Method 2: Completion (The Subtraction Method)
Method 2: Completion (The Subtraction Method) is a Grade 8 algebra skill in Saxon Math Course 3, Chapter 4, where students solve equations by identifying what value needs to be subtracted to complete a transformation or balance a relationship. This method complements other algebraic techniques and builds flexible problem-solving skills for multi-step equations.
Key Concepts
Property Sometimes, it is easier to find the area of a composite figure by imagining it as a larger shape with a piece missing. Total Area = Area of the Large Shape Area of the Missing Piece (Hole).
Examples The "C" Shape: A C shaped figure can be imagined as a large 12 by 10 rectangle (Area = 120) that has a 6 by 4 rectangular hole cut out of it (Area = 24). The total area of the "C" shape is 120 24 = 96 square units. Square with a Hole: A large 12 by 12 square has a smaller 5 by 5 square removed from its center. The remaining area is 144 25 = 119 square units.
Explanation Imagine baking a giant, perfect rectangular cookie, and then using a smaller cookie cutter to take a bite out of it! To find the area of your leftover cookie, you find the area of the whole cookie first, and then subtract the area of the piece you removed. This trick is extremely helpful for shapes that have holes or empty spaces in the middle.
Common Questions
What is the completion or subtraction method for solving equations?
The subtraction method involves subtracting the same value from both sides of an equation to isolate the variable or complete a desired transformation, maintaining the balance of the equation.
When do you use subtraction to solve an equation?
You use subtraction when a positive number is being added to the variable. Subtracting that number from both sides eliminates it and isolates the variable.
How does the subtraction property of equality support this method?
The subtraction property of equality states that subtracting the same value from both sides of an equation preserves equality, which is the foundation of this solving method.
How does this method work with two-step equations?
In a two-step equation, you first use addition or subtraction to address the constant term, then use multiplication or division to address the coefficient of the variable.
Where is the subtraction method for equations taught in Grade 8?
This method is covered in Saxon Math Course 3, Chapter 4: Algebra and Measurement.