Types of Ratio and Proportion

The ratio and proportion concept describes how to solve ratios, several sorts of ratios, the ratio formula, and more. A ratio is a mathematical term for splitting two like or distinct integers. The conversion procedure can be used to convert this phrase from ratio to percentage form. The ‘:’ symbol represents it. Ratios include 4:5, 6:7, 3:7, and so on. The ‘/’ symbol is also used to denote it.

Ratio and Proportion Basics

When comparing 2 quantities of the same kind, the ratio is used. For 2 numbers, p & q, the formula for ratio is expressed as p: q or p/q. Two or more ratios are said to be in proportion when they are equal. The concepts of ratio & proportion are based on fractions. Many other mathematical concepts are built on the foundations of ratio and proportion. Ratio and proportion can be used to solve a variety of everyday problems, such as comparing heights, distances, weights, and times, or adding ingredients to a recipe.

Ratio

A ratio is a comparison of two quantities that is calculated by dividing one by the other. The quotient x/y is called the ratio between x & y if x and y are two values of same kind and with same units, and y is not equal to 0. The colon sign is used to denote ratios (:). This means that the ratio a/b does not have a unit and can be represented as x: y.

Types of Ratios

Compound Ratio

If we take the antecedent as the product of the antecedents of the ratios & We have a mixed or compound ratio when the product of the consequents of ratios. As ax: by is the compound ratio of a:b and x:y.

Duplicate Ratio

The ratio of 2 equal ratios is termed as a duplicate ratio.

Duplicate ratio of a:b is a2: b2

Triplicate Ratio

The triple ratio is the sum of three equal ratios.

Triplicate ratio of a:b, a:b & a:b is a3: b3

Reciprocal Ratio

Reciprocal Ratio of x:y is 1x:1y.

Ratio of Equality

The ratio is called ratio of equality when antecedent & consequent are equal.

Example: 4:4

Proportion

The equality of two ratios is referred to as proportion. The proportion of two equivalent ratios is always the same. Proportions are defined by the symbol (::) & aid in the determination of unknown values. To put it another way, proportion is a statement or an equation that shows that two fractions or ratios are equal. If a: b = c: d, four non – zero quantities, a, b, c, & d, are said to be in proportion. 

Consider the following two ratios: 3:5 and 15:25. In this case, 3:5 = 3/5 = 0.6 and 15:25 = 15/25 = 3/5 = 0.6 can be represented as 3:5 = 3/5 = 0.6. We may claim that these two are proportionate because their ratios are equal.

Types of Proportion

Direct Proportion

The direct proportion between two quantities is defined as such. When one quantity rises, the other rises as well, and vice versa. A direct proportion is denoted by the symbol y∝x. When a car’s speed is raised, for example, it travels more distance in a given amount of time.

Inverse Proportion

The relationship between 2 quantities where one quantity increases while the other declines and vice versa is known as inverse proportion. As a result, inverse proportions are written as y∝1/x. A car, for example, will traverse a fixed distance in far less time as its speed is increased.

Formula For Ratio and Proportion

For two numbers x and y, the formula for ratio is given as

x:y→x/y

Here, 

x = Antecedent

y = Consequent

Proportion of 2 ratios p:q and r:s is

p:q ∷r:s→pq=rs

Here,

q & r = mean terms

p & s = extreme terms

In p:q ∷r:s, the values p & q must be of the be of the same same kind and have the same units, though r & s have the same kind & same units on their own.

Characteristics of Ratio and Proportion

Characteristics of Ratio

Alternendo

p/q=r/s→p/r=q/s 

Invertendo

p/q=r/s→q/p=s/r 

Dividendo

p/q=r/s→p-q/q=(r-s)/s 

Componendo

p/q=r/s→p+q/q=(r+s)s 

Characteristics of Proportion

1. Product of the Extremes = Product of the Means 

2. p : q = q:r then q is the mean proportional and q2 = pr.

3. p, q, r, …. are in continuous proportion then, p:q = q:r = r:s.

4. The 3rd proportional of 2 numbers, p & q is r, so that, p:q = q:r.

5. d is 4th proportional to the numbers p, q, r is s when p:q = r:s.

Conclusion

A ratio is a comparison of quantities with the same unit of measurement. It’s calculated by dividing the first by the second. The quotient x/y is considered as the ratio between x & y if x and y are two values of same kind & with the same units, and y is not equal to 0. Proportion is defined as a comparison between 2 ratios.

For 2 numbers p and q, the formula for ratio is

p:qp/q

The Proportion of 2 ratios p:q and r:s is

p:q ∷r:s→pq=rs

Proportion is divided into 2 parts which are Direct and Inverse Proportion.

The following types of ratios are:

1. Compound Ratio

2. Triplicate Ratio

3. Ratio of Equality

4. Duplicate Ratio

5. Reciprocal Ratio