Question

a) \(\dfrac{15}{11}\) - (\(\dfrac{5}{7}\) - \(\dfrac{18}{11}\)) + \(\dfrac{27}{7}\) 

b) \(\dfrac{39}{5}\)+ (\(\dfrac{9}{4}\) - \(\dfrac{9}{5}\)) - (\(\dfrac{5}{4}\) + 1,2)

c) -1,2 - 0,8 + 0,25 + 5,75 - 2022

d) 0,1 + \(\dfrac{16}{9}\) + 5,1 + \(\dfrac{-20}{9}\) 

Answer 1

a) 15/11 - (5/7 - 18/11) + 27/7

= 15/11 - 5/7 + 18/11 + 27/7

= (15/11 + 18/11) + (-5/7 + 27/7)

= 3 + 22/7

= 43/7

b) 39/5 + (9/4 - 9/5) - (5/4 + 1,2)

= 39/5 + 9/4 - 9/5 - 5/4 - 6/5

= (39/5 - 9/5 - 6/5) + (9/4 - 5/4)

= 24/5 + 1

= 29/5

c) -1,2 - 0,8 + 0,25 + 5,75 - 2022

= (-1,2 - 0,8) + (0,25 + 5,76) - 2022

= -2 + 6 - 2022

= 4 - 2022

= -2018

d) 0,1 + 16/9 + 5,1 + (-20/9)

= (0,1 + 5,1) + (16/9 - 20/9)

= 5,2 - 4/9

= 419/90

Answer 2

a) \(\dfrac{15}{11}-\left(\dfrac{5}{7}-\dfrac{18}{11}\right)+\dfrac{27}{7}=\dfrac{22}{7}+3=\dfrac{43}{77}\)

b) \(\dfrac{39}{5}+\left(\dfrac{9}{4}-\dfrac{9}{5}\right)-\left(\dfrac{5}{4}+\dfrac{6}{5}\right)=\dfrac{24}{5}+1=\dfrac{29}{5}\)

c) \(-1,2-0,8+0,25+5,75-2022=-2+6-2022=-2018\)

d) \(0,1+\dfrac{16}{9}+5,1+\dfrac{-20}{9}=\dfrac{26}{5}-\dfrac{4}{9}=\dfrac{214}{45}\)