bài 1:

\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)

\(=\left(\frac{6}{11}+\frac{5}{11}\right)+\frac{1}{3}\)

\(=\frac{11}{11}+\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}\)

bài 2:

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)

\(=\left(\frac{1}{2}+\frac{1}{20}\right)+\left(\frac{1}{6}+\frac{1}{12}\right)\)

\(=\frac{11}{20}+\frac{1}{4}=\frac{11}{20}+\frac{5}{20}=\frac{15}{20}=\frac{3}{4}\)

bài 3: 

a) \(\frac{3}{2}\cdot\frac{4}{5}\cdot\frac{2}{3}=\left(\frac{3}{2}\cdot\frac{2}{3}\right)\cdot\frac{4}{5}=1\cdot\frac{4}{5}=\frac{4}{5}\)

b) \(\frac{6}{7}\cdot\frac{5}{3}\cdot\frac{7}{6}=\left(\frac{6}{7}\cdot\frac{7}{6}\right)\cdot\frac{5}{3}=1\cdot\frac{5}{3}=\frac{5}{3}\)

bài 4: 

a) \(\frac{2}{5}\cdot\frac{1}{4}+\frac{3}{4}\cdot\frac{2}{5}=\frac{2}{5}\cdot\left(\frac{1}{4}+\frac{3}{4}\right)=\frac{2}{5}\cdot1=\frac{2}{5}\)

b) \(\frac{6}{11}:\frac{2}{3}+\frac{5}{11}:\frac{2}{3}=\left(\frac{6}{11}+\frac{5}{11}\right):\frac{2}{3}=1:\frac{2}{3}=\frac{3}{2}\)

Bài 1: 

  6/11 + 1/3 + 5/11 

= ( 6/11 + 5/11) + 1/3

= 11/11 + 1/3

= 1 + 1/3 

= 3/3 +1/3  

= 4/3 

Bài 2: 

1/2 + 1/6 + 1/12 + 1/20 

= ( 1/2 + 1/6 + 1/12 ) + 1/20 

= ( 6/12 + 2/12 + 1/12 ) + 1/20 

=9/12 + 1/20 

= 3/4 +1/20  

= 15/20 + 1/20 

= 16/20 = 4/5

 Bài 3:

a) \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\) \(=\left(\frac{3}{2}\times\frac{2}{3}\right)\times\frac{4}{5}\)\(=1\times\frac{4}{5}=\frac{4}{5}\) 

b)  \(\frac{6}{7}\times\left(\frac{5}{3}\times\frac{7}{6}\right)\) \(=\frac{6}{7}\times\frac{35}{18}\)\(=\frac{1\times5}{7\times3}=\frac{5}{21}\)   

Bài 4:

a) 2/5  x 1/4 + 3/4 x 2/5 

= 2/5 x ( 1/4  + 3/4) 

 = 2/5 x  1 

= 2/5

 b) 6/11 : 2/3 +5/11 : 2/3 

=  ( 6/11 + 5/11) x 3/2 

= 11/11 x 3/2  

= 1 x 3/2  

=  3/2  

....  

a) \(\frac{16}{35}+\frac{8}{35}=\frac{24}{35}\)

b)\(\frac{160}{77}-\frac{28}{77}=\frac{132}{77}=\frac{12}{1}=12\)

c)\(\frac{72}{180}=\frac{18}{45}\)

d) \(\frac{90}{360}=\frac{1}{4}\)

Ta có \(x.a=b\)

\(x=b:a\)

Do đó \(-\frac{3}{5}.x=\frac{5}{6}\)

\(x=\frac{5}{6}:\frac{-3}{5}\)

\(x=-\frac{1}{2}\)

Tương tự 

2. \(x=\frac{6}{8}:\frac{2}{4}=\frac{3}{2}\)

Bạn tự làm câu 3

1.\(\frac{-3}{5}\).x=\(\frac{5}{6}\)

x=\(\frac{5}{6}\):\(\frac{-3}{5}\)

x=\(\frac{-25}{18}\)

2.\(\frac{2}{4}\):x=\(\frac{6}{8}\)

\(\frac{1}{2}\):x=\(\frac{3}{4}\)

x=\(\frac{1}{2}\):\(\frac{3}{4}\)

x=\(\frac{2}{3}\)

3.\(\frac{67}{89}\).x=\(\frac{12}{13}\)

x=\(\frac{12}{13}\):\(\frac{67}{89}\)

x=\(\frac{1068}{871}\)

