Direct Proportion
Two quantities a and b are said to be in direct proportion if they increase or decrease together. In other words, the ratio of their corresponding values remains constant. This means that,
a/ b = k
where k is a positive number, then the quantities a and b are said to vary directly.
In such a case if the values b1, b2 of b corresponding to the values a1, a2 of a, respectively then it becomes;
a1//b1 = a2 /b2
The direct proportion is also known as direct variation.
Directly Proportion Symbol
The symbol used to represent the direct proportion is “∝”.
Consider the statement,
a is directly proportional to b
This can be written using the symbol as:
a ∝ b
Consider the other statement, a = 2b
In this case, it shows that a is proportional to b, and the value of one variable can be found if the value of other variable is given.
For example:
Let b=7
Therefore, a = 2 x 7 = 14
Similarly, if you take the value of “a” as 14, you will find the value of b
Such that
14 = 2 x b
14/ 2 = b
Therefore, b=7
Inverse Proportion
The value is said to inversely proportional when one value increases, and the other decreases. The proportionality symbol is used in a different way. Consider an example; we know that the more workers on a job would reduce the time to complete the task. It is represented as:
Number of workers ∝ (1/ Time taken to complete the job)
Inverse Proportion Definition
Two quantities a and b are said to be in inverse proportion if an increase in quantity a, there will be a decrease in quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant. Sometimes, it is also known as inverse variation
That is, if ab = k, then a and b are said to vary inversely. In this case, if b1, b2 are the values of b corresponding to the values a1, a2 of a, respectively then a1 b1 = a2 b2 or a1/a2 = b2 /b1
The statement ‘a is inversely proportional to b is written as
a ∝ 1/b
Here, an equation is given that involves the inverse proportions that can be used to calculate the other values.
Let,
a = 25/b
Here a is inversely proportional to b
If one value is given, the other value can be easily found.
Say b=10
a= 25/10 = 2.5
Similarly, if a = 2.5, the value of b can be obtained.
2.5 = 25/b
b= 25/2.5 = 10
How to solve problems with Direct Proportion?
How to solve problems with Inversely Proportional variables?
x1 y1 = x2 y2 = x2 y2 = x2 y2