Direct and Inverse Proportion Average

The ratio is a comparison of two quantities with similar units. And when two ratios are similar, the four quantities that constitute these two ratios are said to be in proportion with each other. Proportion is used for the comparison of two ratios with each other. 

There are two ways in which two ratios can be proportional to each other. The two types are direct proportions and inverse proportions. This is based on how a change in one quantity affects another quantity. Let us learn about these two types of proportions; the symbols used to represent them and their formulas.

Proportions

Before we dive into types of proportions, understand what proportions are.

Suppose the ratio of quantity a to quantity b is a:b and the ratio of quantity c to quantity d is c:d. Suppose the ratio a:b is equal to the ratio p:q.

Then the quantities a, b, p, and q are said to be in with each other. It can be represented as given below.

a:b::p:q, which is equal to a/b = p/q.

Types of Proportions

When two quantities are said to be in proportions, they can either be directly proportional to each other or inversely proportional to each other.

This classification is based on whether an increase in one quantity leads to an increase or decrease in the other quantity.

The directly proportional symbol is different from the inversely Proportional symbol.

Let’s study these two types of proportions in depth.

Direct Proportion

Two quantities are said to be directly proportional to each other if an increase in one quantity means increasing the other quantity, and a decrease in quantity means a decrease in the other quantity.

Suppose A and B are two quantities, and A is directly proportional to B.

Then there will exist a constant k such that B = k × A.

Note that this constant K is a non-zero value.

This value K is termed as the constant of proportionality or the proportionality constant.

The symbol used to depict the direct proportionality is ” ∝ . ” It looks like the Greek alphabet Alpha.

Using this symbol, the above proportionality can be expressed as:

A ∝ B

In direct proportion, one of the two values is multiple of the other value.

In the above-stated example, quantity B is the multiple of quantity A.

Examples of Direct Proportion

 Direct proportion is served in the following situations.

When an object is travelling at a constant speed, according to the formula of speed,

speed = distance/time

Here the distance is directly proportional to the time quantity, and the speed here is the proportionality constant.

Properties of Direct Proportion

Following are properties of direct proportion:

• If one of the quantities that are in direct proportion increases, the other quantity increases as well.

• If one of the quantities that are in direct proportion decreases, the other quantity decreases as well.

• During any change in the quantities, the corresponding proportionality ratio K always remains constant.

• Direct proportionality is also called direct variation.

Let’s see when two ratios are said to be inversely proportional to each other.

Inverse proportion

The inverse question is the opposite of the direct proportion. Two quantities are said to be inversely proportional to each other if the increase in one quantity means a decrease in the other quantity.

Suppose A and B are two quantities that are said to be inversely proportional to each other. There will exist a constant K such that:

A= K/B

Note that K is always a non-zero number.

In inverse proportion, two quantities are proportional to the reciprocal of each other.

The product of two quantities that are inversely proportional to each other is always constant.

The graph of two is inversely proportional to each other is a rectangular hyperbola on the cartesian coordinate plane.

The inversely proportional symbol is “∝. “

Example of Inverse Proportion

As stated above, the formula for an object at constant speed is 

speed = distance/time

Here time is said to be inversely proportional to speed.

It is represented as:

Speed ∝ 1/Time

As speed is proportional to time, when the speed of an object increases, the time is taken by that object to complete the distance will decrease.

Properties of Inverse Proportion

Following are properties of two quantities inversely proportional to each other.

• If the first of two quantities inversely proportional to each other increases, the other quantity decreases.

• If the first of two quantities are inversely proportional to each other decreases, the other quantity increases.

• The variation in the corresponding ratios is always inverse.

• Inverse proportion is also called the indirect variation.

The directly proportional symbol and the inversely proportional symbol both look like ∝. The only difference is in the representation.

Conclusion

Ratios help in the comparison of two quantities with the same units. And proportions help in comparison of two ratios. If two ratios are equal to each other, then four quantities that make up the two ratios are said to be in proportion.

There are two types of proportions. That is proportion and inverse proportion. In the direct proportion, as one quantity increases, the other quantity also increases. However, in inverse proportion, as one quantity increases, the other one decreases. The product of quantities remains constant if they are inversely proportional. Proportionality is expressed by the symbol ∝, similar to the Greek alphabet Alpha.