Math Homework-easy but I need someone to explain how to do it!!

My math teacher does not teach us anything so can someone please explain this to me:
Determine if the ratios are proportional
9 over 27 and 6 over 20 - Are the proportional and how did you find that out?
21 over 14 and 18 over 12 - Are the proportional and how did you find that out?

Find a ratio equvalent to the givin ration. Then use the ratio to the given
number.
10 over 12 and 45 over 50 and 9 over 15
Thank you!

What you do is
1. First, simplify the fractions.
2. Multiply the top number of the first fraction with the bottom number of the second fraction.
3. Then multiply the bottom number of the first fraction with the top number of the second fraction

So try the first problem.
9 over 27 and 6 over 20
So first simplify.
9 over 27 = 1 over 3

Now the other fraction.
6 over 20 = 3 over 10

So now you have 1/3 and 3/10
Multiply top number of the first fraction with the bottom number of the second fraction then vice versa.

3 x 3 = 9
1 x 10 = 10

9 is not equal to 10, so NO, this one isnt in proportion. Why? Because 9 isnt equal to 10.

THEN (sorry this is sooo long)
To find an equivalent ratio to the given ratio, all you have to do is simplify.
So 10 over 12
Simplify that
10 over 12 = 5 over 6

sorry this was long

9/27= 1/3, 6/20 does not equal 1/3, so they are not proportional to each other.

21/14= 3/2, 18/12= 3/2, so they are proportional

I am not sure what you mean by the last part, so I will exclude myself from that part of the question unless you rephrase. Hope it helps anyways.