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28 October
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What is the difference between proportion and rate and portion ?Feel free to just provide example sentences.
What is the difference between proportion and rate and portion ?Feel free to just provide example sentences.
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 Armenian
 English (US) Near fluent
Let's take an example, that example being uniform motion. Suppose you're driving down the highway without slowing down or speeding up. And let's suppose that in 12 minutes you traverse 10 miles. Then the rate that you're traveling is 10/12 miles per minute. That's the same rate as 50 miles per hour. The reason it's the same rate is because of the proportion 10 : 12 = 50 : 60 there being 60 minutes in an hour. The expression 10 : 12 is a ratio.
A ratio a : b is named by two magnitudes, the antecedent a and the consequent b. (Sometimes ratios are continued and are named by more than two numbers.) A proportion a : b = c : d is a statement that two ratios a : b and c : d are equal.
A rate a/b is the interpretation of a ratio a : b as a quotient.
A bit more on ratios and proportions
There are a few other terms that go along with ratios and proportions. Some aren't used much anymore, but they all appear in Euclid's Elements. Before the advent of symbolic algebra and equations, much of mathematics was described in terms of ratios and proportions.
The ratio inverse to a : b is the ratio b: a. Taking the ratio a : b jointly results in the ratio (a + b) : b. Taking the ratio (a + b) : b separately results in the ratio a : b. Taking the ratio (a + b) : a in conversion results in the ratio (a + b): b When a : b = b: c, a : c is called the duplicate ratio of a : b; when a : b = b : c = c : d, a : d is called the triplicate ratio of a : b. Essentially, these are the square and cube of the original ratio.
The proportion alternate to a : b = c : d is the proportion a : c = b : d.
Before symbolic algebra, various rules for proportions were used to derive conclusions. For example, if a : b = d: e and b: c = d: f, then, ex aequali, you may conclude that a: c = d: f. Also, if two ratios are: с equal, then so are they taken jointly, taken separately, and taken in conversion.
 Armenian
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