

= $\frac{-5}{12}.\frac{-27}{3}=\frac{-5}{12}.\left(-9\right)=\frac{15}{4}$