K MIK NHÉ

\(\frac{4}{13}+\frac{9}{5}=\frac{137}{65}\)

\(3-\frac{2}{16}=\frac{23}{8}\)

\(\frac{12}{31}\times\frac{1}{19}=\frac{12}{589}\)

\(\frac{3}{8}\div\frac{9}{12}=\frac{1}{2}\)

\(\text{Trả lời :}\)

\(\frac{4}{13}+\frac{9}{5}=\frac{137}{65}\)

\(3-\frac{2}{16}=\frac{23}{8}\)

\(\frac{12}{31}\times\frac{1}{19}=\frac{12}{589}\)

\(\frac{3}{8}\div\frac{9}{12}=\frac{1}{2}\)

\(\text{~~Học tốt~~}\)

Mình làm cách lớp 6 nha bạn, cách lớp 4 mình không biết.
\(\frac{1}{2}.x+\frac{1}{5}.x=\frac{2}{5}\)
\(\Rightarrow x.\left(\frac{1}{2}+\frac{1}{5}\right)=\frac{2}{5}\)
\(\Rightarrow x.\frac{7}{10}=\frac{2}{5}\)
Giờ thành tìm x rồi!
\(x=\frac{7.5}{2.10}\)
\(x=1\frac{3}{4}\)
Xong!

\(\frac{1}{2}\times x+\frac{1}{5}\times x=\frac{2}{5}\)

   \(x\times\left(\frac{1}{2}+\frac{1}{5}\right)=\frac{2}{5}\)

                  \(x\times\frac{7}{10}=\frac{2}{5}\)

                              \(x=\frac{2}{5}:\frac{7}{10}\)

                              \(x=\frac{4}{7}\)

\(\Rightarrow x\times\left(\frac{1}{2}+\frac{3}{2}\right)=\frac{4}{5}\)

\(\Rightarrow x\times\frac{4}{2}=\frac{4}{5}\)

\(\Rightarrow x\times2=\frac{4}{5}\)

\(\Rightarrow x=\frac{4}{5}\div2\)

\(\Rightarrow x=\frac{4}{5}\times\frac{1}{2}\)

\(\Rightarrow x=\frac{2}{5}\)

\(x\times\frac{1}{2}+\frac{3}{2}\times x=\frac{4}{5}\)

\(x\times\left(\frac{1}{2}+\frac{3}{2}\right)=\frac{4}{5}\)

\(x\times2=\frac{4}{5}\)

\(x=\frac{4}{5}:2\)

\(x=\frac{2}{5}\)

Chọn B

c) Các phân số được sắp xếp theo thứ tự từ lớn đến bé là:

A.\(\frac{5}{6};\frac{2}{3};\frac{4}{2}\)

B.\(\frac{4}{2};\frac{5}{6};\frac{2}{3}\)

C.\(\frac{2}{3};\frac{4}{2}:\frac{5}{6}\)

D.\(\frac{4}{2};\frac{2}{3};\frac{5}{6}\)

Khoanh B 

Câu 1:\(\frac{12}{23}\times\frac{9}{28}+\frac{11}{23}\times\frac{9}{28}\)

\(=\frac{9}{28}\times\left(\frac{12}{23}+\frac{11}{23}\right)\)

\(=\frac{9}{28}\times\frac{23}{23}\)

\(=\frac{9}{28}\times1\)

\(=\frac{9}{28}\)

Câu 2:

\(3+\frac{1}{9}+\frac{3}{9}+2+\frac{5}{9}+3+2\)

\(=\left(3+2+2+3\right)+\left(\frac{1}{9}+\frac{3}{9}+\frac{5}{9}\right)\)

\(=10+\frac{9}{9}\)

\(=10+1\)

\(=11\)

\(\frac{12}{23}x\frac{9}{28}+\frac{11}{23}x\frac{9}{28}=\)\(\left(\frac{12}{23}+\frac{11}{23}\right)x\frac{9}{28}\)\(=\) \(1x\frac{9}{28}=\frac{9}{28}\)

\(3+\frac{1}{9}+\frac{3}{9}+2+\frac{5}{9}+3+2\)\(=\) \(\left(\frac{1}{9}+\frac{3}{9}+\frac{5}{9}\right)+\left(3+2+3+2\right)\)\(=\) \(1+3+2+3+2=\)\(11\)