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Ratio and proportion in mathematics. Difference

Do you know the mathematical concepts of ratio and proportion?

The online ratio and proportion simulations in mathematics on this page will help you understand these two important concepts. Learn what mathematical ratio and mathematical proportion are, what is the difference between them and discover some of their most important applications

What are ratio and proportion in mathematics

Ratio and proportion in mathematics are two fundamental concepts  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.

Mathematical ratio

Mathematical 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.

Mathematical proportion

Mathematical proportion, 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.

Applications of ratio and proportion in mathematics

Ratio and proportion in mathematics 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, ratios and proportions 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.

In summary, the ratio and proportion simulations in mathematics on this page will help you understand and differentiate these two important concepts. Take advantage of them!

Ratio and proportion simulations in mathematics

Ratio and proportion in mathematics


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 mathematical ratio


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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Mathematical 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.


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