---
title: Ratios & Proportions
description: Ratios and proportions compare quantities and establish relationships between different scales. You will understand how to write, simplify, and solve ratios, use proportions to find unknown values, and apply these concepts to scale drawings and rate problems.
category: mathematics
subcategory: arithmetic-and-pre-algebra
difficulty: beginner, intermediate, advanced
url: /subject/ratios-and-proportions
---

# Ratios & Proportions

Ratios and proportions compare quantities and establish relationships between different scales. You will understand how to write, simplify, and solve ratios, use proportions to find unknown values, and apply these concepts to scale drawings and rate problems.

## Available Resources

1 Books • 4 Websites

## Websites

### 1. Math is Fun - Ratios

A short reference page defining ratios, showing how to write them in colon and fraction form, simplify them, and scale them up or down. Worked examples and quick practice questions let a learner compare quantities and solve basic sharing problems.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.mathsisfun.com/numbers/ratio.html

**Tags:** ratios, simplifying-ratios, equivalent-ratios, pre-algebra

### 2. Khan Academy Ratios & Proportions

Khan Academy's pre-algebra unit on ratios, rates and proportions, combining short video lessons with graded practice exercises. Learners finish able to compute unit rates, test whether two ratios are proportional, and solve proportion and percent word problems.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/pre-algebra/ratio-and-proportion

**Tags:** ratios, rates, proportions, unit-rates, pre-algebra

### 3. NRICH: Ratio, Proportion and Rates of Change — Short Problems

About seventy short challenge problems on ratio, proportion, rates, speed and time, curated by Cambridge's NRICH project from UK maths challenges. Each carries a star difficulty rating and a full worked solution; printable worksheet selections are linked.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://nrich.maths.org/9256

**Tags:** ratios, proportions, rates-of-change, speed-distance-time, problem-solving

### 4. mathsisfun.com

MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathsisfun.com

**Tags:** websites, mathematics-statistics, algebra

## Books

### 1. Teaching Fractions and Ratios for Understanding (5th Edition)

**Author:** Susan J. Lamon

Research-based account of rational-number reasoning: ratio, rate, unit rate, relative versus absolute comparison and proportional-reasoning strategies, developed through activities meant to be solved by reasoning rather than algorithms, with student work samples analysed chapter by chapter. The right pick for a tutor, parent or serious self-learner who wants to know why learners fail at proportions.

**Difficulty:** Advanced | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/1032936002?tag=edmonddante07-20

**Tags:** proportional-reasoning, rational-numbers, fractions, ratios, mathematics-education

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