Ratio

Proportions are built from ratios. A "ratio" is just a comparison between, or a relating of, two different things. For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the rest are women, so:

35 – 15 = 20

...there are twenty women in the group. The language "the ratio of (this) to (that)" means that (this) comes before (that) in the comparison. So, if one were to express "the ratio of men to women", then the ratio, in English words, would be "15 men to 20 women" (or just "15 to 20").


The order of the items in a ratio is very important, and must be respected; whichever word came first in the ratio (when expressed in words), its number must come first in the ratio. If the expression had been "the ratio of women to men", then the in-words expression would have been "20 women to 15 men" (or just "20 to 15").

source: twinkl.co.uk

Expressing the ratio of men to women as "15 to 20" is expressing the ratio in words. There are two other notations for this "15 to 20" ratio:

odds notation: 15 : 20

fractional notation: 15/20

 You should be able to recognize all three notations; you will probably be expected to know them, and how to convert between them, on the next test. For example:

There are 16 ducks and 9 geese in a certain park. Express the ratio of ducks to geese as a ratio with a colon, as a fraction (do not reduce), and in words.
They want "the ratio of ducks to geese", so the number for the ducks comes first (or, for the fractional form, on top). So my answer is:

16:9, 9/16, 16 to 9

The ratio from a representative group can also be used to provide percentage information.

In the class above, what percentage of students passed the class? (Round your answer to one decimal place.)
I already know that the representative group contains 12 students, of which 7 passed the class. Converting this to a percentage (by dividing, and then moving the decimal point, as explained here), I get:

7/12 = 0.583333... = 58.3333...%

They want the answer rounded to one decimal place, so my answer is:

58.3% passed



This article was originally published on The purplemath. Read the original article.

Source:
https://www.purplemath.com/modules/ratio.htm