Unit 6 Summary

Pre-Algebra · Axiom Academy

SUMMARY Unit 6 Summary: Ratios & Proportions A review of how proportional reasoning lets us scale quantities and keep relationships consistent across many different contexts. A ratio compares two quantities; a rate compares two different units, and a unit rate standardizes it to "per one unit." A proportion sets two ratios equal ( a/b = c/d ); cross-multiplication ( ad = bc ) solves for any missing value. Similar figures share the same shape with equal corresponding angles, and their sides stay in a constant scale factor . Direct variation ( y = kx ) grows together; inverse variation ( xy = k ) trades one quantity off against the other. Proportional reasoning is multiplicative thinking — understanding how quantities scale together rather than just adding. A ratio compares two quantities and shows their relative size. It can be written three ways: 3:4 , "3 to 4," or . A rate is a special ratio comparing different units (like miles per hour), and a unit rate has a denominator of 1. Simplify: divide both terms by their greatest common factor — 12:18 becomes 2:3 . Compare with unit rates: standardizing to "per one unit" makes two rates easy to compare. A proportion is an equation stating that two ratios are equal — the fundamental tool for proportional reasoning. When two quantities keep a constant ratio they are proportional, so doubling one doubles the other. When to use: map scales, currency exchange, recipe adjustments — any constant-ratio situation.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.