Question

Johnny has a board that is 5 ¾ feet long. He wants to divide it into three equal pieces to make shelves out of them. How long will each shelf be (in feet)?

Answer 1

In this problem, we want to apply mixed number division.

We are given the following information:

• one long piece of board is 5 3/4

,

• divide it into three sections

To divide these, we should first change the mixed number into an improper fraction.

`5(3)/(4)\rightarrow(4(5)+3)/(4)=(23)/(4)`

Next, we need to set up the division question:

`(23)/(4)/3`

When we divide fractions, we are actually multiplying by the reciprocal.

Rewrite 3 as it's reciprocal:

`3\rightarrow(3)/(1)\rightarrow(1)/(3)`

Now we will rewrite the expression as a multiplication problem:

`(23)/(4)*(1)/(3)`

Next, we can multiply the fractions:

`(23)/(4)*(1)/(3)=(23*1)/(4*3)=(23)/(12)`

Finally, we need to rewrite this as a mixed number:

`\begin{gathered} (23)/(12)\rightarrow(12+11)/(12)\rightarrow(12)/(12)+(11)/(12)=1+(11)/(12) \\ \\ \boxed{1(11)/(12)} \end{gathered}`

Each piece of wood will be 1 and 11/12 ft each.