#### Explanation:

As Fred has worked for $8 , 4 \frac{1}{2} , 3 \frac{3}{4} , 7 \frac{1}{2} , 4 \frac{3}{4}$ hours during the week,

total number of hours worked is

$8 + 4 \frac{1}{2} + 3 \frac{3}{4} + 7 \frac{1}{2} + 4 \frac{3}{4}$

= $8 + 4 + 3 + 7 + 4 + \frac{1}{2} + \frac{3}{4} + \frac{1}{2} + \frac{3}{4}$

= $26 + \frac{2}{4} + \frac{3}{4} + \frac{2}{4} + \frac{3}{4}$

= $26 + \frac{10}{4} = 26 + \frac{5}{2} = 26 + 2 \frac{1}{2} = 28 \frac{1}{2}$ hours

and at $5.15 per hour he earns $28 \times 5.15 + \frac{1}{2} \times 5.15$= $28 \times 5 + 28 \times 0.15 + 2.575$= $140 + 4.20 + 2.575$= $146.775 \cong 146.78$Hence Fred earns $146.78 during the week.