Ratio and proportion

Do you know the mathematical concepts of ratio and proportion?

The online ratio and proportion simulations on this page will help you understand these two important mathematical concepts, how they relate to each other and how they differ.

Ratio and proportion are two fundamental concepts in mathematics that are used to compare and relate quantities or magnitudes to each other. These ideas are widely used in various fields, such as physics, economics, statistics and everyday problem solving.

Ratio refers to the comparison between two quantities or numbers and is expressed as the quotient of two terms. For example, if you have 4 apples and 2 oranges, the ratio of apples to oranges would be 4:2 or 4/2, which simplifies to 2:1 or 2/1. This indicates that there are twice as many apples as oranges.

Ratio, on the other hand, is an equality between two ratios. It is established when two ratios are equivalent. For example, if you have 6 lemons and 3 limes, and you also have 9 oranges and 4 bananas, you can state the ratio between lemons, limes, oranges and bananas as 6:3 = 9:4. This indicates that the ratio of lemons to limes is the same as the ratio of oranges to bananas.

Ratio and proportion are useful tools in many situations. For example, in proportionality problems they are used to solve proportional equations and determine unknown values. They are also fundamental in the calculation of percentages, scales and in data analysis. In statistics, ratios and proportions are used to compare groups and analyze trends.

In addition, ratio and proportion are useful in everyday life. For example, when calculating discounts in a store, ratio is used to determine the amount of money saved relative to the original price. They are also used to dilute chemical solutions, mix ingredients in cooking recipes, or adjust the proportions in a color mixture.

Below are several simulations and other educational resources, which can also serve as very illustrative examples. In addition, a selection of books and courses is included to help you broaden your knowledge of this subject.

Concepts
Unit
Playground

Ratio and proportion

Play with your left and right hand in different ways to explore ratios and proportions. Start in the Discover screen to find each ratio that the challenge asks for using your hands. Then, on the Create screen, set up your own challenge ratios. Once you have found a challenge ratio, try moving both hands while maintaining the challenge ratio through proportional reasoning.

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Unit rates

Discover the price/quantity ratio while shopping for fruit, vegetables, and candy. Build a double number line and look for patterns. Challenge yourself on the race track by comparing two cars with different distance/time ratios!

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Proportion playground

Play with ratios and proportions by designing a necklace, shooting paint balloons, playing pool, or buying apples! Make predictions about ratios before they are revealed.