key term - Division Property of Equality

Definition

The division property of equality states that if two expressions are equal, then dividing both expressions by the same non-zero number results in two new expressions that are also equal. This property allows for solving equations by isolating the variable through division.

5 Must Know Facts For Your Next Test

1. The division property of equality allows you to divide both sides of an equation by the same non-zero number to isolate the variable.
2. Dividing both sides of an equation by the same number does not change the equality, as long as the number is not zero.
3. The division property of equality is one of the key tools used in the process of solving linear equations.
4. Applying the division property of equality is often necessary when an equation contains a variable in the denominator.
5. Understanding the division property of equality is crucial for solving more complex equations that require multiple steps.

Review Questions

• Explain how the division property of equality can be used to solve linear equations.
  • The division property of equality states that if two expressions are equal, then dividing both expressions by the same non-zero number results in two new expressions that are also equal. This property allows you to isolate a variable in an equation by dividing both sides by the coefficient of the variable. For example, to solve the equation $5x = 20$, you would divide both sides by 5 to get $x = 4$. This step-by-step process of using the division property to isolate the variable is a key technique for solving linear equations.
• Describe how the division property of equality is related to the concept of inverse operations in solving equations.
  • The division property of equality is closely tied to the idea of inverse operations in equation solving. Division is the inverse operation of multiplication, just as subtraction is the inverse of addition. When solving an equation, you often need to undo the operations performed on the variable in order to isolate it. The division property allows you to divide both sides of an equation by the same non-zero number, which is the inverse operation of multiplying both sides by that number. This inverse operation step is crucial for systematically solving equations and isolating the variable.
• Analyze how the division property of equality can be used to solve equations with variables in the denominator.
  • Equations with variables in the denominator can be challenging to solve, but the division property of equality provides a useful strategy. By applying the division property, you can isolate the variable by dividing both sides of the equation by the expression containing the variable. For example, to solve the equation $\frac{x}{2} = 4$, you would divide both sides by $\frac{1}{2}$ to get $x = 8$. This step-by-step process of using the division property to isolate the variable is essential for solving a wide range of equations, including those with variables in the denominator.

Related terms

Equation:

A mathematical statement that shows two expressions are equal, often containing variables that need to be solved for.

Isolate: To separate a variable or expression from the other terms in an equation in order to find its value.

Inverse Operations:

Operations that undo each other, such as addition and subtraction or multiplication and division, used to solve equations.