We are asked to determine the quotient of miles over hours for 12 5/6 miles and 2/3 hours. To do that we determine the quotient as follows:
[tex]r=\frac{12\text{ }\frac{5}{6}}{\frac{2}{3}}[/tex]Now we convert the mixed fraction into a regular fraction using the following relationship:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Applying the relationship we get:
[tex]r=\frac{12+\frac{5}{6}}{\frac{2}{3}}[/tex]Now, we solve the operation in the numerator:
[tex]r=\frac{\frac{77}{6}}{\frac{2}{3}}[/tex]Now, we use the following relationship to solve the quotient:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}[/tex]Applying the relationship we get:
[tex]r=\frac{\frac{77}{6}}{\frac{2}{3}}=\frac{77}{6}\times\frac{3}{2}[/tex]Solving the operations:
[tex]r=\frac{231}{12}=19.25[/tex]Therefore, the quotient is 19.25 miles per hour.
