The Division Property of Equality states that dividing both sides of an equation by the same non-zero number maintains the equality. In simpler terms, if you divide both sides of an equation by the same number (except zero), the equation remains balanced.
Understanding the Division Property of Equality
The Division Property of Equality is a fundamental principle in algebra that helps solve equations. It's based on the idea that if two quantities are equal, then dividing both quantities by the same non-zero number will result in two new quantities that are also equal.
Examples
Here are some examples illustrating the Division Property of Equality:
- Example 1: If 2x = 10, then dividing both sides by 2 gives x = 5.
- Example 2: If 3y + 6 = 15, then dividing both sides by 3 gives y + 2 = 5.
Practical Insights
The Division Property of Equality is used extensively in solving equations, particularly when isolating a variable. It's a crucial tool for manipulating equations and finding solutions.
Solutions
The Division Property of Equality is used to solve equations by isolating the variable. This involves dividing both sides of the equation by the coefficient of the variable.
- Example: To solve the equation 4x = 20, we divide both sides by 4:
- 4x / 4 = 20 / 4
- x = 5
Conclusion
The Division Property of Equality is a fundamental concept in algebra that allows us to manipulate equations by dividing both sides by the same non-zero number. This property is essential for solving equations and isolating variables.
