What a ratio is
Three trumpets for every two drums. How do you say how two amounts go together, in a way that still holds when everything gets bigger?
Where you are 3 inside
What this area is about
There are two ways to compare 3 trumpets with 2 drums. Subtracting says there is 1 more trumpet. A ratio says how they go together: for every 3 trumpets, 2 drums, written 3 : 2. Double the band and the difference changes, but the ratio does not. This area is what a ratio says, what it compares, and how to tell which of two ratios is larger.
How these fit together
Definitions. What a ratio is: language and notation gives the ways to say and write one: “3 to 2”, 3 : 2, “for every 3 trumpets, 2 drums”. Part-to-part and part-to-whole ratios separates comparing one part with another from comparing a part with the whole: 2 red flags to 5 white is 2 : 5, but red flags are \displaystyle \frac{2}{7} of all the flags, not \displaystyle \frac{2}{5}.
A procedure. Deciding which of two ratios is larger scales both so they share one amount, then compares the other.
A path through it
Language and notation first, then part-to-part and part-to-whole ratios. Comparing two ratios needs equivalent ratios as well, so it comes after that area.
Finish here and you are ready for scaling a ratio, tape diagrams, unit price and percent as a rate per hundred.