What is the definition of distributive property in math?
The distributive property in math refers to a fundamental property of numbers and expressions that relates multiplication and addition or subtraction. It states that 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. Symbolically, it is represented as:
a * (b + c) = (a * b) + (a * c)
or
a * (b - c) = (a * b) - (a * c)
The distributive property in math refers to the property that allows you to multiply a sum or difference by a number. It states that when you multiply a number by a sum or difference, you can distribute the multiplication to each term within the parentheses or brackets. Mathematically, the distributive property can be defined as:
For any numbers a, b, and c:
a(b + c) = ab + ac (Distributive Property of Multiplication over Addition)
a(b - c) = ab - ac (Distributive Property of Multiplication over Subtraction)
This property is often used to simplify expressions and solve equations in algebra.
The distributive property is a fundamental concept in mathematics that is used to simplify expressions and perform operations with numbers. It states that when multiplying a number by the sum or difference of two other numbers, you can distribute or multiply the number to each term inside the parentheses.
The formal definition of the distributive property can be expressed as follows:
For any real numbers a, b, and c:
a * (b + c) = a * b + a * c
a * (b - c) = a * b - a * c
In simpler terms, the distributive property allows you to multiply a number by each term inside a set of parentheses and then simplify the resulting expression by combining like terms.
To understand and apply the distributive property, follow these steps:
1. Identify the expression or equation where the distributive property needs to be used.
2. Identify the term that is being multiplied by the parentheses.
3. Multiply the term by each term inside the parentheses using the distributive property.
4. Simplify the resulting expression by combining like terms, if applicable.
By following these steps and applying the distributive property, you can simplify complex expressions and perform mathematical operations more efficiently.