Question

1

Marty saws off
of a wooden board. Then, he saws off
Alu
of what is left of the board. Finally,
1
he saws
off of this remaining piece of board. What fraction of the original board is left?

Answer 1

Fraction of the original board left =
`(2)/(15)`

Explanation:

Let the length of the board is = l feet

Marty saws off
`(1)/(5)` of a wooden board.

Length of the board left = l -
`((1)/(5))l`

=
`((4)/(5))l` feet

He saws off
`(3)/(4)th` of the remaining board,

Board left =
`((4)/(5))l-[((4)/(5))l* ((3)/(4))]`

=
`(4)/(5)l-(3)/(5)l`

=
`(1)/(5)l` feet

He finally saws off
`(1)/(3)`rd of the remaining board.

Board left =
`(1)/(5)l-[(1)/(5)* (1)/(3)]l`

=
`((1)/(5)-(1)/(15))l`

=
`(2)/(15)l` feet

Fraction of the original board left =
`((2)/(15)l)/(l)`

=
`(2)/(15)`