Give each answer as mixed number in simplest form

Step-by-step explanation:
[tex] = \frac{1}{2} + ( - 5 \frac{9}{10} ) [/tex]
[tex] = \frac{1}{2} - 5 \frac{9}{10} \\ [/tex]
[tex] = \frac{1}{2} - \frac{5 \times 10 + 9}{10} \\ [/tex]
[tex] = \frac{1}{2} - \frac{59}{10} \\ [/tex]
[tex] = \frac{1}{2} \times \frac{5}{5} - \frac{59}{10} \\ [/tex]
[tex] = \frac{5}{10} - \frac{59}{10} \\ [/tex]
[tex] = \frac{5 - 59}{10} \\ [/tex]
[tex] = - \frac{54}{10} \\ [/tex]
[tex] = - \frac{27}{5} \\ [/tex]
Answer:
[tex]-5 \frac{2}{5}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} +\left( -5\frac{9}{10} \right)[/tex]
[tex]= \frac{1}{2} -\left( 5\frac{9}{10} \right) \ \ \ \text{(recall\ :\ + - = - )}[/tex]
[tex]= \frac{1}{2} -\left( 5+\frac{9}{10} \right)[/tex]
[tex]= \frac{1}{2} -5 - \frac{9}{10} \right)[/tex]
[tex]= \frac{5}{10} -5 - \frac{9}{10} \right)[/tex]
[tex]= -5 + \frac{5}{10} - \frac{9}{10} \right)[/tex]
[tex]= -5 - \frac{4}{10}[/tex]
[tex]= -5 - \frac{2}{5}[/tex]
[tex]= -5 \frac{2}{5}[/tex]