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REY [17]
3 years ago
6

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 w

hole piece of rope.
How long is each piece of rope?
WRITE THE ANSWER AS A FRACTION AND DECIMAL.
Mathematics
2 answers:
Anastasy [175]3 years ago
6 0
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 <em>a</em> units long and you divide it into <em>b</em> equal parts, then each equal part will be <em>c </em>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}&#10;{}^\text{length of}_\text{each piece}&#10;&= \dfrac{8\text{ yard}}{\text{9 piece} } \\&#10;&= 8/9 \text{ yards per piece} \\&#10;&= 0.\overline{8} \text{ yards per piece}&#10;\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}&#10;\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) \\&#10;&= 8&#10;\end{aligned}
Doss [256]3 years ago
5 0
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.
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Answer:

(a) x = -2y

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Note that there is no addition and subtraction in this equation.

Let's put these equations in the form y = kx.

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