Ratios, rates, proportional relationships, and units
Ratios, rates, and proportions show up in roughly a quarter of Problem-Solving and Data Analysis questions. Most are straightforward once you set up the relationship correctly.
Core Idea
A proportion states that two ratios are equal:
Understanding
Three ideas drive this entire topic:
1. Ratios compare same-type quantities; rates compare different-type quantities. "3 red to 5 blue" is a ratio. "45 miles per hour" is a rate — miles and hours are different units.
2. Proportional relationships are linear through the origin. If
3. Units are your error-checker. When you set up a proportion or do a conversion, track the units. If the units on both sides don't match, something is wrong. Dimensional analysis — canceling units like fractions — catches setup mistakes before you ever solve.