Giải bài 49 trang 42

Đề bài

Tìm x biết:

a) $\frac{6}{7}.x=\frac{18}{23}$

b) $\frac{15}{119}.x=1$

c) $x:\frac{5}{6}=\frac{4}{7}$

d) $x-\frac{3}{7}:\frac{9}{14}=\frac{-7}{3}$

e) $\frac{9}{13}.x=\frac{11}{8}-\frac{125}{1000}$

g) $\left(x-\frac{1}{2}\right):\frac{3}{11}=\frac{11}{4}$

Lời giải chi tiết

a) $\frac{6}{7}.x=\frac{18}{23}\Rightarrow x=\frac{18}{23}:\frac{6}{7}\Rightarrow x=\frac{18}{23}.\frac{7}{6}=\frac{18.7}{23.6}=\frac{21}{23}$

b) $\frac{15}{119}.x=1\Rightarrow x=1:\frac{15}{119}\Rightarrow x=\frac{119}{15}$

c) $x:\frac{5}{6}=\frac{4}{7}\Rightarrow x=\frac{5}{6}.\frac{4}{7}=\frac{5.4}{6.7}=\frac{10}{21}$

d)

 $\begin{array}{c}x-\frac{3}{7}:\frac{9}{14}=\frac{-7}{3}\Rightarrow x-\frac{3}{7}.\frac{14}{9}=\frac{-7}{3}\\ \Rightarrow x-\frac{2}{3}=\frac{-7}{3}\Rightarrow x=\frac{2}{3}+\frac{-7}{3}=\frac{-5}{3}\end{array}$

e)

 $\begin{array}{c}\frac{9}{13}.x=\frac{11}{8}-\frac{125}{1000}\Rightarrow \frac{9}{13}.x=\frac{11}{8}-\frac{1}{8}\Rightarrow \frac{9}{13}.x=\frac{10}{8}\\ \Rightarrow \frac{9}{13}.x=\frac{5}{4}\Rightarrow x=\frac{5}{4}:\frac{9}{13}\Rightarrow x=\frac{5}{4}.\frac{13}{9}=\frac{5.13}{4.9}=\frac{65}{36}\end{array}$

g)

 $\begin{array}{c}\left(x-\frac{1}{2}\right):\frac{3}{11}=\frac{11}{4}\Rightarrow x-\frac{1}{2}=\frac{11}{4}.\frac{3}{11}\\ \Rightarrow x-\frac{1}{2}=\frac{3}{4}\Rightarrow x=\frac{1}{2}+\frac{3}{4}=\frac{2}{4}+\frac{3}{4}=\frac{5}{4}\end{array}$