Question

47/53. ( 17/3 - 53/47) + 17/3 .( 6/17 - 47/53)

Answer 1

`47/53*(17/3-53/47)+17/3*(6/17-47/53)`

`=47/53*17/3-1+6/3-17/3*47/53`

`=2-1+17/3*47/53-17/3*47/53`

`=1`

Answer 2

\(\dfrac{47}{53}.\left(\dfrac{17}{3}-\dfrac{53}{47}\right)+\dfrac{17}{3}.\left(\dfrac{6}{17}-\dfrac{47}{53}\right)\) 

\(=\dfrac{47}{53}.\dfrac{17}{3}-\dfrac{47}{53}.\dfrac{53}{47}+\dfrac{17}{3}.\dfrac{6}{17}-\dfrac{17}{3}.\dfrac{47}{53}\) 

\(=\left(\dfrac{47}{53}.\dfrac{17}{3}-\dfrac{17}{3}.\dfrac{47}{53}\right)+\left(\dfrac{-47}{53}.\dfrac{53}{47}+\dfrac{17}{3}.\dfrac{6}{17}\right)\) 

\(=\left(1-1\right)+\left(-1+2\right)\) 

\(=0+1\) 

\(=1\)