What is an Inverse Operation?
The operation that “undoes” the original operation
An inverse operation is a math operation that reverses the effect of another operation.
Addition and subtraction are inverse operations. Adding a number and then subtracting the same number brings you back to where you started. Let’s try adding three to 8 and then subtracting it:
8 + 3 − 3 = 8
After adding and subtracting the same number, we arrive back at 8.
Why? Because subtracting 3 from 3 is zero. Zero is the identity property for addition and subtraction which means that adding or subtracting 0 from a number does not change its value.
Multiplication and division are also inverse operations. Multiplying a number and then dividing by the same number also returns you to the starting value. Let’s try multiplying by 2 and then dividing the product by the same number, 2:
6 × 2 ÷ 2 = 6
Why? Because dividing 2 by 2 is one. One is the identity property for multiplication and subtraction, which means that multiplying or dividing a number by one does not change its value.
Inverse operations are like “undoing” a step in math. They’re especially helpful when solving equations or checking your work.
Other examples of inverse operations include:
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Squaring and taking a square root
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Doubling a number and then halving it
When Do Students Learn About Inverse Operations?
Students are first introduced to the concept of inverse operations in elementary school and evolve their understanding from addition and subtraction to more complex algebraic operations throughout middle school.
Grades 2–3 – Introduction to Inverse Operations
Students begin to understand the concept of inverse operations when they learn basic addition/subtraction and multiplication/division fact families.
Grades 4–5 – Using Inverse Operations in Problem Solving
Students use inverse operations to check answers and solve basic equations.
Grades 6+ – Inverse Operations in Algebra
Students apply inverse operations to solve for variables in multi-step equations and inequalities.
