Question

how do ratios work

Answer 1

A ratio is a comparison of two numbers by division.
A ratio can be given in different ways:
1/2, 1:2, 1 to 2 are all ways of expression the same ratio, which is read "1 to 2".

Answer 2

Notice that one way of writing a ratio is as a fraction.
Using the example above, 1/2 means 1 divided by 2.
Since a ratio can be written as a fraction, then the rules of fractions apply.

Let's say you set a set of books.
There are 5 books in French, and 10 books in English.
The ratio of French books to English books is 5/10, read "5 to 10".
Since 5/10 is a correct way of writing a ration (as a fraction), and since fractions can be reduced, you can reduce 5/10 to 1/2.
That means that a ratio of 5/10 is the same as a ratio of 1/2.

When you say that items are in a specific ratio, such as French books to English books are in a ratio of 1 to 2, you are not saying that there are exactly 1 French book and 2 English books.
You are saying that no matter the number of French books there are, there are twice as many English books.

Answer 3

Just one more thing.
When you set two ratios equal to each other, you have a proportion.
A proportion is a very useful tool in solving many problems.

Answer 4

Really, just one more thing.
Percentages are ratios based on a comparison with 100.
When you say 50%, it means 50/100, 50 out of 100, or 50 to 100.
A percentage is always a ratio of a number and 100.
Let's look at 50%.
50% means 50/100, or 50 to 10, or 50 out of 100.
We now reduce 50/100 by dividing both the numerator and denominator by 50, and we get 1/2.
I'm sure you know that 1/2 means half.
Now you see how 50% also means 1/2.

Answer 5

This is just a brief explanation.
If you are learning ratios, and you have specific problems you need help with, just post your questions, and someone will help you.