Proportion
Two ratios are supposed to describe the same comparison, and one of their four numbers is missing. How do you write that down, and how do you find the missing number?
Where you are 3 inside
What this area is about
A proportion is a statement that two ratios are equivalent, written a : b = c : d or \displaystyle \frac{a}{b} = \frac{c}{d} with b and d not 0. It is how a fixed comparison, such as stock to servings in a soup, gets carried from one size to another. This area says what the statement means, how to solve it, and how to build one from a word problem.
How these fit together
The definition. What a proportion says: two ratios of positive numbers are equivalent when the second is the first with both parts multiplied by the same positive number.
The procedure. Solving a proportion finds the unknown that makes the two ratios equal: by scaling across from one ratio to the other, through a unit rate, by multiplying both sides, or by cross products, the last two working whatever the numbers are.
The setup. Setting up proportions from word problems decides which number goes on top and which underneath, matching units on both sides, and first checks that the situation keeps a fixed ratio at all.
A path through it
What a proportion says comes first, then solving one, then setting one up from words.
Finish here and proportional relationships, scale drawings, similar figures, percent problems and equations from proportions and percents all use it.