Of course, let's evaluate the expressions step-by-step:
### (i) Evaluate [tex]\(\frac{-3}{5} + \frac{7}{5} + \frac{-1}{5}\)[/tex]
1. Note that all three fractions have the same denominator, which is 5.
2. Combine the numerators directly:
[tex]\[
\frac{-3 + 7 - 1}{5}
\][/tex]
3. Simplify the numerator:
[tex]\[
-3 + 7 - 1 = 3
\][/tex]
4. So, the fraction simplifies to:
[tex]\[
\frac{3}{5}
\][/tex]
### (iv) Evaluate [tex]\(\frac{-16}{9} + \frac{-5}{12} + \frac{7}{18}\)[/tex]
1. To combine these fractions, find a common denominator. The least common denominator (LCD) for 9, 12, and 18 is 36.
2. Convert each fraction to have the denominator of 36:
- [tex]\(\frac{-16}{9}\)[/tex]:
[tex]\[
\frac{-16}{9} \times \frac{4}{4} = \frac{-64}{36}
\][/tex]
- [tex]\(\frac{-5}{12}\)[/tex]:
[tex]\[
\frac{-5}{12} \times \frac{3}{3} = \frac{-15}{36}
\][/tex]
- [tex]\(\frac{7}{18}\)[/tex]:
[tex]\[
\frac{7}{18} \times \frac{2}{2} = \frac{14}{36}
\][/tex]
3. Combine the fractions over the common denominator of 36:
[tex]\[
\frac{-64 - 15 + 14}{36}
\][/tex]
4. Simplify the numerator:
[tex]\[
-64 - 15 + 14 = -65
\][/tex]
5. So, the fraction simplifies to:
[tex]\[
\frac{-65}{36}
\][/tex]
Hence, the results are:
- [tex]\(\frac{-3}{5} + \frac{7}{5} + \frac{-1}{5} = \frac{3}{5} \approx 0.6 \)[/tex]
- [tex]\(\frac{-16}{9} + \frac{-5}{12} + \frac{7}{18} = \frac{-65}{36} \approx -7.58\)[/tex]
So, the final answers are:
1. [tex]\(\frac{3}{5} \approx 0.6\)[/tex]
2. [tex]\(\frac{-65}{36} \approx -7.58\)[/tex]
