Respuesta :
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.
[tex]5\frac{3}{4}\rightarrow\frac{4(5)+3}{4}=\frac{23}{4}[/tex]Next, we need to set up the division question:
[tex]\frac{23}{4}\div3[/tex]When we divide fractions, we are actually multiplying by the reciprocal.
Rewrite 3 as it's reciprocal:
[tex]3\rightarrow\frac{3}{1}\rightarrow\frac{1}{3}[/tex]Now we will rewrite the expression as a multiplication problem:
[tex]\frac{23}{4}\times\frac{1}{3}[/tex]Next, we can multiply the fractions:
[tex]\frac{23}{4}\times\frac{1}{3}=\frac{23\times1}{4\times3}=\frac{23}{12}[/tex]Finally, we need to rewrite this as a mixed number:
[tex]\begin{gathered} \frac{23}{12}\rightarrow\frac{12+11}{12}\rightarrow\frac{12}{12}+\frac{11}{12}=1+\frac{11}{12} \\ \\ \boxed{1\frac{11}{12}} \end{gathered}[/tex]Each piece of wood will be 1 and 11/12 ft each.
