Question

If A:B=2:5 and B:C=4:2 find A:C

Answer 1

Given A:B = 2:5, and B:C = 4:2

`\begin{gathered} (A)/(B)=(2)/(5) \\ \text{Convert this such that }A\text{ is on the left side} \\ \\ \text{Multiply both sides by }B \\ B\mleft((A)/(B)=(2)/(5)\mright)B \\ \cancel{B}\mleft(\frac{A}{\cancel{B}}=(2)/(5)\mright)B \\ A=(2B)/(5) \end{gathered}`
`\begin{gathered} (B)/(C)=(4)/(2) \\ \text{Convert this such that }C\text{ is on the left side} \\ \\ \text{Get the reciprocal} \\ (C)/(B)=(2)/(4) \\ \text{Multiply both sides by }B \\ B\mleft((C)/(B)=(2)/(4)\mright)B \\ \cancel{B}\mleft(\frac{C}{\cancel{B}}=(2)/(4)\mright)B \\ C=(2B)/(4) \end{gathered}`

Substitute values for A and B

`\begin{gathered} (A)/(C)=((2B)/(5))/((2B)/(4)) \\ \\ \text{Recall that division by fraction is done by multiplying the numerator to the} \\ \text{reciprocal of the denominator} \\ (A)/(C)=((2B)/(5))/((2B)/(4))\Longrightarrow(2B)/(5)*(4)/(2B) \\ \\ (A)/(C)=\frac{\cancel{2B}}{5}*\frac{4}{\cancel{2B}} \\ (A)/(C)=(4)/(5) \end{gathered}`

Therefore, A:C is 4:5.