Distributive Property

Distributive Property of Maths Explained

The distributive property states that for every number a, and every number b, a *(b + c) = (a*b) + (a* c). In other words, the distributive property states that you can multiply a number by a sum, and then add the products together, and you will get the same result as multiplying the numbers and then adding them together. Distributive Property of Maths Explained.

Understanding the Distributive Property

The distributive property states that for any real numbers a, b, and c, a(b+c) = ab+ac. This property can be rewritten in terms of grouping symbols to produce the following equation:

(a+b)c = ac+bc

Steps to Follow in the Distributive Property

The distributive property is a mathematical property that states that for every number a, and every number b, a multiplied by (b + c) is equal to a multiplied by b multiplied by c. In symbols, this can be written as:

a(b + c) = a(b) · c

To understand the distributive property, let’s work through an example. Say we want to find out what (2 + 3) · 4 is.

We can approach this problem in a few different ways. The first way would be to simply add 2 + 3 and then multiply that result by 4.

(2 + 3) · 4 = (5) · 4 = 20

Another way to solve this problem would be to first multiply 2 and 3 together to get 6. Then we would add 4 to that result to get 10. Finally, we would multiply 10 by 4 to get 40.

(2 + 3) · 4 = 6 · 4 = 24

Types of Distributive Property

There are three types of distributive property:

1. Associative Property
2. Commutative Property
3. Distributive Property

Distributive Property Definition

The distributive property is a mathematical property that states that a sum can be distributed evenly across a set of terms.

Distributive Property Formula

The distributive property states that for any real numbers a, b, and c,

a(b + c) = ab + ac.

This equation says that when we multiply a number by a sum, we get the sum of the products.

Distributive Property with Variables

If you are given a problem with variables, you can use the distributive property to help you solve it. For example, if you are given the problem 5x + 3y = 9, you can use the distributive property to simplify the equation to 5x + 3y = 9.

Distributive Property of Addition

For any real numbers a, b, and c,

a + (b + c) = (a + b) + c.

Distributive Property of Subtraction

For any real numbers a, b, and c,

a – (b – c) = (a – b) + (a – c)

Distributive Property of Multiplication

For any real numbers a, b, and c:

a(b+c) = ab+ac.

Distributive Property of Division

The distributive property of division states that for any real numbers a, b, and c,

a ÷ (b + c) = a ÷ b + a ÷ c.

Solved Examples

Example 1:

The average of two numbers is 9. What are the two numbers?

The two numbers are 9 and 9.

Distributive Property of Maths Explained.