# Relationship between ratio and proportion

### Difference Between Ratio and Proportion (with Comparison Chart) - Key Differences

A worksheet to demonstrate the relationship between ratio and proportion. Pupils can make their own up at the bottom. This is a good start of. In this lesson we'll be learning about proportions, ratios and their use in real life situations. Firstly, let's define a ratio. A ratio is a comparison between numbers of . A ratio is a comparison or relation between quantities, it is an abstract number. As for proportion, any three terms are given, the fourth may be found.

Four numbers p, q, r, s are considered to be in proportion if p: Here p, q, r, s are called the terms of proportion, wherein p is the first term, q is the second term, r is the third term, and s is the fourth term.

## Ratios and Proportions

The first and fourth term are called extremes while the second and third term are called means i. Further, if there are three quantities in continuous proportion, then the second quantity is the mean proportion between the first and third quantity. Important properties of proportion are discussed below: Invertendo — If p: Ratio is defined as the comparison of sizes of two quantities of the same unit.

Proportion, on the other hand, refers to the equality of two ratios. The ratio is an expression while proportion is an equation which can be solved. The ratio is represented by Colon: In contrast proportion, is denoted by Double Colon:: The ratio represents the quantitative relationship between two categories. As opposed to proportion, which shows the quantitative relationship of a category with the total. In a given problem, you can identify whether they are in ratio or proportion, with the help of keywords they use i.

Example There are total 80 students in class, out of which 30 are boys and rest of the students are girls.

• Difference Between Ratio and Proportion
• Ratio or Proportion?

Now find out the following: Have you ever thought about what these two words really mean? They are often used together as a phrase, "ratio and proportion", but are they in fact different terms for the same mathematical concept?

### Ratios and Proportions

If asked the difference by a pupil, how might you respond? I have to admit that I did not consciously reflect on the exact meaning of ratio or proportion until I began my teacher training. I suspect that this won't come as a particular surprise, but should I be worried about the definitions of these terms?

One of the difficulties we are often faced with in the classroom is familiarising children with the mathematical definition of a word which is also used in everyday language. Perhaps this applies to some extent to ratio and proportion? Somewhere in the depths of my mind, I seem to remember being told that ratio compares part to part whereas proportion compares part to whole.

But what does that really mean? And is it the whole story? Let's look at ratio first. In my mind, ratio is the comparison between two or more quantities. According to the Oxford English Dictionary online, ratio is 'the relation between two similar magnitudes in respect of quantity, determined by the number of times one contains the other integrally or fractionally '.

For example, on a bottle of orange squash it might say "dilute one part concentrate to four parts water". The amount of water required is given in terms of the amount of concentrate.

The National Numeracy Framework suggests that, when first introduced to children, this idea might be better expressed as "for every 1 part concentrate, we need 4 parts water". This ratio can be illustrated very clearly using simple pictures: In the classroom, "for every " can be modelled by actually drawing 4 "water rectangles" next to every "concentrate rectangle" so that pupils will be able to decide how many parts water are needed for a certain number of parts concentrate.

At a higher level, they will then be in a position to confirm whether or not a given pictorial representation describes the same ratio. Of course, having orange and white counters or cubes would be another way of depicting the concentrate and water. It is not too much of a leap then to introduce slightly different vocabulary for the same thing? In discussion with colleagues, we also realised that when we talk about ratios, it is perfectly appropriate to ignore units.

We might say that the ratio of apples to pears is 3 to 1 and this goes against the grain in terms of consistency of units. Surely this can only make the understanding of ratio more problematic? Mathematical dictionaries often include the word "fraction" in their definition of ratio.

So how does proportion fit in with this? The Numeracy Framework indicates that by the end of Year 6, children should be able to 'relate fractions to simple proportions'.

So, it seems that fractions are related to proportion too. Looking again at the Oxford English Dictionary, we find proportion defined as 'a portion or part in its relation to the whole; a comparative part, a share; sometimes simply, a portion, division, part'. At first sight, this would seem to agree with my original hunch.

If we look back at the image above, we can describe the same situation in terms of proportion: Put slightly differently, we might say 1 in every 5 parts is concentrate. This time we are relating the amount of concentrate 1 part to the whole 5 parts. However, if we turn to a mathematical dictionary again, we are told that 'the proportion of two quantities is their ratio' McGraw-Hill, The Collins Dictionary of Mathematics expands on this a little outlining proportion as the 'relationship between four numbers or quantities in which the ratio of the first pair equals the ratio of the second pair'.