Giải câu 60 bài 8: Luyện tập sgk Toán 7 tập 1 Trang 31

a.   $(\frac{1}{3}.x):\frac{2}{3}=1\frac{3}{4}:\frac{2}{5}$

<=> $(\frac{1}{3}.x):\frac{2}{3}=\frac{7}{4}:\frac{2}{5}$

<=> $\frac{x}{3}:\frac{2}{3}=\frac{7}{4}.\frac{5}{2}$

<=> $\frac{x}{3}:\frac{2}{3}=\frac{35}{8}$

<=> $\frac{x}{3}=\frac{35}{8}.\frac{2}{3}$

<=> $\frac{x}{3}=\frac{35}{12}$

<=> $x.12=35.3$

<=> $x.12=105$

<=> $x=105:12=\frac{35}{4}$

Vậy $x=\frac{35}{4}$

b.  $4,5:0,3=2,25:(0,1.x)$

<=> $\frac{9}{2}:\frac{3}{10}=\frac{9}{4}:\frac{1}{10}x$

<=> $\frac{9}{2}.\frac{10}{3}=\frac{9}{4}:\frac{1}{10}x$

<=> $15=\frac{9}{4}:\frac{1}{10}x$

<=> $\frac{1}{10}x=\frac{9}{4}:15$

<=> $\frac{1}{10}x=\frac{9}{4}:\frac{1}{15}$

<=> $\frac{1}{10}x=\frac{3}{20}$

<=> $x=\frac{3}{20}:\frac{1}{10}$

<=> $x=\frac{3}{20}.10$

<=> $x=\frac{3}{2}$

Vậy $x=\frac{3}{2}$.

c.  $8:(\frac{1}{4}.x)=2:0,02$

<=> $8:(\frac{1}{4}.x)=2:\frac{2}{100}$

<=> $8:(\frac{1}{4}.x)=100$

<=> $\frac{1}{4}.x=8:100$

<=> $\frac{1}{4}.x=\frac{2}{25}$

<=> $x=\frac{2}{25}:\frac{1}{4}$

<=> $x=\frac{2}{25}.4$

<=> $x=\frac{8}{25}$

Vậy $x=\frac{8}{25}$.

d.  $3:2\frac{1}{4}=\frac{3}{4}:(6.x)$

<=> $3:\frac{9}{4}=\frac{3}{4}:(6.x)$

<=> $\frac{4}{3}=\frac{3}{4}:(6.x)$

<=> $6.x=\frac{3}{4}:\frac{4}{3}$

<=> $6.x=\frac{9}{16}$

<=> $x=\frac{9}{16}:6$

<=> $x=\frac{9}{16}:\frac{1}{6}$

<=> $x=\frac{3}{32}$

Vậy $x=\frac{3}{32}$.