Problem 31 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$\frac{1}{3}(12+6 r)$$

Step-by-Step Solution

Answer

The expression \(\frac{1}{3}(12+6r)\) without parentheses is \(4 + 2r\).

Step 1: Apply the Distributive Property

Apply the distributive property \(a*(b+c) = a*b + a*c\), in this case, \(a = \frac{1}{3}\), \(b = 12\), and \(c = 6r\). Multiply \(\frac{1}{3}\) by both 12 and \(6r\) separately.

Step 2: Multiply \(\frac{1}{3}\) and 12

\(\frac{1}{3} * 12 = 4\), as 12 divided by 3 equals to 4.

Step 3: Multiply \(\frac{1}{3}\) and 6r

\(\frac{1}{3} * 6r = 2r\), as 6 divided by 3 equals to 2, leaving us with 2r.

Step 4: Combine the Results

Combine the results to get the expression without parentheses which is \(4 + 2r\).