Tìm x, biết: a) 6/7*x=18/23; b) 15/119*x=1; c) x:5/6=4/7;  d) x-3/7:9/14=-7/3

Giải SBT Toán 6 Cánh diều Bài 4: Phép nhân, phép chia phân số  

Bài 49 trang 42 SBT Toán 6 Tập 2:

Tìm x, biết:

a) $\frac{6}{7}\cdot x=\frac{18}{23}$ ;                   b) $\frac{15}{119}\cdot x=1$;

c) $x:\frac{5}{6}=\frac{4}{7}$;                       d) $x-\frac{3}{7}:\frac{9}{14}=\frac{-7}{3}$;

e) $\frac{9}{13}\cdot x=\frac{11}{8}-\frac{125}{1000}$;       g) $\left(x-\frac{1}{2}\right):\frac{3}{11}=\frac{11}{4}$.

Lời giải

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

$x=\frac{18}{23}:\frac{6}{7}$

$x=\frac{18}{23}\cdot \frac{7}{6}$

$x=\frac{3.7}{23}=\frac{21}{23}$.

Vậy $x=\frac{21}{23}$.

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

$x=1:\frac{15}{119}$

$x=\frac{119}{15}$.

Vậy $x=\frac{119}{15}$.

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

$x=\frac{4}{7}\cdot \frac{5}{6}$.

$x=\frac{2.5}{7.3}=\frac{10}{21}$ 

Vậy $x=\frac{10}{21}$.

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

$x-\frac{3}{7}.\frac{14}{9}=\frac{-7}{3}$

$x-\frac{2}{3}=\frac{-7}{3}$

$x=\frac{-7}{3}+\frac{2}{3}$

$x=\frac{-5}{3}$.

Vậy $x=\frac{-5}{3}$.

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

$\frac{9}{13}\cdot x=\frac{11}{8}-\frac{1}{8}$

$\frac{9}{13}\cdot x=\frac{10}{8}$

$\frac{9}{13}\cdot x=\frac{5}{4}$

$x=\frac{5}{4}:\frac{9}{13}$

$x=\frac{5}{4}.\frac{13}{9}$

$x=\frac{65}{36}$

Vậy $x=\frac{65}{36}$.

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

$x-\frac{1}{2}=\frac{11}{4}\cdot \frac{3}{11}$

$x-\frac{1}{2}=\frac{3}{4}$

$x=\frac{3}{4}+\frac{1}{2}$

$x=\frac{3}{4}+\frac{2}{4}$

$x=\frac{5}{4}$.

Vậy $x=\frac{5}{4}$.