Giải bài 49 trang 42 sách bài tập Toán 6 – Cánh Diều Tập 2

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)

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

e)

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

g)

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