Ratios

Introduction:

This chapter takes us much further and adds to our already existing knowledge about Ratio and Proportion. We will have to use many of the algebraic manipulations learnt earlier, use them with expertise to solve problems in this chapter.

Proportions are built from ratios. A "ratio" is just a comparison between 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 ratio of men to women is 15 to 20. Notice that, in the expression "the ratio of men to women", "men" came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been "the ratio of women to men", then the numbers would have been "20 to 15". 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 for your test. Given a pair of numbers, you should be able to write down the ratios. For example: There are 16 ducks and 9 geese in a certain park. Express the ratio of ducks to geese in all three formats. Consider the above park. Express the ratio of geese to ducks in all three formats.