Question

Jake needs 9 pieces of rope that are each the same length. He cuts the pieces from a rope that is 8 yards long and uses up the whole piece of rope.
How long is each piece of rope?
WRITE THE ANSWER AS A FRACTION AND DECIMAL.

Answer 1

ANSWERS
Each rope has a length of 8/9 yards, or $0.\overline{8}$ 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.

   $\begin{aligned} {}^\text{length of}_\text{each piece} &= \dfrac{8\text{ yard}}{\text{9 piece} } \\ &= 8/9 \text{ yards per piece} \\ &= 0.\overline{8} \text{ yards per piece} \end{aligned}$

Each piece is 8/9th of a yard or $0.\overline{8}$ 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:

   $\begin{aligned} \underbrace{\frac{8}{9} + \frac{8}{9} + \frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9} +\frac{8}{9}}_{\text{9 pieces, each of them 8/9th of a yard long}} &= 9 \cdot \left(\frac{8}{9} \right) \\ &= 8 \end{aligned}$

Answer 2

9 pieces of rope form an 8 yard long rope

Divide.

8/9 yards of rope.

8/9 is approximately 0.89.

So 8/9 yards of rope or 0.89 yards of rope.