Direct, inverse and indirect proportionality - Math Central
If two quantities X and Y are inversely proportional, then they are generally represented as: to y having two values y1 and y2 respectively, then by the definition of inverse variation, we have . Consider the given inverse relationship function. (The meaning of indirect when applied to proportional quantities sounds the terminology "inversely proportional" to describe the relationship between two. Two values are said to be in direct proportion when increase in one results in an increase in the other. Similarly, they are said to be in indirect proportion when.
Inverse Proportion | eMathZone
Where does this leave us? I struggle to make any conclusions from the above -the boundaries between the two seem very blurred to me.
At best, I feel happy with my understanding of ratio but it appears that the word proportion is used in two different ways. I would be very keen to hear your own thoughts on this matter which I would add to this article.
Perhaps you have clear definitions in your own mind that might help?
If you can shed light on "ratio and proportion", let us know by emailing primary. Click here to read what Phil had to say. Veronica Bates from Colchester also sent us her thoughts which you can read here.
- A sense of proportion
- Direct and inverse proportions
- Inverse Proportion
Thank you also to Bruce Moody, from New Zealand, who has contributed these ideas. Debby Sanjaya, from Indonesia, emailed to say: I just want to share my understanding. I think proportion is a ratio of the quantity of a part in its relation to the whole.
Ratio or Proportion? : czechbattlefield.info
Someone who remained anonymous wrote: I would argue, ratio is part to part and proportion is part to whole. They mean different things. I would say it is 1: I claim the ratio is 1 to 3 or 1: You can read what he had to say here. Someone else found a useful bit of information on http: A proportion or proportional situation occurs when two things are related in such a way that the ratios of corresponding parts are equal.
It would then seem that the Collins Dictionary of Mathematics has the better definition, " This also seems to stress the importance of similarity between the objects or situations. Still, there is some ambiguity in the use of the word "proportion".
Perhaps this is merely an incorrect use of the word "proportional".
Regardless, "proportional" in a description is always assumed to be "directly" proportional unless another word, "inversely" is present. I think proportionality and the ability to express proportionality mathematically is a major idea in a student's maths education. Another closely related topic is rate or unit rate. Is a rate a ratio? Not in terms of consistency of units, but in terms of proportional situations it is.
Thinking of rates as ratios, which will fit into the proportion model, helps students solve problems involving rate. Hi I read your article with interest - the way I have come to terms with these two in my mind is that the ratio focuses on the relationship of the split of the whole into parts whilst the proportion shows the 'gap'- or 'space between' which needs to be maintained - almost like it provides the track or parallel lines the figures must travel along to maintain their relationship - am I way off the mark?
I would say that ratio is the relationship between two quantities. Proportion is the a subset of this, in that the two quantities are a part and the whole of the same thing. The concept of proportional extends this idea to any two quantities that have a constant multiplicative relationship.
So ratio is now just one way of representing a proportional relationship, with other ways being fraction, equation, graph, bar diagram etc. So our proportional relationship can be rewritten from: If we look at our previous two examples: We will use this fact in several parts of the course.GCSE Maths Revision - Direct and Inverse proportion
Other Proportional Relationships Proportional relationships can get more complicated than simply directly or inversely proportional. Very often quantities depend on the square root or cube of another quantity. One relationship we will see a number of times on the course is called inverse square proportionality.
For example we will later see that the force between two masses due to gravity is inversely proportional to the square of the distance between the masses, or: Detecting Proportionality As explained in the introduction, physics and science in general are concerned not just with theory, but practice as well.
As part of this course, you need to be able to recognise when relationships are proportional, particularly as a result of your experiments. You do this by drawing a graph of the relationship. The following graphs illustrate various types of proportionality: Proportional relationships show a straight line through the origin.
Ratio or Proportion?
Inversely proportional relationships show a characteristic curve. Plotting the relationship as an inverse leads to a regular proportional graph. Other proportional relationships will have their own characteristic graphs, but can always be replotted to make a proportional graph.