Inverse Proportion: A Detailed Explanation Inverse proportion involves two quantities inversely related. This means that as one quantity increases, the other...
Inverse proportion involves two quantities inversely related. This means that as one quantity increases, the other decreases, and vice versa. For example, if you have a machine that can produce 10 units of output for every 2 units of input, then the inverse proportion would be 5 (since output halves for every unit of input).
Formal Definition:
Let a and b be two real numbers with the following relationship:
a/b = k
where k is a constant.
Then, the inverse proportion is:
b/a = k
This means that the ratio of b to a is equal to the reciprocal of the ratio of a to b.
Solving Inverse Proportion:
Solving an inverse proportion involves finding the value of b given the value of a. This can be done by switching the roles of a and b:
b = ka
where k is the constant from the original equation.
Examples:
If a machine produces 20 units of output for every 4 units of input, then the inverse proportion would be 4 (since output halves for every 2 units of input).
If you have a classroom with 30 students and 3 teachers, then the inverse proportion would be 10 (since the number of students is divided by the number of teachers).
A machine can produce 100 units of output for every 5 units of input. Therefore, the inverse proportion would be 5 (since the output is divided by the input)