Question

A number line going from 0 to 1. StartFraction 5 Over 6 EndFraction is labeled on the line.
Luke has a board 5
6
of a yard long. He needs to cut the board into 5 equal sections.

Use the expression
to find the length of each section.
Each section is
yard long.

Answer 1

To find the length of each section when Luke cuts his board, we can divide the total length of the board by the number of sections he wants.

1. We know the length of the board is \( \frac{5}{6} \) yards.
2. Luke wants to cut the board into 5 equal sections.

We can represent the length of each section with the expression:

\[
\text{Length of each section} = \frac{5/6}{5}
\]

Now, to simplify this expression, we can rewrite the division as multiplication by the reciprocal:

\[
\frac{5/6}{5} = \frac{5}{6} \times \frac{1}{5}
\]

Multiplying the fractions, we get:

\[
\frac{5 \times 1}{6 \times 5} = \frac{5}{30} = \frac{1}{6}
\]

Therefore, the length of each section is:

\[
\frac{1}{6} \text{ yard long.}
\]