What is the difference between equivalent ratios and proportions

The goal should be that they eventually understand and become skilled with the abstraction a fraction. The concept being abstract means, that it can be applied in a wide variety situations and can be used as a model for many concrete examples.

The key to understanding is eventually seeing what is common between seemingly different things. That is why it is not so useful to go into abstract explanations of what is the difference between the "definition" of a fraction and a ratio.

Just explain it in the minimalistic sense of what the notation means, and then focus on developing their understanding of the concept of a fraction. Sign up to join this community.

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Asked 6 years, 9 months ago. Active 11 months ago. Viewed 26k times. Improve this question. Isaiah 1 1 gold badge 3 3 silver badges 7 7 bronze badges. Abdallah Abusharekh Abdallah Abusharekh 1 1 gold badge 8 8 silver badges 20 20 bronze badges. Does having a clear distinction between these concepts make it easier to solve any real-world problems?

Especially if you are careful to use units? I found the wikipedia page to be quite useful: en. Show 7 more comments. Active Oldest Votes.

Improve this answer. Burt Furuta Burt Furuta 6 6 silver badges 10 10 bronze badges. A 3 to 4 ratio, as in cooking, means for every 7 cups of stuff used, 4 are of one type, and 3, the other. The example doesn't make this clear. Add a comment. Tamisha Thompson Tamisha Thompson 5 5 bronze badges. Karl Karl 1, 1 1 gold badge 8 8 silver badges 14 14 bronze badges. Some additional evidence that ratio and fraction are distinct concepts: The ratios and both make sense. In other words, ratios are just elements of real projective spaces!

Please don't tell this to your 5th graders. Steven Gubkin Steven Gubkin Alecos Papadopoulos Alecos Papadopoulos 1, 7 7 silver badges 14 14 bronze badges. Dan Fox Dan Fox 4, 11 11 silver badges 28 28 bronze badges.

People just use "ratio" because it is simpler to say than a "proportional relationship". Likewise, people use "rate" instead of "speed", then they wonder why kids don't understand what rate is.

SE: First of all, I would leave out ratios entirely, if possible. Why are ratios less expressive? How to explain the difference? Jasper Jasper 1, 11 11 silver badges 19 19 bronze badges. It nicely points out the fact that ratios written this way aren't technically numbers. For one thing, fractions are ratios. Rational numbers are numbers that can be expressed as ratios.

Great job! Going to use it in my lesson. On the rocks. Mix is teh debil yes, "teh"; not "the". Peter Moomaw Peter Moomaw 11 3 3 bronze badges. Whereas proportion is a ratio between 2 fractions. MathGuy MathGuy 9 1 1 bronze badge. It is the number that can be used to express one quantity as a fraction of the other ones. Ratios are denoted by the symbol of the colon :.

Proportion refers to a part, share, or number considered in relation to a whole, majorly a comparative relation. Two equivalent ratios are always in proportion. It is an equation or statement that is used to depict that the two ratios or fractions are equal. It is a mathematical comparison between two numbers. Accordingly, the ratios are said to be directly proportional to each other, if two sets of given numbers are increasing or decreasing in the same ratio.

It describes the direct relationship between two quantities, if one quantity increases, the other quantity also increases and vice-versa. Let's take an example, you must have noticed that if the speed of a car is increased, then it covers more distance in a fixed amount of time.

It describes the indirect relationship between two quantities, if one quantity increases, the other quantity decreases and vice-versa. Let's take the example of a vehicle. As the speed of a vehicle is increased, it will cover a fixed distance in less time. Now, in order to find proportion for the two ratios, a:b and c:d. Now, let us consider the two ratios - and Since both the ratios are equal, we can say that these are two are proportional.

Here, 3 and 25 are the extremes, while 5 and 15 are the means. Given ratios are and Here, both the ratios are equal. Therefore, and are in proportion. Example 2: Out of the total number of students in a class that is The number of students who like Math and the ones who like Science is in the ratio Find the number of students who like Math and the ones who like Drawing. Proportions and ratios worksheets Proportions - Integers The Magic Square Learn about the History of pi The number Pi has Most downloaded worksheets Vectors measurement of angles What is Mathemania?

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