Question

Do the ratios 4ft./6ft. and 12sec/18sec form a proportion? Why or why not?

Answer 1

Yes! There are 3 different explanations I have. Pick your favorite.

Explanation:

So we are asked to see if the following equation holds:

`\frac{4 \text{ ft }}{6 \text{ ft}}=\frac{12 \text{ sec }}{18 \text{sec}}`

The units cancel out ft/ft=1 and sec/sec=1.

So we are really just trying to see if 4/6 is equal to 12/18

Or you could cross multiply and see if the products are the same on both sides:

`(4)/(6)=(12)/(18)`

Cross multiply:

`4(18)=6(12)`

`72=72`

Since you have the same thing on both sides then the ratios given were proportional.

OR!

Put 4/6 and 12/18 in your calculator. They both come out to have the same decimal expansion of .66666666666666666(repeating) so the ratios gives are proportional.

OR!

Reduce 12/18 and reduce 4/6 and see if the reduced fractions are same.

12/18=2/3 (I divided top and bottom by 6)

4/6=2/3 (I divided top and bottom by 2)

They are equal to the same reduced fraction so they are proportional.