Concept of Inverse Proportion Inverse proportion is a special relationship between two numbers where the product of the two numbers is equal to a constant. T...
Inverse proportion is a special relationship between two numbers where the product of the two numbers is equal to a constant. This constant is equal to the reciprocal of the other number.
For example:
If we have 3 and 10, their product is 30, which is equal to 10/3.
Similarly, if we have 4 and 8, their product is 32, which is equal to 8/4.
Inverse proportion establishes a reciprocal relationship between two numbers. This means that if we have a number a and b such that a * b = k, then b * a = k, where k is the constant.
Here are some key points about inverse proportion:
It is an equivalence relation, which means that any two numbers that are proportional to each other will also be proportional to each other in the reverse direction.
Inverse proportion is not applicable to all types of ratios. For example, if we have a ratio of 1:2, it is not inverse proportion with the ratio of 2:4.
Inverse proportion can be used to solve problems involving ratios, as it allows us to find the missing number in a ratio given the other number.
Examples:
If a tree is 10 meters high and its shadow is 5 meters long, then the tree's width is inversely proportional to its height. This means that if the tree grows to 15 meters high, its shadow will be 7.5 meters long.
If you have a recipe that calls for 1 cup of flour and 2 cups of water, the ratio of flour to water is inversely proportional. This means that if you double the amount of water, you need to halve the amount of flour to maintain the same ratio