Given:
The expression is
[tex]-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)[/tex]
To find:
The value of the expression.
Solution:
We have,
[tex]-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)=-2\dfrac{1}{3}+10\dfrac{1}{6}[/tex]
Convert the mixed fraction in improper fraction.
[tex]=-\dfrac{2\times 3+1}{3}+\dfrac{10\times 6+1}{6}[/tex]
[tex]=-\dfrac{6+1}{3}+\dfrac{60+1}{6}[/tex]
[tex]=-\dfrac{7}{3}+\dfrac{61}{6}[/tex]
Taking LCM, we get
[tex]=\dfrac{-2(7)+61}{6}[/tex]
[tex]=\dfrac{-14+61}{6}[/tex]
[tex]=\dfrac{42}{6}[/tex]
Convert it into mixed fraction.
[tex]=\dfrac{6(7)+5}{6}[/tex]
[tex]=7\dfrac{5}{6}[/tex]
Therefore, the correct option is C.
