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).

Step-by-step 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} &= \frac{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{(8)/(9) + (8)/(9) + (8)/(9) +(8)/(9) +(8)/(9) +(8)/(9) +(8)/(9) +(8)/(9) +(8)/(9)}_{\text{9 pieces, each of them 8/9th of a yard long}} &= 9 \cdot \left((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.