Multiplication Property of Equality

Definition

The multiplication property of equality states that if two expressions are equal, then multiplying both expressions by the same non-zero number will result in two new expressions that are also equal. This property allows for the manipulation of linear equations to isolate a variable and solve for its value.

5 Must Know Facts For Your Next Test

1. The multiplication property of equality is used to isolate a variable in a linear equation by multiplying both sides of the equation by the same non-zero number.
2. Applying the multiplication property of equality allows you to remove coefficients from the variable term, making it easier to solve for the variable's value.
3. The multiplication property of equality is a crucial step in the general strategy for solving linear equations, which involves isolating the variable on one side of the equation.
4. When using the multiplication property of equality, it is important to ensure that the multiplier is a non-zero number, as dividing by zero is undefined.
5. The multiplication property of equality, along with the division property of equality, enables the transformation of linear equations into simpler forms that can be solved more easily.

Review Questions

• Explain how the multiplication property of equality can be used to solve a linear equation.
  • The multiplication property of equality states that if two expressions are equal, then multiplying both expressions by the same non-zero number will result in two new expressions that are also equal. This property can be used to solve a linear equation by isolating the variable on one side of the equation. For example, if the equation is $2x + 4 = 10$, we can multiply both sides by $1/2$ to get $x + 2 = 5$, which is easier to solve for the variable $x$.
• Describe the role of the multiplication property of equality in the general strategy for solving linear equations.
  • The general strategy for solving linear equations involves a series of steps, and the multiplication property of equality is a crucial part of this process. After isolating the variable term on one side of the equation, the multiplication property of equality is used to remove any coefficients from the variable term, making it easier to solve for the variable's value. This step, along with the division property of equality, allows the equation to be transformed into a simpler form that can be solved more easily, ultimately leading to the solution of the original linear equation.
• Analyze the importance of the non-zero requirement when applying the multiplication property of equality to solve linear equations.
  • The multiplication property of equality states that if two expressions are equal, then multiplying both expressions by the same non-zero number will result in two new expressions that are also equal. The requirement for the multiplier to be a non-zero number is critical because dividing by zero is undefined. If the multiplier were to be zero, the resulting equation would not be equivalent to the original equation, as multiplying any number by zero would give a result of zero, regardless of the original values. Adhering to the non-zero requirement ensures that the transformations made using the multiplication property of equality preserve the original relationship between the expressions, allowing for the successful solution of the linear equation.

Related terms

Division Property of Equality: The division property of equality states that if two expressions are equal, then dividing both expressions by the same non-zero number will result in two new expressions that are also equal. This property, along with the multiplication property, is used to solve linear equations.

Linear Equation: A linear equation is an equation in which the highest exponent of the variable is 1. Linear equations can be solved using the properties of equality, such as the multiplication and division properties.

Variable: A variable is a symbol, usually a letter, that represents an unknown quantity in an equation. Variables are used in linear equations and their values are determined through the process of solving the equation.