Sure, let's go through each part step-by-step.
### Part (iv):
We need to simplify the expression:
[tex]$ \frac{-2}{3} + \left( \frac{3}{4} + \frac{1}{-5} \right) $[/tex]
First, let's simplify the term inside the parentheses:
[tex]$ \frac{3}{4} + \frac{1}{-5} $[/tex]
Second, we combine these results:
[tex]$ \frac{-2}{3} + \left( \frac{3}{4} + \frac{1}{-5} \right) $[/tex]
The final simplified result for this expression is:
[tex]$ -0.11666666666666659 $[/tex]
### Part (i):
We need to simplify the expression:
[tex]$ \frac{2}{3} + \frac{-3}{5} + \frac{1}{6} + \frac{-8}{15} $[/tex]
To do this, we perform each addition step-by-step:
1. Combine [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{-3}{5}\)[/tex].
2. Add [tex]\(\frac{1}{6}\)[/tex] to the result.
3. Finally, add [tex]\(\frac{-8}{15}\)[/tex].
The simplified result for this expression is:
[tex]$ -0.30000000000000004 $[/tex]
