ANSWERS
Each rope has a length of 8/9 yards, or [tex]0.\overline{8} [/tex] yards (repeating digit is 8).
EXPLANATION
Division can be used to solve this problem.
In general, the equation "a/b = c" models the following situation: If you have something that is a units long and you divide it into b equal parts, then each equal part will be c units long.
We have a rope that is 8 yards long and we need 9 equal pieces.
Divide 8 yards by 9 to get the length of each piece.
[tex]\begin{aligned}
{}^\text{length of}_\text{each piece}
&= \dfrac{8\text{ yard}}{\text{9 piece} } \\
&= 8/9 \text{ yards per piece} \\
&= 0.\overline{8} \text{ yards per piece}
\end{aligned}[/tex]
Each piece is 8/9th of a yard or [tex]0.\overline{8} [/tex] yards long.
We can confirm this by adding the lengths of the nine equal pieces of rope back up to get the original length of the rope:
[tex]\begin{aligned}
\underbrace{\frac{8}{9} + \frac{8}{9} + \frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9}}_{\text{9 pieces, each of them 8/9th of a yard long}} &= 9 \cdot \left(\frac{8}{9} \right) \\
&= 8
\end{aligned}[/tex]
