The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. For example
[tex]\begin{gathered} \frac{2}{3}\cdot\frac{5}{6}=\frac{2\cdot5}{3\cdot6}=\frac{10}{18} \\ \text{ Now simplify} \\ \frac{10}{18}=\frac{2\cdot5}{2\cdot9}=\frac{5}{9} \\ \text{Then} \\ \frac{2}{3}\cdot\frac{5}{6}=\frac{5}{9} \end{gathered}[/tex]In other words, multiply linearly and simplify
If you have to multiply mixed fractions, first you transform the fraction from mixed to improper and then multiply, for example
[tex]\begin{gathered} 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{3\cdot4+1}{4}\cdot-\frac{8}{5}=\frac{12+1}{4}\cdot-\frac{8}{5}=\frac{13}{4}\cdot-\frac{8}{5} \\ \text{ Apply the law of signs of the multiplication} \\ 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{13}{4}\cdot-\frac{8}{5}=\frac{13\cdot-8}{4\cdot5}=\frac{-104}{20} \\ \text{Simplify} \\ \frac{-104}{20}=\frac{2\cdot-26}{2\cdot10}=\frac{-26}{10} \\ \text{Then} \\ 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{-26}{10} \end{gathered}[/tex]The law of signs for multiplication is
[tex]\begin{gathered} +\cdot+=+ \\ +\cdot-=- \\ -\cdot+=- \\ -\cdot-=+ \end{gathered}[/tex]
