Problem 32 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$\frac{1}{4}(12+8 r)$$

Step-by-Step Solution

Answer

The given algebraic expression without parentheses is \(3 + 2r\).

Step 1: Identify the terms inside the parentheses

In the algebraic expression \(\frac{1}{4}(12+8 r)\), the terms inside the parentheses are \(12\) and \(8r\). These are the terms we are going to distribute the \(\frac{1}{4}\) to.

Step 2: Apply the distributive property

The distributive property states that \(a(b + c) = ab + ac\). Applying this to our algebraic expression we get: \(\frac{1}{4}(12) + \(\frac{1}{4}(8r)\).

Step 3: Simplify the expression

The next step is to simplify the expression by performing the multiplication. This gives us \(3 + 2r\).