Unity is the most important entity in mathematics. Chapter 9 on the Ratio, Proportion and Unitary method elaborates the concepts of ratio and proportions essential to understand most mathematical concepts. The concepts of ratio, proportion and unitary method can also be used for comparing entities.
Ratio and proportion have few similarities, but the major difference between them is that a ratio is used for comparing one part with another part, whereas a proportion is used to express the relationship between two ratios. It also tells us that ratios are often used in comparing mathematical concepts such as converting one unit into another, measuring quantities in a recipe, etc.
Ratios are denoted as follows:
Between two comparable quantities, i.e. 7:8, 1:5, here 7 is called antecedent, and 8 is defined as consequent. These are similar to fractions (7/8, 1/5).
To compare two ratios, write them in the form of fractions. They are said to be equal if they are equal in terms of fractions too. We can also define a ratio as a simplified term of two quantities of the same kind. The ratio can be defined only by two numbers of the same kind and similar units.
Chapter 9-Ratio, Proportion and Unitary method also shed light on the term proportion, which states that two given ratios are related to each other. There are two types of proportions, namely, direct and indirect proportion. When two sets of a given number increase or decrease in the same ratio, it is defined as direct proportion and if they act opposite to each other, they are said to be in inverse proportion. "::" Or "=" is used to denote the proportion. For example, a: b:: c: d, where b and c are known as a mean term, and a and d are referred to as extremes.