Câu 65.

Các tỉ lệ thức có thể lập:

$\dfrac{6}{-27}=\dfrac{-6\dfrac{1}{2}}{29\dfrac{1}{4}}; \dfrac{6}{-6\dfrac{1}{2}}=\dfrac{-27}{29\dfrac{1}{4}}; \dfrac{-27}{6}=\dfrac{29\dfrac{1}{4}}{-6\dfrac{1}{2}}; \dfrac{-6\dfrac{1}{2}}{6}=\dfrac{29\dfrac{1}{4}}{-27}$

Câu 66.

Ta có: `5.625=315; 25.125=315`

`⇒5.625=25.125`

Các tỉ lệ thức có thể lập:

$\dfrac{5}{25}=\dfrac{125}{625};\dfrac{625}{25}=\dfrac{125}{5};\dfrac{5}{125}=\dfrac{25}{625}; \dfrac{625}{125}=\dfrac{25}{5}$

Câu 67.

Ta có: `ad=bc (c,d\ne0)`

`⇒cd\ne0`

Chia cả hai vế cho cd.

$⇒\dfrac{ad}{cd}=\dfrac{bc}{cd}⇒\dfrac{a}{c}=\dfrac{b}{d}$

Câu 68.

- Ta có: `4.256=1024; 16.64=1024`

`⇒4.256=16.64`

Vậy các tỉ lệ thức có thể lập được là:

$\dfrac{4}{6}=\dfrac{64}{256};\dfrac{4}{64}=\dfrac{16}{256};\dfrac{256}{16}=\dfrac{64}{4}; \dfrac{256}{64}=\dfrac{16}{4}$

- Ta có: `16.1024=16384; 64.256=16384`

`⇒16.1024=64.256`

Vậy các tỉ lệ thức có thể lập được là:

$\dfrac{16}{64}=\dfrac{256}{1024}; \dfrac{16}{256}=\dfrac{64}{1024}; \dfrac{1024}{64}=\dfrac{256}{16}; \dfrac{1024}{256}=\dfrac{64}{16}$

- Ta có: `4.1024=4096; 16.256=4096`

`⇒4.104=16.256`

Vậy các tỉ lệ thức có thể lập được là:

$\dfrac{4}{16}=\dfrac{256}{1024}; \dfrac{4}{256}=\dfrac{16}{1024}; \dfrac{1024}{256}=\dfrac{16}{4}; \dfrac{1024}{16}=\dfrac{256}{4}$

Câu 69.

a) $\dfrac{x}{-15}=\dfrac{-60}{x}$

$⇔xx=(-60).(-15)$

`⇔x^2=900`

`⇒`\(\left[ \begin{array}{l}x=30\\x=-30\end{array} \right.\)

b) $\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}$

$⇔x.(-x)=-2.\dfrac{8}{25}$

$⇔-x^2=\dfrac{-16}{25}$

$⇔x^2=\dfrac{16}{25}$

`⇒` \(\left[ \begin{array}{l}x=\dfrac{4}{5}\\x=\dfrac{-4}{5}\end{array} \right.\) 

Câu 70.

a) $3,8:(2x)=\dfrac{1}{4}:2\dfrac{2}{3}$

$⇒(2x)\dfrac{1}{4}=3,8.2\dfrac{2}{3}$

$⇒2.\dfrac{1}{4}x=\dfrac{38}{10}.\dfrac{8}{3}$

$⇒\dfrac{1}{2}x=\dfrac{152}{15}$

$⇒x=\dfrac{152}{15}:\dfrac{1}{2}$

$⇒x=\dfrac{304}{15}$

b) $(0,25x):3=\dfrac{5}{6}:0,125$

$⇒(0,25x).0,125=3.\dfrac{5}{6}$

$⇒(0,25x).0,125=2,5$

$⇒0,25x=2,5:0,125$

$⇒0,25x=20$

$⇒x=80$

c) $0,01:2,5=(0,75x):0,75$

$⇒(0,75x).2,5=0,01.0,75$

$⇒0,75x=0,0075:2,5$

$⇒0,75x=0,003$

$⇒x=0,004$

d) $1\dfrac{1}{3}:0,8=\dfrac{2}{3}:(0,1x)$

$⇒1\dfrac{1}{3}(0,1x)=0,8.\dfrac{2}{3}$

$⇒\dfrac{4}{3}(0,1x)=\dfrac{4}{5}.\dfrac{2}{3}$

$⇒0,1x=\dfrac{8}{15}:\dfrac{4}{3}$

$⇒0,1=\dfrac{2}{5}$

$⇒x=4$

65.

