Multiplication Property of Equality

Definition

The multiplication property of equality states that if two expressions are equal, then multiplying both sides of the equation by the same non-zero number will result in two new expressions that are also equal. This property allows for simplifying and solving equations by isolating the variable through multiplication.

5 Must Know Facts For Your Next Test

1. The multiplication property of equality allows you to simplify equations by multiplying both sides by the same non-zero number.
2. Multiplying both sides of an equation by the same non-zero number does not change the solution to the equation.
3. The multiplication property of equality is particularly useful when solving equations that involve decimals, as it can help isolate the variable.
4. When solving equations using the multiplication property of equality, it is important to ensure that the number you are multiplying by is not zero, as division by zero is undefined.
5. The multiplication property of equality, along with the additive and divisive properties, are fundamental tools for solving a wide range of algebraic equations.

Review Questions

• Explain how the multiplication property of equality can be used to solve equations with decimals.
  • The multiplication property of equality is especially useful when solving equations that involve decimals. By multiplying both sides of the equation by the same non-zero number, you can eliminate the decimal and isolate the variable. This allows you to simplify the equation and find the solution more easily. For example, if you have the equation $3.4x = 17$, you can multiply both sides by $10$ to get $34x = 170$, which is much simpler to solve for $x$.
• Describe how the multiplication property of equality is related to the other properties of equality, such as the additive and divisive properties.
  • The multiplication property of equality, the additive property of equality, and the divisive property of equality are all fundamental tools for solving algebraic equations. They are interconnected and can be used in conjunction to isolate variables and simplify equations. The additive property allows you to add the same number to both sides, the divisive property allows you to divide both sides by the same non-zero number, and the multiplication property allows you to multiply both sides by the same non-zero number. By understanding how these properties work together, you can more effectively solve a wide range of equations.
• Evaluate the importance of the multiplication property of equality in the context of solving equations, particularly in the topics of 'Solving Equations with Decimals' and 'Solving Equations Using the Division and Multiplication Properties of Equality'.
  • The multiplication property of equality is a crucial concept in the context of solving equations, especially when dealing with decimals or when using the division and multiplication properties of equality. This property allows you to isolate variables and simplify equations by multiplying both sides by the same non-zero number. In the topic of 'Solving Equations with Decimals', the multiplication property is particularly useful for eliminating decimal values and making the equations easier to solve. Similarly, in the topic of 'Solving Equations Using the Division and Multiplication Properties of Equality', the multiplication property is a fundamental tool for manipulating equations and isolating variables. Understanding and effectively applying the multiplication property of equality is essential for successfully navigating these topics and solving a wide range of algebraic equations.

Related terms

Additive Property of Equality: The additive property of equality states that if two expressions are equal, then adding the same number to both sides of the equation will result in two new expressions that are also equal.

Divisive Property of Equality: The divisive property of equality states that if two expressions are equal, then dividing both sides of the equation by the same non-zero number will result in two new expressions that are also equal.

Isolating a Variable: The process of manipulating an equation to get a single variable on one side, typically using the properties of equality.