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Learn Ratios and Proportions

Compare quantities, scale recipes and read maps with confidence.

Free to start. Built from a single prompt. No credit card.

A ratio compares two quantities, like 3 cups of flour to 2 cups of sugar, written 3:2 or 3/2. A proportion says two ratios are equal, which lets you scale: if 3 cups of flour need 2 of sugar, then 9 cups need 6. Ratios and proportions drive recipes, map scales, unit prices, speeds, mixing paint and similar triangles in geometry, and they are the bridge from fractions to algebra. The core skills are simplifying ratios, finding unit rates, and setting up and solving proportions correctly. Learnr builds a ratios and proportions course for your level and teaches it in short interactive lessons with everyday examples.

How to learn Ratios and Proportions, step by step

Build ratio tables before equations. For a 3:2 flour-to-sugar recipe, make a table: 3 and 2, 6 and 4, 9 and 6. Tables show that scaling means multiplying both quantities by the same number.
Compare with unit rates. Divide to get a rate per one: $4.50 for 3 pounds is $1.50 per pound. Unit prices let you decide which grocery package really is cheaper.
Share amounts in a ratio using parts. To split 20 marbles in a 3:2 ratio, count 5 total parts, so each part is 4 marbles, giving 12 and 8. Drawing bars of equal-sized blocks helps children see this.
Set up proportions with matching units. Keep the same units in the same position: 3 cups over 4 people equals x cups over 20 people. Cross multiply to get 4x = 60, so x = 15.
Apply scale factors to maps and shapes. On a map where 1 inch is 25 miles, 3.5 inches is 87.5 miles. Then use the same reasoning on similar triangles, where matching sides share one ratio.
Practice everyday scaling a little each day. Double recipes, compare unit prices and convert speeds. Pair that with brief daily Learnr lessons, with a streak to stay consistent, so proportional reasoning becomes second nature.

What you'll learn

Write and simplify ratios in all three notations
Find unit rates and compare unit prices
Split a quantity in a given ratio
Set up and solve proportions with cross multiplication
Use scale factors for maps, models and similar figures

What's inside your Ratios and Proportions course

A sample path Learnr builds for Ratios and Proportions. Your real course adapts to your goal and level.

1. What a ratio is and how to write it
2. Equivalent ratios and ratio tables
3. Unit rates and unit prices
4. Sharing in a ratio
5. Solving proportions
6. Scale drawings, similar figures and direct variation

How long does it take to learn Ratios and Proportions?

Most learners become comfortable with ratios, rates and proportions in about 2 to 5 weeks at 2 to 4 hours a week. Younger students meeting ratios for the first time usually need a bit longer and lots of concrete examples.

What you need before you start

Multiplication and division facts and working with simple fractions. Knowing how to find equivalent fractions makes equivalent ratios almost automatic.

Common mistakes to avoid

Reversing a ratio's order. A boys-to-girls ratio of 2:3 is not the same as 3:2, so keep the order the question gives.
Adding the same amount to both parts instead of multiplying. Turning 3:2 into 5:4 by adding 2 changes the ratio.
Mismatching units when setting up a proportion, such as putting cups on top of one fraction and people on top of the other.

How Learnr builds your course

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Ratios and Proportions questions, answered

What is the difference between a ratio and a fraction?

A fraction compares a part to a whole, while a ratio can compare any two quantities, including part to part. A 3:2 ratio of red to blue means red makes up 3/5 of the total.

How do I explain ratios to a child?

Use snacks or blocks. Lay out 2 crackers for every 1 cheese slice, then double and triple the groups, showing that the pattern stays the same while the totals grow.