Các tỉ lệ thức có thể lập:

$\dfrac{6}{-6\dfrac{1}{2}}=\dfrac{-27}{29\dfrac{1}{4}}; \dfrac{6}{-27}=\dfrac{-6\dfrac{1}{2}}{29\dfrac{1}{4}}; \dfrac{-6\dfrac{1}{2}}{6}=\dfrac{29\dfrac{1}{4}}{-27}; \dfrac{-27}{6}=\dfrac{29\dfrac{1}{4}}{-6\dfrac{1}{2}}$

66.

$\dfrac{5}{25}=\dfrac{125}{625};\dfrac{625}{25}=\dfrac{125}{5};\dfrac{5}{125}=\dfrac{25}{625}; \dfrac{625}{125}=\dfrac{25}{5}$

67.

`ad=bc (c,d\ne0)⇒cd\ne0`

Chia cả hai vế cho cd.

$⇒\dfrac{ad}{cd}=\dfrac{bc}{cd}⇒\dfrac{a}{c}=\dfrac{b}{d}$

68.

- Tỉ lệ thức có thể lập:

$\dfrac{4}{64}=\dfrac{16}{256}; \dfrac{4}{6}=\dfrac{64}{256}; \dfrac{256}{64}=\dfrac{16}{4}; \dfrac{256}{16}=\dfrac{64}{4}$

- Tỉ lệ thức có thể lập:

$\dfrac{1024}{64}=\dfrac{256}{16}; \dfrac{16}{64}=\dfrac{256}{1024}; \dfrac{1024}{256}=\dfrac{64}{16}; \dfrac{16}{256}=\dfrac{64}{1024}$

- Tỉ lệ thức có thể lập:

$\dfrac{1024}{16}=\dfrac{256}{4}; \dfrac{4}{256}=\dfrac{16}{1024}; \dfrac{1024}{256}=\dfrac{16}{4}; \dfrac{4}{16}=\dfrac{256}{1024}$

69.

a) $\dfrac{x}{-15}=\dfrac{-60}{x}$

$⇒xx=(-60).(-15)$

`⇒x^2=900`

`⇒x=30` và `x=-30`

b) $\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}$

$⇒x.(-x)=-2.\dfrac{8}{25}$

$⇒-x^2=\dfrac{-16}{25}$

$⇒x^2=\dfrac{16}{25}$

$⇒x=\dfrac{4}{5}$ và $x=\dfrac{-4}{5}$

70.

a) $3,8:(2x)=\dfrac{1}{4}:2\dfrac{2}{3}$

$⇒(2x)\dfrac{1}{4}=3,8.2\dfrac{2}{3}$

$⇒\dfrac{1}{2}x=\dfrac{152}{15}$

$⇒x=\dfrac{152}{15}:\dfrac{1}{2}$

$⇒x=\dfrac{304}{15}$

b) $(0,25x):3=\dfrac{5}{6}:0,125$

$⇒(0,25x).0,125=3.\dfrac{5}{6}$

`⇒(0,25x).0,125=2,5`

`⇒0,25x=2,5:0,125`

`⇒0,25x=20`

`⇒x=80`

c) `0,01:2,5=(0,75x):0,75`

`⇒(0,75x).2,5=0,01.0,75`

`⇒0,75x=0,0075:2,5`

`⇒0,75x=0,003`

`⇒x=0,004`

d) $1\dfrac{1}{3}:0,8=\dfrac{2}{3}:(0,1x)$

$⇒1\dfrac{1}{3}(0,1x)=0,8.\dfrac{2}{3}$

$⇒\dfrac{4}{3}(0,1x)=\dfrac{4}{5}.\dfrac{2}{3}$

$⇒0,1x=\dfrac{8}{15}:\dfrac{4}{3}$

$⇒0,1=\dfrac{2}{5}$

`⇒x=4`