Question

A company has budgeted 5 1/5 hours to complete a project, with 1/4 of the time spent on research. How much time does the company plan to spend on research? Express your answer as a mixed number.

Answer 1

Since 1/4 of 5 1/5 will be spent on research, we have to multiply both fractions. First lets write 5 1/5 as an improper fraction:

$\begin{gathered} 5\frac{1}{5}=\frac{5(5)+1}{5}=\frac{25+1}{5}=\frac{26}{5} \\ \end{gathered}$

then, we have the following:

$(5\frac{1}{5})(\frac{1}{4})=(\frac{26}{5})(\frac{1}{4})$

now, using the general rule for the product of fractions:

$\begin{gathered} \frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d} \\ b,d\ne0 \end{gathered}$

in this case, we have:

$\frac{26}{5}\cdot\frac{1}{4}=\frac{26\cdot1}{5\cdot4}=\frac{26}{20}=\frac{13}{10}=1\frac{3}{10}$

therefore, the time spent of research will be 1 3/10 hours