Question

A carpenter wants to cut a board that is 5/6 ft long into pieces that are 5/16 ft long. The carpenter will use the expression shown to calculate the number of pieces that can be cut from the board.5/6 divided by 5/16How many pieces can be cut from the board?

Answer 1

`\begin{gathered} \text{Length of the board}=(5)/(6)\text{ ft} \\ \text{Length of one piece }=(5)/(16)\text{ ft} \\ \end{gathered}`

The expression which is used to calculate the number of pieces that can be cut from the board is:

`(5)/(6)/(5)/(16)`

We solve this by changing the division sign to multiplication and taking the reciprocal of the second fraction.

Therefore:

`\begin{gathered} (5)/(6)/(5)/(16)=(5)/(6)*(16)/(5) \\ =(16)/(6) \\ =2\text{ }(4)/(6) \\ =2(2)/(3)\text{ pieces} \end{gathered}`

The carpenter can cut 2 2/3 pieces from the board.