The symbol : denotes that the two ratios are in proportion
[tex]\begin{gathered} 2\frac{1}{2}\colon3\frac{1}{2}=n\colon2 \\ we\text{ can rewrite it as } \\ \frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }} \\ In\text{ this form we can easily se}e\text{ that in order to solve for n , we just have to multiply both sides of the equation by 2} \\ 2\cdot\mleft\lbrace\frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }}\mright\rbrace\cdot2 \\ =\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=n \\ n=\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=\frac{5}{3\frac{1}{2}}=\frac{5}{\frac{7}{2}}=5\cdot\frac{2}{7}=\frac{10}{7} \\ \\ \end{gathered}[/tex][tex]2\frac{1}{2}\colon3\frac{1}{2}=n\colon2[/tex]we can rewrite the expression as :
[tex]\frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }}[/tex]Now we can see easily that that in order to solve for n , we just have to multiply both sides of the equation by 2
[tex]2\cdot\lbrace\frac{2\frac{1}{2}}{3\frac{1}{2}}=\frac{n}{2\text{ }}\rbrace\cdot2[/tex][tex]=\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=n[/tex][tex]n=\frac{2\cdot2\frac{1}{2}}{3\frac{1}{2}}=\frac{5}{3\frac{1}{2}}=\frac{5}{\frac{7}{2}}=5\cdot\frac{2}{7}=\frac{10}{7}[/tex]