Question

Determine if it is a true proportion. Please choose the correct letter

Answer 1

Given the equation:

`((3)/(5))/((14)/(2))=((1)/(2))/((35)/(6))`

Let's determine if the proportion is a true proportion.

If the proportionis true, it means the ratio on both sides if the equality are equal.

Now, let's find the ratios.

For the first ratio:

`\begin{gathered} ((3)/(5))/((14)/(2)) \\ \\ =(3)/(5)/(14)/(2) \\ \\ \text{ Flip the fraction on the right and change the division symbol to mutilication:} \\ =(3)/(5)*(2)/(14) \\ \\ =(3)/(5)*(1)/(7) \\ \\ =(3*1)/(5*7) \\ \\ =(3)/(35) \end{gathered}`

For the second ratio:

`\begin{gathered} ((1)/(2))/((35)/(6)) \\ \\ =(1)/(2)/(35)/(6) \\ \\ \text{ Flip the fraction on the right and change the division symbol to mutilication:} \\ =(1)/(2)*(6)/(35) \\ \\ =(1*6)/(2*35) \\ \\ =(6)/(70) \\ \\ =(3)/(35) \end{gathered}`

After simlifying, we have:

`(3)/(35)=(3)/(35)`

Since the equation is true, we can say the proortion is true because it has a constant ratio.