15 2 R Distributive Property Calculator

The distributive property is a fundamental algebraic rule that simplifies multiplication over addition or subtraction. This calculator helps you apply the distributive property to expressions like 15 × (2 + r).

What is the Distributive Property?

The distributive property states that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products. Mathematically, this is expressed as:

a × (b + c) = (a × b) + (a × c)

This property is widely used in algebra to simplify expressions and solve equations. It's particularly useful when dealing with variables and complex expressions.

How to Use This Calculator

To use the calculator:

Enter the value for 'r' in the input field
Click the "Calculate" button
View the expanded form of 15 × (2 + r)
See the step-by-step solution

The calculator will show you the expanded form of the expression and demonstrate each step of the calculation.

The Formula

The distributive property formula for 15 × (2 + r) is:

15 × (2 + r) = (15 × 2) + (15 × r) = 30 + 15r

This formula shows how to distribute the multiplication over the addition inside the parentheses.

Worked Example

Let's solve 15 × (2 + 4):

First, multiply 15 by 2: 15 × 2 = 30
Then, multiply 15 by 4: 15 × 4 = 60
Add the two results: 30 + 60 = 90

The final result is 90, which matches the expanded form 30 + 60.

FAQ

What is the distributive property used for?: The distributive property is used to simplify algebraic expressions and make calculations easier. It's a fundamental tool in algebra and higher mathematics.
Can the distributive property be applied to subtraction?: Yes, the distributive property can be applied to subtraction. The formula is a × (b - c) = (a × b) - (a × c).
Is the distributive property the same as the factoring?: No, the distributive property is about expanding expressions, while factoring is about taking common factors out of terms.
When should I use the distributive property?: Use the distributive property when you need to simplify expressions with multiplication over addition or subtraction.
Can the distributive property be used with more than two terms?: Yes, the distributive property can be extended to more than two terms. For example, a × (b + c + d) = (a × b) + (a × c) + (a × d).