Answer:
see below:-
Step-by-step explanation:
Given,
[tex] \displaystyle{5 \frac{1}{6} + 2 \frac{1}{3} - 5 \frac{11}{12} }[/tex]
[tex] \displaystyle{ \frac{31}{6} + \frac{7}{3} \ - \frac{71}{12} }[/tex]
[tex] \therefore{\displaystyle{ \frac{31}{6} + \frac{7}{3} - \frac{71}{12} = \frac{31 \times 2 + 7 \times 4 - 71 \times 1}{12} }}[/tex]
[tex] = \displaystyle{ \frac{62 + 28 - 71}{12} }[/tex]
[tex]\displaystyle{ = \frac{90 - 71}{12} }[/tex]
[tex]\displaystyle{ = \frac{19}{12} }[/tex]
[tex]\displaystyle{1 \frac{7}{12} }[/tex]
[tex] \quad\hookrightarrow\quad \sf {\dfrac{19}{12}\: or \: 1\dfrac{7}{12} }[/tex]
We will solve the given mixed fraction in 2 steps :
[tex] \implies\quad \tt {5\dfrac{1}{6}+2\dfrac{1}{3}-5\dfrac{11}{12} }[/tex]
[tex] \implies\quad \tt { \dfrac{(6\times 5)+1}{6}+\dfrac{(3\times 2)+1}{3}-\dfrac{(12\times 5)+11}{12}}[/tex]
[tex] \implies\quad \tt { \dfrac{30+1}{6}+\dfrac{6+1}{3}-\dfrac{60+11}{12}}[/tex]
[tex] \implies\quad \tt { \dfrac{31}{6}+\dfrac{7}{3}-\dfrac{71}{12}}[/tex]
[tex] \implies\quad \tt { \dfrac{(2\times31)+(4\times 7)-(1\times 71)}{12} }[/tex]
[tex] \implies\quad \tt { \dfrac{62+28-71}{12}}[/tex]
[tex] \implies\quad \tt { \dfrac{90-71}{12}}[/tex]
[tex] \implies\quad \tt {\dfrac{19}{12} }[/tex]
[tex] \implies\quad\underline{\underline {\pmb{\tt {1\dfrac{7}{12} }}}}[/tex]
