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αAπΣ∞∂θ√x²≠∫÷≤%+−½αβΔλφ³≈∑°
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Unit 2~50 min3 lessons · 8 videosGADOE framework↗

Ratios & Proportional Relationships

Use ratios and rates to compare quantities, then use proportional reasoning to solve real-world problems.

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Study guide

Unit 2: Ratios & Proportional Relationships

Your progress

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On this page

  • Written lessons
  • Objectives & vocabulary
  • Video walkthroughs
  • Worksheets
  • Extra practice
  • Unit quiz
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 1 · Learn

Written lessons

Quick read-throughs in plain language — then hit the videos below.

A ratio compares two things. 2 cups flour to 3 cups sugar = 2:3 (or 2/3 or "2 to 3").

Order matters! Flour to sugar (2:3) is not the same as sugar to flour (3:2). Multiply both parts by the same number to get an equivalent ratio — like 4:6.

Try it

Write the ratio of 5 dogs to 8 cats.

Goals

Learning objectives

By the end of this unit, you should be able to:

  • ✓Write and interpret ratios in multiple ways
  • ✓Find and use unit rates (price per unit, miles per hour)
  • ✓Recognize proportional relationships in tables and graphs
  • ✓Use equivalent ratios to solve problems

Key vocabulary

Ratio
A comparison of two quantities.
Rate
A ratio that compares two different units.
Unit rate
A rate with a denominator of 1.
Proportion
An equation that says two ratios are equal.
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 2 · Watch

Video walkthroughs

Each video covers one topic from this unit — read the short blurb below to find the right one.

Khan Academy

Introduction to Ratios

What a ratio is and how to write one to compare two quantities.

Watch on YouTube
Math Antics

Ratios & Rates

See how ratios show up in everyday comparisons.

Watch on YouTube
Other

Rates and Unit Rates

Find cost per item, speed, and other per-one rates.

Watch on YouTube
Other

Rates and Unit Rates (extra examples)

More practice turning a rate into a unit rate.

Watch on YouTube
Khan Academy

Proportional Relationships

Spot when two quantities grow together at a steady rate.

Watch on YouTube
Math Antics

Proportions

Set up and solve equations where two ratios are equal.

Watch on YouTube
Math Antics

Simplifying Fractions

Shrink fractions to simplest form — useful before comparing ratios.

Watch on YouTube
Khan Academy

Equivalent Fractions

Find different fractions that name the same amount.

Watch on YouTube
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 3 · Practice

Practice worksheets

Adam's curated problem sets — preview here or open in Google Drive.

Worksheet — Ratios & proportions

Mixed practice across the unit.

Open in DriveDownload
More practice

External resources

Hand-picked links from Khan Academy and trusted worksheet libraries.

Khan Academy

Ratios & proportions practice

Open resource
Math Worksheets 4 Kids

Ratio worksheets

Open resource
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Step 4 · Check

Unit 2 quiz

A few quick questions to make sure the big ideas stuck. Retake as many times as you want.

Unit 2: Ratios & Proportional Relationships

Question 1 of 3

Easy

A car drives 180 miles in 3 hours. What is the unit rate in miles per hour?

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
←Previous · Unit 1Number System & Operations→Next up · Unit 3Expressions & Equations