Subtraction and Addition Properties of Equality
The Subtraction and Addition Properties of Equality are foundational Grade 6 algebra rules from enVision Mathematics: if a = b, then a - c = b - c (subtraction) and a + c = b + c (addition). These properties guarantee that whatever you do to one side of an equation, doing the same to the other side preserves equality. Students use these to solve one-step equations like x + 5 = 12 (subtract 5 from both sides) or x - 3 = 8 (add 3 to both sides). They are the logical basis for all equation-solving strategies in algebra.
Key Concepts
Property Subtraction Property of Equality For all real numbers $a$, $b$, and $c$, if $a = b$, then $a c = b c$.
Addition Property of Equality For all real numbers $a$, $b$, and $c$, if $a = b$, then $a + c = b + c$. When you add or subtract the same quantity from both sides of an equation, you still have equality.
Examples To solve $p 7 = 12$, we use the Addition Property. Add 7 to both sides: $p 7 + 7 = 12 + 7$, which simplifies to $p = 19$.
Common Questions
What is the Subtraction Property of Equality?
The Subtraction Property states: if a = b, then a - c = b - c. Subtracting the same value from both sides of an equation keeps the equation balanced.
What is the Addition Property of Equality?
The Addition Property states: if a = b, then a + c = b + c. Adding the same value to both sides of an equation preserves equality.
How do you use these properties to solve equations?
To solve x + 5 = 12, apply the Subtraction Property: subtract 5 from both sides → x = 7. To solve x - 3 = 8, apply the Addition Property: add 3 to both sides → x = 11.
Why do these properties work?
Equality means both sides represent the same value. Any operation applied equally to both sides cannot change that balance — the equation stays true.
Where are these properties taught in enVision Mathematics?
The Addition and Subtraction Properties of Equality are covered in enVision Mathematics, Grade 6, as part of algebraic equations and properties content.
What is the difference between the two properties?
Subtraction Property: subtract the same from both sides. Addition Property: add the same to both sides. Both are used to isolate the variable, depending on whether a number is being added or subtracted in the equation.
What mistakes do students make using these properties?
Students sometimes apply the operation to only one side of the equation, or confuse which operation to use (subtracting when they should add, or vice versa) to isolate the variable.