Ratio
Three trumpets for every two drums. How do you describe how two amounts go together, so the description still holds when everything is scaled up or down?
Where you are 6 inside
What this area is about
A ratio compares two amounts by multiplying, not subtracting: 3 : 2 says “for every 3 of one, 2 of the other”. Multiply both amounts by the same positive number and the ratio stays the same. That one fact runs through rates, proportions and scale drawings.
How these fit together
Definitions. What a ratio is gives the language and notation, part-to-part and part-to-whole ratios, and how to tell which of two ratios is larger. Equivalent ratios and ratio tables scales both amounts by one positive number and keeps track of it in tables and diagrams.
Ratios of different units. Rate and unit rate compares amounts in different units, such as boxes and minutes, and divides to get the amount for exactly one.
Results and procedures. A proportion states that two ratios are equivalent, \displaystyle \frac{a}{b} = \frac{c}{d} with b and d not 0, and solves for a missing number. Proportional relationships are pairs of quantities with y = kx for one fixed k, recognized in a table, graph or equation, set beside the inverse pattern xy = k. Scale drawings multiply every length by one positive scale factor and keep the angles, so a map gives real lengths.
A path through it
What a ratio is and equivalent ratios go together, in either order. Then rate and unit rate, then proportion, then proportional relationships, and scale drawings last.
Ratio leads on to percent, a ratio out of 100, and to similarity and partitioning a segment in a ratio in geometry.