Beep, beep, back the truck up. Let's quickly remember that a ratio is a comparison of two related quantities found by dividing one quantity by another. To write a ratio, you can either write the two numbers as a fraction, write the two numbers with a colon (no, not that kind of colon! Gross!) in the middle, or write the word "to" in between the two numbers.
Let's say we have 3 blue stars, 5 red stars, and 2 gold stars. There are oodles of ratios we can write about the number of stars we have. We could write a ratio comparing blue stars to red stars (3⁄5), red stars to gold stars (5⁄2), or gold stars to all stars (2⁄10).
It's important to know that the ratio of gold stars to red stars (2⁄5) is not the same as the ratio of red stars to gold stars (5⁄2). If we turn the words around, the numbers will follow.
Sample Problem
What is the ratio of cats to dogs?
The ratio of cats to dogs will name how many cats there are compared to how many dogs there are. Since there are three cats and five dogs, our choices are ⅗, 3:5, and 3 to 5. Cover your eyes, cat lovers. The dogs win this time.
Sample Problem
Mrs. Greene's geometry class has 14 girls and 12 boys. What is the ratio of girls to total students?
Since there are 14 girls and 26 total students, the ratio is 14:26. We could also write it as 14 to 26 or 
. Or, we could get really fancy and say 7:13, 7 to 13, or 
.
Whaaaa?! Yes, it's true. In very much the same way that we can manipulate fractions, we can also manipulate ratios. We can reduce them to their simplest terms, convert them to percentages, and, most importantly for our purposes today, find equivalent ratios. When you do find two equivalent ratios, you've got yourself a proportion. But hold your horses, we'll get to that in a minute.
Sample Problem
At the local park, children have the choice of spinning until they puke on the merry-go-round or giving themselves a wicked case of vertigo on the swings. The little thrill-seekers choose the swings over the merry-go-round by a margin of 3 to 1. Last week, 100 kids played at the park. How many of them swung themselves silly?
Saying, "a margin of 3 to 1," is like saying, "a ratio of 3 to 1." Even more helpful, it's like saying, "3 out of 4," or three-fourths, or ¾. So, out of 100 kids on the playground, 75 of them swung themselves silly.