Answer :

Let's solve each part step-by-step.

### Part (b): [tex]\(\frac{80}{6} - \frac{35}{6}\)[/tex]

1. Identify the common denominators:
Since both fractions [tex]\(\frac{80}{6}\)[/tex] and [tex]\(\frac{35}{6}\)[/tex] have the same denominator, we can combine them easily:

[tex]\[ \frac{80}{6} - \frac{35}{6} = \frac{80 - 35}{6} \][/tex]

2. Perform the subtraction in the numerator:
[tex]\[ 80 - 35 = 45 \][/tex]

So, the expression becomes:
[tex]\[ \frac{45}{6} \][/tex]

3. Simplify the fraction:
[tex]\[ \frac{45}{6} = 7.5 \][/tex]

Therefore, [tex]\(\frac{80}{6} - \frac{35}{6} = 7.5\)[/tex].

### Part (c): [tex]\(\frac{75}{2} \times \frac{1}{6}\)[/tex]

1. Multiply the numerators and the denominators:
[tex]\[ \text{Numerator: } 75 \times 1 = 75 \][/tex]
[tex]\[ \text{Denominator: } 2 \times 6 = 12 \][/tex]

So, the expression becomes:
[tex]\[ \frac{75}{12} \][/tex]

2. Simplify the fraction:
[tex]\[ \frac{75}{12} = 6.25 \][/tex]

Therefore, [tex]\(\frac{75}{2} \times \frac{1}{6} = 6.25\)[/tex].