Ta có tỉ thức : \(\dfrac{3}{7} = \dfrac{9}{{21}}\)

Xét \(\dfrac{{3 + 9}}{{7 + 21}}\) = \(\dfrac{{12}}{{28}}\) = \( = \dfrac{3}{7}\)( chia cả tử và mẫu cho 4 )

Xét \(\dfrac{{3 - 9}}{{7 - 21}}\) = \(\dfrac{{ - 6}}{{ - 14}}\)\( = \dfrac{3}{7}\)( chia cả tử và mẫu cho 2 )

Sau khi thực hiện tính các tỉ số ta thấy các kết quả sau khi tối giản của tỉ số bằng với các tỉ só trong tỉ lệ thức đã cho.

\(\dfrac{x-2}{-1,2}=\dfrac{-5}{2}\Rightarrow x=\dfrac{-5.\left(-1,2\right)}{2}+2=\dfrac{6}{2}+2=3+2=5\\ \dfrac{-6}{x+1}=\dfrac{1,8}{9}\Rightarrow x=\dfrac{-6.9}{1,8}-1=\dfrac{-54}{1,8}-1=-30-1=-31\\ \dfrac{-3}{x}=\dfrac{x}{-12}\Rightarrow x=\sqrt{\left(-12\right).\left(-3\right)}=\sqrt{36}=\sqrt{\left(\pm6\right)^2}=\pm6\)

\(\dfrac{x-4}{x-1}=\dfrac{3}{5}\\ \Rightarrow5\left(x-4\right)=3\left(x-1\right)\\ \Leftrightarrow5x-20=3x-3\\ \Leftrightarrow5x-3x=-3+20\\ \Leftrightarrow2x=17\\ \Leftrightarrow x=\dfrac{17}{2}\\ ---\\ \dfrac{1,12}{-10}=\dfrac{11,2}{x}\Rightarrow x=\dfrac{11,2.\left(-10\right)}{1,12}=\dfrac{10.1,12.\left(-10\right)}{1,12}=-100\)

`(6/11 +5/11) xx 3/7`

`= 11/11xx 3/7`

`=1xx3/7`

`=3/7`

__

`3/5 xx 7/9 - 3/5 xx 2/9`

`= 3/5 xx (7/9-2/9)`

`= 3/5 xx 5/9`

`= 15/45`

`= 1/3`

__

`(6/7 -4/7):2/5`

`= 2/7 : 2/5`

`= 2/7 xx 5/2`

`= 10/14`

`= 5/7`

\(\left(\dfrac{6}{11}+\dfrac{5}{11}\right)\times\dfrac{3}{7}\)

\(=1\times\dfrac{3}{7}=\dfrac{3}{7}\)

___________

\(\dfrac{3}{5}\times\dfrac{7}{9}-\dfrac{3}{5}\times\dfrac{2}{9}\)

\(=\dfrac{3}{5}\times\left(\dfrac{7}{9}-\dfrac{2}{9}\right)\)

\(=\dfrac{3}{5}\times\dfrac{5}{9}\)

\(=\dfrac{1}{3}\)

__________

\(\left(\dfrac{6}{7}-\dfrac{4}{7}\right):\dfrac{2}{5}\)

\(=\dfrac{2}{7}\times\dfrac{5}{2}\)

\(=\dfrac{5}{7}\)

\(#WendyDang\)

\(\left(\dfrac{6}{11}+\dfrac{5}{11}\right)\times\dfrac{3}{7}\)

\(=\dfrac{11}{11}\times\dfrac{3}{7}\\ =1\times\dfrac{3}{7}=\dfrac{3}{7}\)

_____

\(\dfrac{3}{5}\times\dfrac{7}{9}-\dfrac{3}{5}\times\dfrac{2}{9}\\ =\dfrac{3}{5}\times\left(\dfrac{7}{9}-\dfrac{2}{9}\right)\\ =\dfrac{3}{5}\times\dfrac{5}{9}\\ =\dfrac{3}{9}\\ =\dfrac{1}{3}\)

