The Distributive Properties | Simplifying and Manipulating Math Expressions Involving Multiplication or Division with Addition or Subtraction

Distributive Laws

The distributive laws are a set of fundamental properties in mathematics that describe how multiplication or division interacts with addition or subtraction

The distributive laws are a set of fundamental properties in mathematics that describe how multiplication or division interacts with addition or subtraction. These laws allow us to simplify and manipulate expressions involving these operations.

There are two distributive laws, known as the distributive property of multiplication over addition and the distributive property of multiplication over subtraction:

1. Distributive Property of Multiplication over Addition:

This law states that multiplying a number by the sum of two or more numbers is equal to multiplying the number by each individual number and then adding the products together. Mathematically, it can be expressed as:

a * (b + c) = a * b + a * c

For example, if we have the expression 3 * (2 + 4), we can use the distributive property to simplify it:

3 * (2 + 4) = 3 * 2 + 3 * 4 = 6 + 12 = 18

So, the distributive property allows us to distribute the multiplication operation over the addition operation.

2. Distributive Property of Multiplication over Subtraction:

This law states that multiplying a number by the difference of two numbers is equal to multiplying the number by each individual number and then subtracting the products. Mathematically, it can be expressed as:

a * (b – c) = a * b – a * c

For example, if we have the expression 5 * (7 – 3), we can apply the distributive property to simplify it:

5 * (7 – 3) = 5 * 7 – 5 * 3 = 35 – 15 = 20

So, the distributive property allows us to distribute the multiplication operation over the subtraction operation.

These distributive laws are crucial in algebraic expressions and equations, as they enable us to simplify and factorize expressions, solve equations, and perform operations more efficiently.

It is important to note that the distributive laws only apply when multiplication or division is involved with addition or subtraction. They do not apply to addition or subtraction operations alone.

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