Inverse Proportion

In mathematics, the two commonly used proportions are direct proportion and inverse proportion. Inverse proportion is the opposite of direct proportion.

Two values are in inverse proportion when one decreases as the other increases. If the product of the two quantities equals a constant value, regardless of the change in their values, they are considered to be in inverse proportion. 
 

The mathematical representation of the inversely proportional relationship of two quantities is given below:

• x and y are two inversely proportional variables, and the product always remains constant(k).

            x × y = k

• The commonly used formula that indicates y is inversely proportional to x:

            y = k/x

• When two sets of values are inversely proportional, their product remains constant.

           x1 × y1 = x2 × y2

Direct and inverse proportionality are mathematical tools that measure the change in one quantity with the change in the other. The key differences between the two are listed below:
 

Learning about inversely proportional relationships helps children understand the mathematical connection between quantities. Let’s look at a few tips and tricks to understand this connection easily:
 

• Students should always remember that when one quantity increases, the other decreases, or vice versa then it is inverse proportion .

• The product of two inversely proportional quantities will always result in the constant. i.e., k = x 1 ×  y1.

• To learn inverse proportionality try to use it in real-life situations. That is where one quantity increases as the other decreases.  For example: The more the number of people, the less time it will take.

• The graph of inverse proportion gives a curved line. i.e., as x goes up, y comes down.

• You can imagine a see-saw to better understand inverse proportionality. i.e., when one rises, the other falls.
   

Inversely proportional relationships can be observed in many real-life situations. Understanding their real-world applications helps students apply the concept quickly. Let’s learn how it can be applied:

• Students can easily apply the concept in situations where an increase in one quantity causes a decrease in the other. For example: the number of people working on a task and its completion time.

• Understanding this relationship helps students quickly learn scientific theories or laws where the quantities are inversely connected. For example, Boyle’s Law states that pressure is inversely proportional to the volume (pressure ∝ 1/volume).

• They will be able to understand the facts, such as why doctors prescribe highly concentrated medicines in lower doses.

• Scientists and chemists utilize the concept to predict how the intensity of one quantity affects another in their inventions or experiments.

• Moreover, we unknowingly apply this concept while cooking. For example, increasing the intensity of heat to decrease the cooking time.