a)

\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right).\\A = \left( {\frac{{30}}{{15}} + \frac{5}{{15}} - \frac{6}{{15}}} \right) - \left( {\frac{{105}}{{15}} - \frac{9}{{15}} - \frac{{20}}{{15}}} \right) - \left( {\frac{3}{{15}} + \frac{{25}}{{15}} - \frac{{60}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} - \left( {\frac{{ - 32}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} + \frac{{32}}{{15}}\\A = \frac{{ - 15}}{{15}}\\A =  - 1\end{array}\)

b)

\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right)\\A = 2 + \frac{1}{3} - \frac{2}{5} - 7 + \frac{3}{5} + \frac{4}{3} - \frac{1}{5} - \frac{5}{3} + 4\\A = \left( {2 - 7 + 4} \right) + \left( {\frac{1}{3} + \frac{4}{3} - \frac{5}{3}} \right) + \left( { - \frac{2}{5} + \frac{3}{5} - \frac{1}{5}} \right)\\A =  - 1 + 0 + 0 =  - 1\end{array}\)

a: \(x:5=\dfrac{15}{14}\\ \Rightarrow x=\dfrac{15}{70}=\dfrac{3}{14}\)

a) \(x:5=\dfrac{4}{7}+\dfrac{1}{2}\)

\(\dfrac{x}{5}=\dfrac{15}{14}\)

\(\Rightarrow x=\dfrac{5.15}{14}=\dfrac{75}{14}\)

b) \(\dfrac{1}{3}+\dfrac{2}{9}\times\dfrac{3}{4}=\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{2}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}\)

\(x\div5=\dfrac{4}{7}+\dfrac{1}{2}\)

\(x\div5=\dfrac{15}{14}\)

\(x=\dfrac{15}{14}\times5\)

\(x=\dfrac{75}{14}\)

b)

\(\dfrac{1}{3}+\dfrac{2}{9}\times\dfrac{3}{4}\)

\(=\dfrac{1}{3}+\dfrac{1}{6}\)

\(=\dfrac{1}{2}\)

\(a,\dfrac{y-1}{y-2}-\dfrac{y+3}{y-4}=\dfrac{-2}{\left(y-2\right)\left(y-4\right)}\)

\(\Leftrightarrow\dfrac{\left(y-1\right)\left(y-4\right)-\left(y+3\right)\left(y-2\right)+2}{\left(y-2\right)\left(y-4\right)}=0\)\(\left(dkxd:y\ne4;2\right)\)

\(\Leftrightarrow y^2-4y-y+4-y^2+2y-3y+6+2=0\)

\(\Leftrightarrow-6y+12=0\)

\(\Leftrightarrow y=2\)\(\left(ktm\right)\)

Vậy ko có bất kì giá trị y nào để 2 biểu thức bằng nhau

\(b,\dfrac{8y}{y-7}+\dfrac{1}{7-y}=8\)

\(\Leftrightarrow\dfrac{8y}{y-7}-\dfrac{1}{y-7}=8\)\(\left(dkxd:y\ne7\right)\)

\(\Leftrightarrow8y-1-8\left(y-7\right)=0\)

\(\Leftrightarrow8y-1-8y+56=0\)(Vô lý)

Vậy ko có bất kì giá trị y nào để biểu thức có giá trị = 8

\(\dfrac{1}{3}\cdot\dfrac{1}{4}+\dfrac{7}{4}:3-\dfrac{2}{3}\)

\(=\dfrac{1}{12}+\dfrac{7}{12}-\dfrac{8}{12}\)

\(=\dfrac{0}{12}=0\)

\(\dfrac{1}{2}\times\dfrac{1}{3}+\dfrac{3}{4}\)

\(=\dfrac{1}{6}+\dfrac{3}{4}\)

\(=\dfrac{2}{12}+\dfrac{9}{12}\)

\(=\dfrac{11}{12}\)

____________________________

\(\dfrac{3}{7}-\dfrac{2}{7}:\dfrac{2}{3}\)

\(=\dfrac{3}{7}-\dfrac{2}{7}\times\dfrac{3}{2}\)

\(=\dfrac{3}{7}-\dfrac{3}{7}\)

\(=0\)

Chúc bạn học tốt

1/2 x 1/3 + 3/4 = 1/6 + 3/4 = 4/24 + 18/24 = 22/24 = 11/12
3/7 - 2/7 : 2/3 = 3/7 - 2/7 x 3/2 = 3/7 - 3/7 = 0

1​×31​+43​

=16+34=61​+43​

=212+912=122​+129​

=1112=1211​

____________________________

37−27:2373​−72​:32​

=37−27×32=73​−72​×23​

=37−37=73​−73​

$=0$

Ta có: \(\left(3\dfrac{3}{4}+\dfrac{4}{7}\cdot\dfrac{7}{16}\right):\dfrac{1}{2}\)

\(=\left(\dfrac{15}{4}+\dfrac{1}{4}\right)\cdot2\)

\(=4\cdot2=8\)

Ta có:\(\left(3\dfrac{3}{4}+\dfrac{4}{7}.\dfrac{7}{16}\right):\dfrac{1}{2}\)

       \(=\left(\dfrac{15}{4}+\dfrac{1}{4}\right).2\)

       \(=\dfrac{16}{4}.2\)

       \(=8\)

= 4 : 1/2 = 4 nhân 2/1  = 8

đáp án = 8

= 4 : 1/2 = 4 nhân 2/1  = 8

đáp án = 8

101/28

43/90

3/4:1/5-1/7

=15/4-1/7

=101/28

7/9-3/5.1/2

=7/9-3/10

=43/90

3/4 : 1/5 - 1/7

=> 3/4 x 5/1 - 1/7

=> 15/4 - 1/7

=> 105/28 - 4/28

=> 101/28

7/9 - 3/5 x 1/2

=> 7/9 - 3/10

=> 70/90 - 27/90

=> 43/90

a. 1/4 + 1/5 + 3/4 + 2/5

=(1/4 + 3/4) + (1/5 + 2/5)

=1 + 3/5

=8/5

b. 2/7 + 5/14 + 1/7 + 3/14

=(2/7 + 1/7) + (5/14 + 3/14)

=3/7 + 4/7

=1