dấu . là dấu nhân đó mk viết nhầm 

\(27\cdot\left(\dfrac{373737}{424242}+\dfrac{373737}{565656}+\dfrac{373737}{727272}\right)\\ =27\cdot\left(\dfrac{37}{42}+\dfrac{37}{56}+\dfrac{37}{72}\right)\\ =27\cdot37\cdot\left(\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)\\ =999\cdot\left(\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}\right)\\ =999\cdot\left(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\\ =999\cdot\left(\dfrac{1}{6}-\dfrac{1}{9}\right)\\ =999\cdot\dfrac{1}{18}\\ =\dfrac{111}{2}\)

\(27.\left(\dfrac{373737}{424242}+\dfrac{373737}{565656}+\dfrac{373737}{727272}\right)=\dfrac{111}{2}\)

\(=18\times\left(\frac{37\times10101}{42\times10101}+\frac{37\times10101}{56\times10101}+\frac{37\times10101}{72\times10101}\right)\)

\(=18\times\left(\frac{37}{42}+\frac{37}{56}+\frac{37}{72}\right)\)

\(=666\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)

\(=666\times\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=666\times\left(\frac{1}{6}-\frac{1}{9}\right)\)

\(=666\times\frac{1}{18}=37\)

\(18\times\left(\frac{373737}{424242}+\frac{373737}{565656}+\frac{373737}{727272}\right)\)

\(=18\times\left(\frac{37}{42}+\frac{37}{56}+\frac{37}{72}\right)\)

\(=18\times\frac{37}{18}\)

\(=37\)

\(18.\left(\frac{373737}{424242}+\frac{373737}{565656}+\frac{373737}{727272}\right)\)

\(=18.\left(\frac{37}{42}+\frac{37}{56}+\frac{37}{72}\right)\)

\(=18.37.\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)

\(=666.\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)\)

\(=666.\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=666.\left(\frac{1}{6}-\frac{1}{9}\right)\)

\(=666.\left(\frac{6}{36}-\frac{4}{36}\right)\)

\(=666.\frac{2}{36}\)

\(=37\)

~ Ủng hộ nhé 

\(A=18\cdot\left(\frac{373737}{424242}+\frac{373737}{565656}+\frac{373737}{727272}\right)\)

\(=18\cdot\left(\frac{37}{42}+\frac{37}{56}+\frac{37}{72}\right)=18\cdot37\cdot\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)

\(=18\cdot37\cdot\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)\)

\(=18\cdot37\cdot\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=18\cdot37\cdot\left(\frac{1}{6}-\frac{1}{9}\right)=18\cdot37\cdot\left(\frac{3}{18}-\frac{2}{18}\right)\)

\(=18\cdot37\cdot\frac{1}{18}=18\cdot\frac{1}{18}\cdot37=1\cdot37=37\)

37/42+37/56+37/72 = 37(1/42+1/56+1/72)=37( 1/6.7 + 1/7.8 + 1/8.9 )= 37( 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9)= 37( 1/6 - 1/9)= 37.1/18=37/18

B = 37/42 + 37/56 + 37/72 

B = 37/18

37/42 + 37/56 +37/72=37/24 + 37/72= 37/18

\(A=18x\left(\frac{373737}{424242}+\frac{373737}{565656}+\frac{373737}{727272}\right)\)

    \(=18x\left(\frac{37x10101}{42x10101}+\frac{37x10101}{56x10101}+\frac{37x10101}{72x10101}\right)\)

     \(=18x\left(\frac{37}{42}+\frac{37}{56}+\frac{37}{72}\right)\)

       \(=18x\frac{37}{18}\)

        \(=37\)

Đáp án:

`649/36` 

Giải thích các bước giải:

 `27`  x  `171717/272727`  `+`  `373737/363636`  `=`

 Rút gọn Phân số ta được:

`=`  `27`  x `17/27`  `+`  `37/36` 

`=`   `17`  `+`  `37/36`  `=`  `649/36`