Respuesta :
Given A:B = 2:5, and B:C = 4:2
[tex]\begin{gathered} \frac{A}{B}=\frac{2}{5} \\ \text{Convert this such that }A\text{ is on the left side} \\ \\ \text{Multiply both sides by }B \\ B\mleft(\frac{A}{B}=\frac{2}{5}\mright)B \\ \cancel{B}\mleft(\frac{A}{\cancel{B}}=\frac{2}{5}\mright)B \\ A=\frac{2B}{5} \end{gathered}[/tex][tex]\begin{gathered} \frac{B}{C}=\frac{4}{2} \\ \text{Convert this such that }C\text{ is on the left side} \\ \\ \text{Get the reciprocal} \\ \frac{C}{B}=\frac{2}{4} \\ \text{Multiply both sides by }B \\ B\mleft(\frac{C}{B}=\frac{2}{4}\mright)B \\ \cancel{B}\mleft(\frac{C}{\cancel{B}}=\frac{2}{4}\mright)B \\ C=\frac{2B}{4} \end{gathered}[/tex]Substitute values for A and B
[tex]\begin{gathered} \frac{A}{C}=\frac{\frac{2B}{5}}{\frac{2B}{4}} \\ \\ \text{Recall that division by fraction is done by multiplying the numerator to the} \\ \text{reciprocal of the denominator} \\ \frac{A}{C}=\frac{\frac{2B}{5}}{\frac{2B}{4}}\Longrightarrow\frac{2B}{5}\times\frac{4}{2B} \\ \\ \frac{A}{C}=\frac{\cancel{2B}}{5}\times\frac{4}{\cancel{2B}} \\ \frac{A}{C}=\frac{4}{5} \end{gathered}[/tex]Therefore, A:C is 4:5.
