Question

A board is 6 1/2 feet long. You cut off a 1 3/4-foot piece and a 2 2/3 foot piece. How much of the original board is left?

Answer 1

Explanation:

The feet long that the board is

`= 6 (1)/(2) \\`

The piece of board cut off

`= 1 (3)/(4) + 2 (2)/(3) \\`

`= (1 * 4 + 3)/(4) + (2 * 3 + 2)/(3) \\`

`= (7)/(4) + (8)/(3) \\`

`= (7)/(4) * (3)/(3) + (8)/(3) * (4)/(4) \\`

`= (21)/(12) + (32)/(12) \\`

`= (53)/(12) \\`

The original board left

`= 6 (1)/(2) - (53)/(12) \\`

`= (13)/(2) - (53)/(12) \\`

`= (13)/(2) * (6)/(6) - (53)/(12) * (1)/(1) \\`

`= (78 - 53)/(12) \\`

`= (25)/(12) \\`

`= 2 (1)/(12) \\`

hope it helped !!!