Inverse Operations
Inverse operations—addition and subtraction undoing each other—is a core Grade 4 concept in Saxon Math Intermediate 4 Chapter 3. When solving an equation like c plus 9 equals 21, students identify that addition is applied to c, then use the inverse operation (subtraction) to isolate the variable: c equals 21 minus 9 equals 12. The golden rule of algebra requires applying the same operation to both sides of the equation to keep it balanced. Mastering this concept enables students to rewrite and solve a wide range of addition and subtraction equations.
Key Concepts
New Concept Addition and subtraction are inverse operations. One operation undoes the other.
What’s next Next, you'll use this concept to rewrite equations and find the missing number in addition and subtraction problems.
Common Questions
What are inverse operations?
Inverse operations are operations that undo each other. Addition and subtraction are inverse operations—adding then subtracting the same number returns to the original value.
How do I use inverse operations to solve c plus 9 equals 21?
The variable c has 9 added to it. Use the inverse operation and subtract 9 from both sides: c plus 9 minus 9 equals 21 minus 9, so c equals 12.
Why must I perform the same operation on both sides of an equation?
An equation is like a balanced scale. Doing the same thing to both sides keeps the balance. Doing it to only one side creates an inequality instead.
Can inverse operations be used with multiplication and division too?
Yes. Multiplication and division are also inverse operations. Division undoes multiplication, and multiplication undoes division.
What does it mean for two operations to undo each other?
If you add 5 to a number and then subtract 5, you return to the original number. The subtraction undoes the addition completely.