**Direct Proportion and Inverse Proportion Class 8 NCERT**

Sometimes a change in the ratio of one amounts to a change in the ratio of another! For example, the more apples you buy, the more money you have to pay. Similarly, increasing the speed of a vehicle will reduce the time it takes to cover some distance. The first is an example of direct proportionality, and the second is an example of measurements of** inverse proportions.**

Direct and inverse ratios show how two quantities are related. Their relationship is known as direct or inverse. The symbol used to indicate proportionality is ‘∝. ‘ For example, if ‘a’ is said to be proportional to ‘b,’ it gets represented as “a∝b.” Furthermore, when we say ‘b’ is the inverse of ‘a’, it is represented as a∝ 1 /b

**What is direct proportion?**

**Direct Proportion:** Suppose you have increased the number of books in your bag. What will happen to its weight? And will increase. Of course, it will, so we call it a direct ratio. We can take two measurements, x, and y, which are assumed to be in direct proportion. Now, what does that mean? It means that the ratio of these two dimensions, x, and y, will always increase and continually decrease by their corresponding values.

We can understand this with the help of an equation. Suppose x / y = k, where k is a positive number or a constant, then x and y are said to vary directly.

If y1 and y2 are the values of y corresponding to x1 and x2 of x, respectively, then we can say:

The ratio is direct between two values when one is multiplied by the other.

For example, 1 cm is equal to 10 mm.

Here, to convert to cm, the product must be 10.

**What is the symbol of direct proportion?**

The symbol of** direct proportion** is “∝”.

Consider the statement,

A is directly proportional to B.

Using the symbol, the symbol can be written as: a∝ b

Consider another statement, a = 2b

In this case, A is shown to be proportional to B, and the value of one variable can be found by entering the value of the other variable.

**What is Inversely Proportional?**

**Inverse Proportion:** Now, what is an inverse ratio? Two dimensions, x, and y, are inversely proportional when increasing the value of x leads to a proportional decrease in y and vice versa. The speed and time of a journey are examples. It is said that when one value increases and the other decreases, the value is inversely proportional. The proportional symbol gets used in another way. Consider an example; we know that having more employees in a task will reduce the time taken to complete the task.

This gets presented as:

Number of workers ∝ (1/ Time to be taken to complete the job)

**Frequently Asked Questions (FAQ) about Direct and Inverse Proportion Ratios**

**Q – What are direct and inverse ratios?**

Ans – The direct ratio shows a direct relationship between two dimensions. The inverse ratio refers to the inverse or indirect relationship between two dimensions.

**Q – What is the variation between direct and inverse ratios?**

Ans – In direct proportion, if one quantity increases or decreases, the other quantity increases or decreases respectively. But indirectly or inversely, if one quantity increases, the other quantity decreases, and vice versa.

**Q – What is an example of a direct ratio?**

Ans – An example of a direct ratio is an increase in the price of a commodity with an increase in the number of items. Therefore, the price is directly proportional to the number of goods.

**Q – What is an example of an indirect ratio?**

Ans – An indirect ratio example is: Time is inversely proportional to the speed of the vehicle. If the speed increases, the vehicle may take

**Q – Does proportional mean the same?**

Ans – When an object is proportional to another object, it does not mean that they are related to each other, the values are the same. However, the constant of proportionality acts as a multiplier.

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