Properties of equality
The properties of equality state that you can add, subtract, multiply, or divide both sides of an equation by the same number and the equation remains true. If x - 5 = 10, adding 5 to both sides gives x = 15. If 4w = 132, dividing both sides by 4 gives w = 33. These four properties (addition, subtraction, multiplication, division) are the tools used to isolate variables and solve equations. Covered in Chapter 7 of Saxon Math Course 2, they are essential for 7th grade algebra.
Key Concepts
Property 1. Addition: If $a = b$, then $a + c = b + c$. 2. Subtraction: If $a = b$, then $a c = b c$. 3. Multiplication: If $a = b$, then $ac = bc$. 4. Division: If $a = b$, and $c ≠ 0$, then $\frac{a}{c} = \frac{b}{c}$.
Examples Addition Property: If $x 5 = 10$, then $x 5 + 5 = 10 + 5$, which means $x = 15$. Subtraction Property: If $y + 8 = 20$, then $y + 8 8 = 20 8$, which means $y = 12$. Division Property: If $4w = 132$, then $\frac{4w}{4} = \frac{132}{4}$, which means $w = 33$.
Explanation These are the four official rules for keeping equations balanced. They promise that if you start with two equal things, they will stay perfectly equal as long as you add, subtract, multiply, or divide the exact same number on both sides. Every step you take when solving an equation is secretly guided by one of these powerful properties.
Common Questions
What are the properties of equality?
There are four properties: Addition (add the same number to both sides), Subtraction (subtract the same number), Multiplication (multiply both sides by the same number), and Division (divide both sides by the same nonzero number).
How do you use the addition property of equality?
If x - 5 = 10, add 5 to both sides: x - 5 + 5 = 10 + 5, so x = 15. You undo the subtraction by adding.
How do you use the division property of equality?
If 4w = 132, divide both sides by 4: 4w/4 = 132/4, so w = 33. You undo multiplication by dividing.
Why are properties of equality important for solving equations?
They are the rules that allow you to manipulate equations without breaking them. Every step in solving an equation uses one of these properties to isolate the variable.
What are common mistakes when applying properties of equality?
The most common mistake is performing an operation on only one side of the equation. Whatever you do to one side must be done to the other to maintain balance.
When do students learn properties of equality?
Saxon Math Course 2 covers these properties in Chapter 7, giving 7th grade students the algebraic foundation for solving one-step and multi-step equations.