Distributive Property Lesson

The distributive property is a fundamental concept in mathematics that describes how multiplication interacts with addition or subtraction within an expression. There are two main aspects of the distributive property; distributive property of multiplication over addition and distributive property of multiplication over subtraction.

The distributive property allows us to simplify expressions and perform operations with greater ease. It involves multiplying a sum or difference of numbers by a factor. The distributive property allows us to take a factor and distribute (multiply) each term (part) within the group by that factor. Hence the name, distributive property.

The distributive property can be defined as follows:

For any three numbers, a, b, and c, the product of a and the sum or difference of b and c is equal to the sum or difference of the products of a and b, and a and c. Mathematically this can be expressed as:

Distributive Property over Addition

a × (b + c) = ab + ac

This means that when you have a number, a, multiplied by the sum of two other numbers, b and c, you can distribute the multiplication to each term inside the parentheses and then add the results.

Example

Distributive Property over Subtraction

a × (b – c) = ab – ac

Similarly, this form of the distributive property tells us that when a number, a is multiplied by the difference of two other numbers, b and c, you can distribute the multiplication to each term inside the parentheses and then subtract the results.

Example

In simpler terms, when using the distributive property, we multiply the outside number (factor), by each term within the parenthesis. This can be used with more than two terms, for example:

Examples

Example 1: Use the distributive property to evaluate the expression 4(3 + 6).

Solution:

Using the distributive property, we will multiply each term inside the parentheses by the factor 4.

Therefore 4(3 + 6) = 36.

Example 2: Use the distributive property to evaluate the expression 5(7 – 3)

Solution:

Using the distributive property, we will multiply each term inside the parentheses by the factor 5.

Therefore, 5(7 – 3) = 20.

Example 3: Use the distributive property to evaluate the expression 3(4 + 5 – 6)

Solution:

Using the distributive property, we will multiply each term inside the parentheses by the factor 3.

FAQs on Distributive Property

1. Why is the Distributive Property important in mathematics?

The distributive property is crucial for simplifying algebraic expressions, solving equations, and manipulating mathematical expressions. It provides a systematic way to break down complex expressions into simpler forms.

2. What is the Distributive Property?

The distributive property is a fundamental mathematical principle that describes how multiplication interacts with addition or subtraction within an expression. It is expressed as a x (b + c) = ab + ac and a (b – c) = ab – ac.

3. How does the Distributive Property work?

The distributive property allows you to distribute or multiply across the terms inside parentheses when you have addition or subtraction. This allows us to simplify expressions and makes it easier to perform calculations.

4. Can the distributive property be used with variables?

Yes, the distributive property applies to numbers and variables, and is very helpful when simplifying expressions with variables.

Here is one example of using the distributive property with variables.

2(x + 5) = 2(x) + 2(5)
= 2x + 10

5. Can the distributive property be used with division?

No, the distributive property does not directly apply to division, however, there are other ways that you can apply properties of mathematics to help you simplify division problems.

6. How does the distributive property help in solving equations?

The distributive property is often used to simplify expressions within equations, making it easier to isolate variables and solve for unknown values. It allows for systematic manipulation of equations to find solutions.