Question

A carpenter has a board that is 2/3 yard wide. He cuts the board into 5 pieces. If all the pieces are the same width, how wide is each piece?

Answer 1

`\huge\boxed{(2)/(15) \text{ yards}}`

Explanation:

We have a board that is
`(2)/(3)` yards long. If we want to cut the board into 5 equal pieces, we must divide
`(2)/(3)` by 5.

`(2)/(3) / 5`

5 is the same thing as
`(5)/(1)`, so:

`(2)/(3) / (5)/(1)`

To divide a fraction by a fraction, we multiply by the reciprocal. This means we take the reciprocal of
`(5)/(1)` and multiply the two fractions.

The reciprocal of
`(5)/(1)` is
`(1)/(5)` - we swap the numerator and denominator.

`(2)/(3) \cdot (1)/(5)`

Multiply the numerator and denominators to get our final fraction:

`2\cdot 1 = 2\\3 \cdot 5 = 15\\\\(2)/(15)`

Hope this helped!