We use the symbol α show inverse proportion. α is a Greek alphabet and it is pronounced as alpha. Inverse proportion is represented using the inversely proportional symbol α as follows:
p α (1 / q)
This representation shows that the variable p is inversely proportional to q. That means as the value of p increases, the value of q decreases. When the value of p decreases, the value of q increases with it.
Example 1: A car starts from a point A and reaches another point B. During its journey from A to B, it covers a distance d. It takes time t to cover the distance d. Express the relation between the variable d and t using the inversely proportional symbol.
Solution: For the moving car, as the time of journey increases the distance d decrease. Thus d and t have inverse proportionality relation with respect to each other. We can represent this relation using the inverse proportionality symbol as follows:
d α (1 / t)
Example 2: A contractor takes work of painting a building. He employs n number of men to do the work. He needs to complete the work in time t. He sees that the work is running behind schedule, so he employs more men, thus increasing the number n. Express the relation between the variable n and t using the sign of inverse proportion.
Solution: As the number of men (n) increases, the time taken (t) to complete the work decreases. Thus n and t are in inverse proportion. We can express the relation as:
n α (1 / t)