Subtracting By Adding The Opposite
Subtracting By Adding The Opposite is a Grade 8 algebra technique in Saxon Math Course 3, Chapter 4, where students rewrite subtraction as adding the opposite (additive inverse) to simplify integer and algebraic computations. This method is essential for working with negative numbers, simplifying algebraic expressions, and solving equations.
Key Concepts
Property Instead of subtracting a number, add its opposite.
Examples $( 15) ( 5) = ( 15) + (+5) = 10$ $9 (+12) = 9 + ( 12) = 3$.
Explanation Why make subtraction hard? Just flip the sign of the number you are subtracting and turn the problem into simple addition! It’s the ultimate math uno reverse card, changing the game from subtraction to a friendly round of adding. Now you are an addition wizard!
Common Questions
What does subtracting by adding the opposite mean?
It means replacing a subtraction problem with an equivalent addition problem. To subtract b from a, add the opposite of b: a minus b equals a plus negative b.
How do you apply this technique with integers?
Change the subtraction sign to addition and change the sign of the number being subtracted. For example, 5 minus negative 3 becomes 5 plus positive 3 = 8.
Why does subtracting by adding the opposite work?
Subtraction and adding the additive inverse are equivalent operations by definition. Any subtraction can be rewritten as addition of the opposite without changing the result.
How does this technique help with algebraic expressions?
Converting subtraction to addition makes it easier to combine like terms, simplify polynomials, and avoid sign errors in multi-step algebra problems.
Where is subtracting by adding the opposite taught in Grade 8?
This technique is covered in Saxon Math Course 3, Chapter 4: Algebra and Measurement.