Ratios, Proportions & Rates
Overview
Scale, speed, unit rates, mixtures, and proportional reasoning for real-world problem solving.
Lessons
Understanding Ratios
Learn what a ratio is, the difference between part-to-part and part-to-whole ratios, and how to write and simplify them.
Equivalent Ratios
Discover how to scale ratios up and down, build ratio tables, and determine whether two ratios are equivalent.
Introduction to Proportions
Understand what a proportion is, how to identify one, and when to use proportional reasoning to solve real-world problems.
Solving Proportions with Cross-Multiplication
Master the cross-multiplication technique for solving proportions, and apply it to multi-step real-world word problems.
Unit Rates and Unit Pricing
Learn to calculate and interpret unit rates, find the best buy between products, and apply unit rates in everyday decisions.
Speed, Distance, and Time
Apply the rate formula d = rt to solve for distance, speed, or time — including multi-leg journey problems.
Scale Factors and Scale Models
Use scale factors to interpret maps and blueprints, build scale models, and convert between model measurements and real-world dimensions.
Percent as a Rate per Hundred
Connect percent to ratio thinking — learn why percent is a rate, how to convert between forms, and how to find a percent of a quantity.
Ratio Word Problems: Mixtures, Recipes, and Dividing in a Ratio
Solve multi-step ratio word problems involving mixtures, recipe scaling, and dividing a total quantity into parts that follow a given ratio.
Rates of Change in the Real World
Understand how rates describe change over time — from fuel efficiency and pay rates to population growth and unit price changes.
Calculators
Ratios, Proportions & Rates 3 Foundations Active
Proportion Solver
Solve for x in a proportion (two equal ratios) like a/b = c/d.
Tutorial Ready
Ratio Solver
Solve for the missing value in a proportion (a/b = c/d).
Tutorial Ready
Speed, Distance & Time
Solve for speed, distance, or time using the d = rt formula. Enter any two values and choose what to calculate — with step-by-step work shown.
Tutorial Ready