#### Answer

$\frac{15}{8}$ inches

#### Work Step by Step

Let $m$ be the distance between consecutive rivets.
Having 16 equally-spaced rivets means the total distance is equal to $15m$.
Thus,
$15m = 28\frac{1}{8}
\\15m \div 15 = 28\frac{1}{8} \div 15
\\m = 28\frac{1}{8} \div 15$
Use the rule $\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}$ to obtain:
$m=28\frac{1}{8} \times \frac{1}{15}$
Convert the mixed number to an improper fraction to obtain:
$\require{cancel}
m=\frac{8(28)+1}{8} \times \frac{1}{15}
\\m=\frac{225}{8} \times \frac{1}{15}
\\m=\frac{\cancel{225}15}{8} \times \frac{1}{\cancel{15}}
\\m=\frac{15}{8}$
Therefore, the distance between consecutive rivets is $\frac{15}{8}$ inches.