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].
