Examples of Inverse Relationships in Math

By Sam Grover; Updated April 24, 2017
Inverse equations are a mathematical relationship.

Inverse relationships are the mathematical equivalent of a see-saw. In an inverse relationship, when one number goes up, the other goes down. Or, one number is multiplied, while the other is divided. This is the raw definition of an inverse relationship, but it is useful to look at it from various perspectives to grasp its meaning in mathematics.

Subtraction and Addition

Subtraction equations have an inverse relationship with addition equations. Doing an inverse calculation yields the inverse result. For example, 7 - 2 = 5. Flipping the equation around produces the inverse: 5 + 2 = 7. Addition and subtraction have inverse properties because they can be calculated in opposite methods.

Multiplication and Division

Multiplication and division also have inverse properties. By multiplying two numbers, you also can divide the product by one of those numbers to find the other number. For example, 9 x 5 = 45. Therefore, 45/5 = 9 and 45/9 = 5. Note, however, that order is not important in multiplication as it is in division. Addition and subtraction of 5 sets of 9 is the same as 9 sets of 5, and so on.

Algebra and Physics

Inverse relationships are found in algebra and physics and allow for the rearrangement of equations. For example, you might be trying to calculate an object's mass but don't have a scale. However, you might know how much force the object will generate at a set velocity.

The equation of force is F = MV. This means that there is an inverse relationship between this equation and M=V/F. This second equation could be used to calculate the object's mass.


A linear relationship in graphing is when one quantity increases and another also increases. An inverse relationship, on the other hand, is when one quantity increases, but the other decreases. Where a linear relationship will be represented by a line extending up on a graph, its inverse relationship will be represented as going down on a graph.

About the Author

Sam Grover began writing in 2005, also having worked as a behavior therapist and teacher. His work has appeared in New Zealand publications "Critic" and "Logic," where he covered political and educational issues. Grover graduated from the University of Otago with a Bachelor of Arts in history.