Answer:
[tex]2 \frac{1}{8} ~\frac{miles}{hour}[/tex]
Step-by-step explanation:
"Per" means division.
"miles per hour" means a distance in miles divided by a time in hours.
We need to divide 5 2/3 miles by 2 2/3 hours.
[tex] \dfrac{5 \frac{2}{3}~miles}{2 \frac{2}{3}~hours}} = [/tex]
Change each mixed numeral into a fraction.
[tex] = \dfrac{\frac{5 \times 3 + 2}{3}~miles}{\frac{2 \times 3 + 2}{3}~hours} [/tex]
[tex] = \dfrac{\frac{17}{3}~miles}{\frac{8}{3}~hours} [/tex]
To divide by a fraction, multiply by its reciprocal.
[tex]= \dfrac{17}{3} \times \dfrac{3}{8} \frac{miles}{hour}[/tex]
[tex]= \dfrac{17}{8} \frac{miles}{hour}[/tex]
[tex]= 2 \frac{1}{8} ~\frac{miles}{hour}[/tex]