_________

\(\left(\dfrac{6}{7}-\dfrac{4}{7}\right):\dfrac{2}{5}\\ =\dfrac{2}{7}\times\dfrac{5}{2}\\ =\dfrac{10}{14}\\ =\dfrac{5}{7}\)

a) \(\dfrac{-2}{5}=\dfrac{-14}{35}\)

b) \(\dfrac{9}{4}=\dfrac{\dfrac{1}{4}}{\dfrac{1}{9}}\)

c) \(\dfrac{\dfrac{7}{4}}{\dfrac{1}{2}}=\dfrac{7}{2}\)

a) Ta có: \(A=\dfrac{4}{7\cdot31}+\dfrac{6}{7\cdot41}+\dfrac{9}{10\cdot41}+\dfrac{7}{10\cdot57}\)

\(=\dfrac{20}{31\cdot35}+\dfrac{30}{35\cdot41}+\dfrac{45}{41\cdot50}+\dfrac{35}{50\cdot57}\)

\(=5\left(\dfrac{4}{31\cdot35}+\dfrac{6}{35\cdot41}+\dfrac{9}{41\cdot50}+\dfrac{7}{50\cdot57}\right)\)

\(=5\left(\dfrac{1}{31}-\dfrac{1}{35}+\dfrac{1}{35}-\dfrac{1}{41}+\dfrac{1}{41}-\dfrac{1}{50}+\dfrac{1}{50}-\dfrac{1}{57}\right)\)

\(=5\left(\dfrac{1}{31}-\dfrac{1}{57}\right)\)

Ta có: \(B=\dfrac{7}{19\cdot31}+\dfrac{5}{19\cdot43}+\dfrac{3}{23\cdot43}+\dfrac{11}{23\cdot57}\)

\(=\dfrac{14}{31\cdot38}+\dfrac{10}{38\cdot43}+\dfrac{6}{43\cdot46}+\dfrac{22}{46\cdot57}\)

\(=2\left(\dfrac{7}{31\cdot38}+\dfrac{5}{38\cdot43}+\dfrac{3}{43\cdot46}+\dfrac{11}{46\cdot57}\right)\)

\(=2\left(\dfrac{1}{31}-\dfrac{1}{38}+\dfrac{1}{38}-\dfrac{1}{43}+\dfrac{1}{43}-\dfrac{1}{46}+\dfrac{1}{46}-\dfrac{1}{57}\right)\)

\(=2\left(\dfrac{1}{31}-\dfrac{1}{57}\right)\)

Suy ra: \(\dfrac{A}{B}=\dfrac{5\left(\dfrac{1}{31}-\dfrac{1}{57}\right)}{2\left(\dfrac{1}{31}-\dfrac{1}{57}\right)}=\dfrac{5}{2}\)

\(7\dfrac{4}{5}và9\dfrac{1}{2}\\ Tacó:7< 9\\ \Rightarrow7\dfrac{4}{5}< 9\dfrac{1}{2}\\ 7\dfrac{1}{6}và3\dfrac{4}{5}\\ Tacó:7>3\\ \Rightarrow7\dfrac{1}{6}>3\dfrac{4}{5}\)

Câu cuối không phải hỗn số

Lời giải:

1.

$3\frac{1}{4}-2\frac{1}{3}=3+\frac{1}{4}-(2+\frac{1}{3})$

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

$=1+\frac{1}{4}-\frac{1}{3}=\frac{5}{4}-\frac{1}{3}=\frac{11}{12}$

2. 

$6\frac{5}{9}+2\frac{5}{6}=6+\frac{5}{9}+2+\frac{5}{6}=8+\frac{5}{6}+\frac{5}{9}=8+\frac{25}{18}=8+1+\frac{7}{18}=9+\frac{7}{18}=9\frac{7}{18}$
3.

$6\frac{5}{9}-2\frac{5}{6}=6+\frac{5}{9}-(2+\frac{5}{6})$

$=6+\frac{5}{9}-2-\frac{5}{6}$
$=(6-2)+\frac{5}{9}-\frac{5}{6}$
$=4+\frac{5}{9}-\frac{5}{6}=\frac{41}{9}-\frac{5}{6}=\frac{67}{8}$

\(=\dfrac{2}{3}+\dfrac{1}{3}.\left(\dfrac{7}{18}\right):\dfrac{7}{12}\)

\(=\dfrac{2}{3}+\dfrac{7}{54}:\dfrac{7}{12}\)

\(=\dfrac{2}{3}+\dfrac{2}{9}\)

\(=\dfrac{8}{9}\)