How could be given two ratios are equivalent

ratio

I'm currently learning Maths and got interested in Ratios. Currently, I'm going through equivalent ratio lesson and found that to be magical somehow.

I am impressed that given two ratios can have same value, but I don't know how is it possible and I know the rule and can say whether they are equivalent or not but still I don't understand how it works behind the scenes.

Example

Super Salad Dressing is made with 8 mL of oil for every 3 mL of vinegar.
I found that based on rule, 80ml and 30 ml = 8mL and 3mL, if I write it mathematically, 
it would be 80:30 == 8:3 

If I compare both of them physically, they are not equivalent because 80 Ml larger than 8 Ml and even tho It's amazing that they are equivalent.

Best Answer

If I compare both of them physically, they are not equivalent

If you compare which physically?

because 80 Ml larger than 8 Ml

There's no reason to compare the $80$ Ml to the $8$ Ml. $80$ Ml is $\frac 83$ times bigger than $30$ Ml. So they are in ratio of $8:3$. And $8$ Ml is $\frac 83$ times bigger than $3$ Ml. So they are in ratio of $8:3$. And the Pacific Ocean at $704,000,000$ cubic kilometers is $\frac 83$ times bigger than the Indian Ocean at $264,000,000$ cubic kilometers. So there are in ration of $8:3$.

A ratio compares the sizes of two different things in proportion to each other. The absolute size doesn't matter.

If you are trying to compare $80$ ml to $8$ ml they are in $10:1$ proportional. And that is the same proportion that $30$ ml is to $3$ ml.

If you compare the oil to vinegar there is always $\frac 83$ more oil than vinegar no matter what size your recipe is.

And if you are comparing the two different recipes: the bigger recipe is $10$ times bigger than the smaller recipe. So the bigg recipe will have $10$ times as much oil, or $10$ times as much vinegar or $10$ times as many eggs, etc.

and even tho It's amazing that they are equivalent.

Actually it's very dull and mundane and would be very weird if they weren't.