Answer:
[tex]\boxed{11\frac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{Number of stones} = \frac{\text{Length of path}}{ \text{ Length of each stone}}\\[/tex]
[tex] = 2\frac{5 }{ 6} \div \frac{ 1}{ 4}\\[/tex]
Convert the mixed number to an improper fraction
[tex]2\frac{5 }{ 6} \div \frac{ 1}{ 4} = \frac{17}{6}\div\frac{ 1}{ 4}\\[/tex]
Invert the denominator and change division to multiplication
[tex]\frac{17}{6}\div\frac{ 1}{ 4} = \frac{17}{6}\times \frac{ 4}{ 1}\\[/tex]
Cancel the 2s
[tex]\frac{17}{6}\times \frac{ 4}{ 1} = \frac{17}{3}\times \frac{ 2}{ 1}\\[/tex]
Multiply numerators and denominators.
[tex]\frac{17}{3}\times \frac{ 2}{ 1} = \frac{ 34}{ 3}\\[/tex]
Convert the improper fraction to a mixed number.
[tex]\frac{ 34}{ 3} = 11\frac{1}{3}\\[/tex]
It takes [tex]\boxed{11\frac{1}{3}}[/tex]stones to complete the path.
